4HE Fluid Mechanics April-1996 Part A (20 X 2 = 40 marks) 1.
An ideal ideal fluid fluid is an an incompre incompressibl ssiblee and __________ __________ fluid. fluid.
2.
For a e!ton e!tonian ian fluid fluid s"ear s"ear stress stress is directl# directl# propor proportiona tionall to __________ __________..
$.
%inemati %inematicc &iscosit# &iscosit# of of a li'uid li'uid is d#namic d#namic &iscos &iscosit# it# di&ided di&ided b# its its _________ __________. _.
4.
n * +* +* , s#stem s#stem of of dimensio dimension* n* Po!er Po!er is is represen represented ted as ______ __________. ____.
-.
eber e ber number number is ratio ratio of inerti inertial al force force to __________ __________ force. force.
/.
For incompr incompressi essible ble fluid* fluid* continuit continuit# # e'uation e'uation in interal interal form form is = __________. __________.
.
n flo! flo! net e'uipo e'uipotenti tential al lines lines are are ort"oona ort"oonall !it" !it" __________ __________..
3.
elati&e elati&e rou"ne rou"ness ss of a pipe surface surface is its its absolute absolute rou"ness rou"ness di&ided di&ided b# its its __________. __________.
5.
n laminar laminar flo! t"rou" t"rou" pipe as e#nolds e#nolds number number increases increases t"e t"e friction friction coeffici coefficient ent _________ __________. _.
10. Pitot Pitot 67tatic 67tatic tube measures measures __________ __________ pressure. pressure. 11. ,urbulent &elocit# fluctuations fluctuations in a flo! flo! is measured measured b# __________ meter. meter. 12. For a solid sp"ere fallin fallin under ra&it# at terminal terminal settlin &elocit# &elocit# in a fluid t"e buo#ant force is e'ual e'ual to __________. 1$. Pressure dra dra on a bod# bod# is due to t"e formation formation of __________. 14. 8run9s 8run9s e'uation e'uation relates relates ________ __________. __. 1-. eciprocatin pumps are suitable for for "i" pressure pressure rise and __________ disc"are. disc"are. 1/. An e:ample of Positi&e Positi&e displacement displacement pump is __________. 1. n a centrifual pump as "ead increases increases disc"are disc"are __________. 13. Po!er re'uired re'uired b# a fan is proportional proportional to t"e t"e disc"are* pressure rise and and __________. 15. Pump suitable suitable for for corrosi&e corrosi&e li'uid li'uid is __________. __________. 20. Fans "a&e "a&e __________ __________ pressure pressure rise rise t"an blo!ers. blo!ers. Part ; (- X 12 = /0 marks) <, 6
21. a) 8:plain 8:plain t"e follo! follo!in in terms terms i.
apor pr pressure
ii.
;ulk modulus
b) 7tate t"e Pascal9s la! of pressure at a point. c) "at are t"e desirable properties of manometric fluid. >r 22. a) A soap bubble -0 mm in diameter diameter contains a pressure (in e:cess e:cess of atmosp"eric) of 2 bar. bar. Find t"e surface tension in t"e soap film. b) f a 1 m diameter pipe carr#in air at a &elocit# of $.3 m?s m?s is to be modelled modelled for d#namic d#namic similarit# similarit# b# a !ater pipe of diameter 10 cm* !"at !ould be t"e &elocit# of !ater. (@ata to be i&en ρair = = 1.1/ k?m$B µair = = 1.31 : 106- k?m.secB &elocit# of !ater = 2.4$- m?sec ) <, 6 2$. a) C"eck !"et"er !"et"er t"e follo!in function function is a &alid potential function function
φ = A(:2 6 #2) (DesB t"e i&en is a &alid potential function) b) A sip"on consistin consistin of a $ cm diameter diameter tube is used to drain !ater from a tank. ,"e outlet end of t"e t"e tube is 2 m belo! t"e !ater surface in t"e tank. electin friction* calculate t"e disc"are. f t"e peak point of t"e sip"on is 1.4 m abo&e t"e !ater surface in t"e tank* estimate t"e pressure of fluid at t"e point of sip"on. (1-.54 m$?"rB /.5/ kPa abs ) >r 24. a) @istinuis" @istinuis" bet!een +aminar and ,urbulent ,urbulent flo! !it" e:ample e:ample b) @istinuis" bet!een subsonic flo! and supersonic supersonic flo! c) 8:plain t"e term E;oundar# +a#erE and friction dra. <, 6 2-. a) 8:plain t"e !orkin principle of a ot !ire !ire anemometer. anemometer. b) ater ater flo!s t"rou" t"rou" a ent enturi uri meter !"ic" !"ic" "as a diameter diameter at t"e inlet inlet of 1.2 m and and a diameter of 0./ m at t"e t"roat. ,"e difference in pressure bet!een t"e main and t"e t"roat is measured b# a differential mercur# aue* !"ic" s"o!s a deflection of -.1 cm. Find t"e disc"are t"rou" t"e meter and also calculate t"e &elocit# of !ater at t"e t"roat. ,ake t"e coefficient coefficient of disc"are of t"e meter as 0.53.
21. a) 8:plain 8:plain t"e follo! follo!in in terms terms i.
apor pr pressure
ii.
;ulk modulus
b) 7tate t"e Pascal9s la! of pressure at a point. c) "at are t"e desirable properties of manometric fluid. >r 22. a) A soap bubble -0 mm in diameter diameter contains a pressure (in e:cess e:cess of atmosp"eric) of 2 bar. bar. Find t"e surface tension in t"e soap film. b) f a 1 m diameter pipe carr#in air at a &elocit# of $.3 m?s m?s is to be modelled modelled for d#namic d#namic similarit# similarit# b# a !ater pipe of diameter 10 cm* !"at !ould be t"e &elocit# of !ater. (@ata to be i&en ρair = = 1.1/ k?m$B µair = = 1.31 : 106- k?m.secB &elocit# of !ater = 2.4$- m?sec ) <, 6 2$. a) C"eck !"et"er !"et"er t"e follo!in function function is a &alid potential function function
φ = A(:2 6 #2) (DesB t"e i&en is a &alid potential function) b) A sip"on consistin consistin of a $ cm diameter diameter tube is used to drain !ater from a tank. ,"e outlet end of t"e t"e tube is 2 m belo! t"e !ater surface in t"e tank. electin friction* calculate t"e disc"are. f t"e peak point of t"e sip"on is 1.4 m abo&e t"e !ater surface in t"e tank* estimate t"e pressure of fluid at t"e point of sip"on. (1-.54 m$?"rB /.5/ kPa abs ) >r 24. a) @istinuis" @istinuis" bet!een +aminar and ,urbulent ,urbulent flo! !it" e:ample e:ample b) @istinuis" bet!een subsonic flo! and supersonic supersonic flo! c) 8:plain t"e term E;oundar# +a#erE and friction dra. <, 6 2-. a) 8:plain t"e !orkin principle of a ot !ire !ire anemometer. anemometer. b) ater ater flo!s t"rou" t"rou" a ent enturi uri meter !"ic" !"ic" "as a diameter diameter at t"e inlet inlet of 1.2 m and and a diameter of 0./ m at t"e t"roat. ,"e difference in pressure bet!een t"e main and t"e t"roat is measured b# a differential mercur# aue* !"ic" s"o!s a deflection of -.1 cm. Find t"e disc"are t"rou" t"e meter and also calculate t"e &elocit# of !ater at t"e t"roat. ,ake t"e coefficient coefficient of disc"are of t"e meter as 0.53.
(1.01/ m$?secB $.-54 m?sec) >r 2/. a) Compare t"e merits merits and demerits of >rifice >rifice meter and ent enturi uri meter in t"e measurement measurement of flo!. b) A -o trianular notc" is disc"arin under submered conditions. ,"e ,"e &erte: of t"e notc" is at a "ei"t of $0 cm from t"e c"annel bed. ,"e ele&ation of !ater surfaces upstream and do!nstream of t"e notc"* measured from t"e c"annel bed are - cm and -0 cm respecti&el#. respecti&el#. Assumin Assumin Cd = 0./* estimate t"e disc"are o&er t"e notc". <, 6 2. A !ater !ater softener consists of a &ertical &ertical tube -0 mm diameter diameter and packed to a "ei"t of 0.- m !it" !it" ion6 e:c"ane resin particle. ,"e particles ma# be considered as sp"ere !it" a dia of 1.2- mm. ater flo!s o&er t"e bed* because of ra&it# as !ell as pressure difference* at a rate of $00 cc?s. ,"e bed "as a porosit# of 0.$. Calculate t"e pressure drop. (-.-15 ;ar) >r 23. @eri&e an e:pression for minimum minimum fluidiGation fluidiGation &elocit#. &elocit#. Also Also i&e its p"#sical sinificance. sinificance. <, 6 25. 8:plain t"e !orkin principle principle of an Air6lift Air6lift pump pump !it" a neat sketc". "at "at are its merits and and demerits o&er con&entional centrifual pump. >r $0. 8:plain t"e &arious &arious pump c"aracteristics c"aracteristics and indicate indicate t"e s"ut6off s"ut6off "ead and and desin point.
4HE Fluid Mechanics - October 1996 Part A 6 (20 X 2 = 40 marks) 1.
,"e unit unit of speci specific fic !ei"t !ei"t of of a fluid fluid in 7 s#stem s#stem is ________ ______________ ______..
2.
>ne cent centipo ipoise ise is is e'ual e'ual to _____ ________ ______ ______ ___ Pa.7 Pa.7..
$.
,"e pressure pressure inside inside a soap bubble bubble !ill be ___________ ______________ ___ t"an t"e surround surroundin in atmosp"er atmosp"eric ic pressure. pressure.
4.
Hi&e an e:ampl e:amplee of non6e!to non6e!tonian nian fluid fluid ________ _____________ ______. _.
-.
,"e unit unit of one one standard standard atmosp atmosp"eri "ericc pressure pressure is is 101.$2 101.$2 _________ ______________ _____..
/.
Haue Haue pressure pressure is absolu absolute te pressure pressure _______ ____________ _______ __ atmosp"er atmosp"eric ic pressure. pressure.
.
@#namic @#namic similari similarit# t# is is simil similarit# arit# of ______ ___________ ________. ___.
3.
n * +* +* , s#stem s#stem dime dimension nsion of of anular anular &eloci &elocit# t# is ______ ____________ ________. __.
5.
,"e densit# densit# of manomet manometric ric fluid fluid used in an in&ert in&erted ed manometer manometer s"ould s"ould be ________ _____________ ______ _ t"an t"e densit# of flo!in fluid.
10. For stead# incompressible incompressible fluid fluid flo!* t"e continuit# e'uation e'uation is ______________. ______________.
11.
is t" t"e e' e'uation of of &o &orticit# alon ______________ a: a:is.
12.
is t"e e'uation of a ______________ in t!o dimensional flo!.
1$. For flo! o&er flat plate* t"e critical e#nolds number number is ______________. ______________. 14. e#nolds number number is t"e ratio of inertial force force and ______________ ______________ force. 1-. ac" number number is t"e ratio of _________ ______________ _____ to __________ ______________. ____. 1/. Cd of an orifice is al!a#s ______________ t"an Cc. 1. ,"e suppressed s"arp crested crested !eir is 0./ m "i" and disc"ares disc"ares !ater at a "ead "ead of 1.2 m. ,"e coefficient coefficient of disc"are of t"e !eir is ______________. 13. ,"e as flo! &elocit# t"rou" a fluidiGed bed s"ould s"ould be less t"an or e'ual to ______________ ______________ &elocit#. &elocit#. 15. Hi&e an e:ample e:ample of rotar# rotar# pump pump ___________ ______________. ___. 20. ;lo!ers are suitable suitable for ______________ disc"are disc"are t"an t"an compressors. compressors. Part ; 6 (- X 12 = /0 marks) 21. (a) 7ketc" stress &ersus &ersus strain diaram for for on6e!tonian on6e!tonian fluid. (b) A <6tube differential mercur# manometer is connected bet!een t!o pipes X and D. Pipe X contains carbon tetra c"loride (sp.r 1.-54) under a pressure of 10$ k?m2 and pipe D contains oil (sp.r 0.3) under a pressure of 12 k?m k?m2. Pipe X is 2.- m abo&e pipe D. ercur# le&el in t"e limb connected to pipe X is 1.m belo! t"e center line of pipe D. Find t"e manometer readin in cm. >r 22. (a) 7tate an# an# t"ree dimensionless dimensionless number related related to fluid flo! flo! and e:plain e:plain t"eir sinificance. sinificance. (b) 8:plain t"e term EHeometric similarit#E and E%inematic similarit#E. similarit#E. 2$. (a) @etermine !"et"er t"e &elocit# &elocit# components i&en belo! satisf# satisf# t"e e'uation of continuit# continuit#
u = 2:2 I G# & = 62:# I $#$ I $G# ! = 61.-G2 6 2:# 6 /#G. (@oes not satisf# t"e e'uation of continuit#)
(b) A 1- cm diameter pipe is reduced to .- cm diameter t"rou" radual contraction. At t"is contraction t"e difference in pressure bet!een t"ese t!o points is 4 cm of mercur#. ;# nelectin losses* calculate t"e disc"are of !ater. (0.01451 m$?sec) >r 24. (a) 8:plain t"e term EForm @raE and EFriction @raE. (b) An oil of relati&e densit# 0.52 and d#namic &iscosit# 0.032 Pa.7 flo!s in an 30 mm diameter pipe. n a distance of 20 m t"e flo! "as a "ead loss of 2 m. Calculate () t"e mean &elocit# (ii) disc"are (iii) s"ear stress at t"e pipe !all. (2.202 m?secB 0.0110 m$?secB 13.0-4 ?m2) 2-. (a) it" a neat sketc" e:plain t"e !orkin principle of a otameter. (b) A pitot tube is inserted in a pipe of $0 cm diameter. ,"e static pressure of t"e tube is 10 cm of mercur# &acuum. ,"e stanation pressure at t"e center of t"e pipe recorded b# t"e pitot tube is 1 ?cm 2. Calculate t"e rate of flo! of !ater t"rou" t"e pipe* if t"e mean &elocit# of flo! is 0.3- times t"e central &elocit#. (24./2/ m$?min) >r 2/. (a) 8:plain t"e !orkin principle of a manetic flo! meter. (b) A rectanular !eir 0.- m "i" and 1.- m lon is to be used for disc"arin !ater from a tank under a "ead of 0.- m. 8stimate t"e disc"are () !"en it is used as a suppressed !eir (ii) !"en it is used as a contract !eir. r 23. (a) @iscuss t"e mec"anism of fluidiGation. (b) Hi&e some industrial applications of fluidiGation. 25. (a) "at are t"e applications of diap"ram pumpJ (b) ame an# t"ree positi&e displacement pump and e:plain t"e !orkin principle of an# one t#pe. >r $0. it" a neat sketc" e:plian t"e !orkin principle of a centrifual pump. Also e:plain t"e EPriminE of a centrifual pump.
4HE Fluid Mechanics April-1997
Part A (20 X 2 = 40 marks) 1.
ass and !ei"t of a bod# are differentiated in terms of t"e ____________ actin on it.
2.
iscosit# ma# be described as t"e ratio bet!een ____________ and ____________.
$.
Paint is ____________ b# nature.
4.
,orricelli9s e'uation is stated as ____________.
-.
Pressure of a li'uid can be con&erted into t"e ____________ of t"e li'uid b# di&idin b# t"e correspondin densit#.
/.
ater is not a ____________ li'uid.
.
,"e compressible fluid used in an in&erted manometer is ____________.
3.
,"e unit for Poise is ____________.
5.
An ideal fluid "as no ____________ or ____________.
10. ,"e lent" re'uired to establis" full# de&eloped flo! in t"e entire cross section of t"e pipe is called ____________. 11. ,"e skin friction dra ma# be e:pressed b# t"e e'uation F?J. 12. For scalin up laborator# data to an industrial scale* t"e t"ree similarities are ____________* ____________ and ____________. 1$. Froude number is e:pressed as a ratio bet!een ____________ and ____________ forces. 14. A pitot tube is used to measure ____________ &elocities in a pipe line. 1-. ,"e forces actin on an aeroplane fl#in at a constant speed at a i&en altitude are ____________* ____________ and ____________. 1/. ,"e forces actin on a particle in a batc" fluidiGed bed at stead# state are ____________* ____________ and ____________. 1. 8run9s e'uation is useful in predictin t"e ____________ in a packed column. 13. n a centrifual pump* !ater enters at t"e ____________ of t"e impeller. 15. iscous li'uids are transported b# a ____________ pump. 20. >ne se&ent" po!er la! states J = J Part ; (- X 12 = /0 marks) 21. (a) 7tate t"e t#pes of fluids !it" suitable e:amples t"at are not e!tonian b# nature. n a neat diaram mark t"e relation bet!een s"ear stress and &elocit# radient.
>r (b) o! does a < 6 tube manometer functionJ @eri&e an e:pression for (P 1 6 P2) in terms of measurable 'uantities. 22. (a) @efine i.
Form dra
ii.
7kin dra
iii.
;oundar# la#er
i&.
Compressible flo!
&.
7moot" and rou" pipes. >r
(b) @eri&e aen6Poiseuilles e'uation* "i"li"tin t"e assumptions made. 2$. (a) 8:plain t"e !orkin of a rotameter !it" a neat sketc". Appl# ;ernoulli9s principle and deri&e an e:pression for . >r (b) (i) it" neat functional diarams* e:plain t"e instruments used for measure of flo! of ases t"rou" pipelines 100 cm lon and /0 cm in diameter. (ii) ater is drainin from a tank t"rou" a "ole de&eloped at t"e bottom. Calculate t"e coefficient of disc"are if t"e "ead of t"e !ater is maintained at - cm and $$0 cc of !ater is collected in $0 sec. ,"e "ole dia. = 0.43 cm. (0./14) 24. (a) rite an e:planator# note on fluidiGed beds. @eri&e an e:pression for pressure drop in suc" units. >r (b) (i) 7tate t"e industrial applications of fluidiGed beds. (ii) it" a neat diaram* e:plain t"e relations"ips bet!een pressure drop and modified re. 2-. (a) (i) 8:plain !it" neat sketc"es t"e !orkin of a centrifual pump. "at are t"e ad&antaes and demerits of suc" a pumpJ (ii) Plot a rap" to e:plain t"e c"aracteristics of suc" a pump. >r (b) (i) @escribe t"e !orkin of an airlift pump. Hi&e a neat sketc".
(ii) Calculate t"e ;P of a centrifual pump from t"e data i&en belo!
•
7uction "ead = 2.-4 cm
•
@isc"are "ead = 20 k?cm2
•
ei"t of !ater collected in $0 sec = 1- k.
(55.$ att)
4HE Fluid Mechanics October-1997 Part A (20 X 2 = 40 marks) 1.
Hi&e an# t!o e:amples of on6e!tonian fluid.
2.
@efine t"e term E;ulk odulusE.
$.
7tate e!ton9s +a! of &iscosit#.
4.
7tate t"e &alue of specific !ei"t of mercur# in k?m$.
-.
@efine Estream tubeE.
/.
rite t"e differential form of continuit# e'uation for t!o6dimensional stead# flo! of incompressible fluid.
.
"at is E@ra CoefficientE.
3.
rite t"e e:pression for "ead loss due to sudden e:pansion.
5.
@efine t"e term Erelati&e rou"nessE in flo! t"rou" rou" pipes.
10. "at is E"#draulic mean radiusEJ 11. "at is t"e optimum included anle of t"e di&erent section of a &enturi meterJ 12. @efine t"e term E7tanation pressureE. 1$. 7tate an# t!o t#pes of !eirs used for flo! measurement. 14. ame an# t!o metal !ires used in ot !ire anemometer. 1-. For !"at application manetic flo! meter is neededJ 1/. "at factors o&ern t"e Epressure dropE in fluidiGed bedJ 1. @efine t"e term E@esin PointE of a pump. 13. "at is ECritical fluidiGation &elocit#EJ
15. "at is t"e t"eoretical ma:imum suction lift of a centrifual pumpJ 20. ame an# t"ree rotar# t#pe positi&e displacement pumps. Part ; (- X 12 = /0 marks) <, 6 21. a) 8:plain t"e sinificance of t"e propert# &apor pressure in t"e case of li'uid flo!. (-) b) 7"o! t"at e#nolds number is dimensionless. ($) c) 7tate different principles of pressure measurement (4) >r 22. a) 8:plain @imensional anal#sis !it" an e:ample. (/) b) o! does model stud# is made use of in fluid flo! problem. 8:plain !it" an e:ample. (/) <, 6 2$. a) C"eck !"et"er t"e &elocit# component set i&en belo! satisf# t"e e'uation of continuit# (4) u = A sin :# & = 6A sin :# (does not satisf#) b) @istinuis" bet!een +aminar and ,urbulent flo!. "at factors con&ert a laminar flo! into turbulent. (3) >r 24. a) 8:plain t"e ro!t" of ;oundar# la#er for a flo! o&er a flat plate. ndicate +aminar* ,urbulent and +aminar subla#er of boundar# la #er. (/) b) A pipe line of 120 mm diameter carries !ater at t"e rate of $0 ltr?sec. ,"e &iscosit# of !ater is 0.012 poise and friction factor is 0.00-4. Find t"e pressure drop o&er a lent" of 100 m. (/) /$.$$ k?m2) <, 6 2-. a) it" a neat sketc" e:plain t"e use of Pitot6 7tatic tube. (-) b) ater flo!s t"rou" a 10 cm diameter noGGle fitted in a 13 cm diameter pipe. Calculate t"e pressure difference bet!een t"e upstream and t"e e:it* if t"e disc"are is 0.01 m$?s. Assume t"e coefficient of disc"are as 0.5. () (5 ?m2)
>r 2/. a) it" a neat sketc" e:plain t"e !orkin of instruments based on @oppler effect. (/) b) Compare t"e merits and demerits of orifice and &enturi meter for t"e case of fluid flo! measurements. (/) <, 6 2. it" a neat sketc" e:plain t"e process of fluidiGation. 7tate an# t!o applications. (12) >r 23. @ra! t"e dra cur&es for reular and irreular solids and discuss. (12) <, 6 25. 8:plain t"e operation of an Airlift pump. Also indicate its merit o&er ot"er t#pes. (12) >r $0. A centrifual pump "as an impeller of outer diameter $0cm. ,"e lea&in tips are radial at outlet. For a rotational speed of 14-0rpm* calculate t"e net "ead de&eloped for a manometric efficienc# of 30K.(12) (21.1- m)
4HE Fluid Mechanics - April 1998 Part A (20 : 2 = 40 arks) 1.
@ifferentiate bet!een compressible and incompressible fluids.
2.
"at is kinematic &iscosit#J rite its unit.
$.
rite t"e p"#sical sinificance of e#nolds number.
4.
"at is t"e relations"ip bet!een t"e dra coefficient and e#nolds number in t"e 7toke9s la! rane (e#nolds number L 1)J
-.
rite t"e principle of orifice meter.
/.
"at is t"e "ead loss of t"e fluid at t"e entrance of a strai"t pipeJ
.
8:plain 9Ca&itation9 in pumps.
3.
@efine 9inimum fluidiGation &elocit#9.
5.
@efine 98'ui&alent diameter9 for fluid flo! t"rou" c"annels of non6circular cross section.
10. rite t"e principle of anetic flo! meter. 11. rite continuit# e'uation for t"ree dimensional motion of an incompressible fluid.
12. Hi&e t!o industrial applications of packed beds. 1$. rite ;ernoulli9s e'uation. 7tate its assumptions. 14. @ifferentiate bet!een reciprocatin and centrifual pumps. 1-. 8:plain t"e principle of "ot !ire anemometer. 1/. @efine 9olumetric efficienc#9 of t"e positi&e displacement pump. 1. @efine P7 in centrifual pumps. 13. "at are t"e t!o t#pes of fluidiGationJ 15. rite t"e aen Poiseuille9s e'uation for laminar flo! in e!tonian fluid. 20. Pressure drop is __________ in lobe &al&e as compared to ate &al&e. Part ; (- : 12 = /0 arks) 21. (a) Classif# fluids. it" t"e "elp of a neat sketc"* e:plain t"e principle and applications of an inclined manometer. (/) (b) @efine "#drostatic e'uilibrium. 8:press mat"ematicall# t"e condition of " #drostatic e'uilibrium. (/) >r 22. (a) An open tank "olds certain amount of li'uid !"ose relati&e densit# is 1.2-. ,"e tank is fitted !it" a manometer to a certain point of its !all and it s"o!s a pressure of P ae = 0.$- atm* !"at is t"e "ei"t of li'uid le&el in t"e tank from t"e point of connection of t"e manometer. (4) (b) "at are t"e ad&antaes of dimensional anal#sisJ 7tate ;uckin"am π t"eorem. (4) (c) "at are t"e time6dependent fluidsJ Classif# t"em !it" e:amples. (4) 2$. (a) @efine Fannin9s friction factor. o! is it related to t"e pressure dropJ (/) (b) Pro&e for laminar flo! of e!tonian fluids t"rou" a pipe* u?u ma: = 1 6 (r?r !)2 (/) >r 24. (a) rite t"e continuit# and momentum e'uations for one6dimensional fluid flo!. (4) (b) @iscuss t"e boundar# la#er formation durin laminar and turbulent fluid flo!. (4) (c) o! !ill #ou calculate t"e e#nolds number and friction factor for a pseudo plastic fluidJ (4) 2-. (a) 8:plain t"e principle* construction and !orkin of a &enturi meter !it" t"e "elp of a neat sketc". (/) (b) A "oriGontal &enturi meter "a&in a t"roat diameter of 20 mm is set in a - mm .@. pipeline. ater at 1-oC is flo!in t"rou" t"e line. A manometer containin mercur# under !ater measures t"e pressure
differential o&er t"e instrument. "en t"e manometer readin is -00 mm* calculate t"e flo! rate. ,ake C d = 0.53. (/) >r 2/. (a) it" t"e "elp of a neat sketc"* e:plain t"e !orkin principle and operation of a rotameter. (/) (b) 8:plain t"e &elocit# measurement b# Pitot tube !it" t"e "elp of a neat sketc". (/) 2. (a) @eri&e 8run9s e'uation for determinin t"e pressure drop t"rou" a packed bed. (/) (b) rite t"e important applications of fluidiGation tec"ni'ue in industries. (/) >r 23. (a) 8:plain t"e terms 9+oadin9 and 9Floodin9 in packed to!ers. (4) (b) A packed bed of catal#st consistin of sp"erical particles of 1-0 µm diameter is subMected to fluidiGation b# usin oil of densit# 500 k?m$. f t"e densit# of particles be 2-00 k?m $* determine t"e mass flo! rate of oil per unit area of bed to initiate fluidiGation. Porosit# of bed = 0.43* d#namic &iscosit# of oil is 0.00$ Pa.s. Assume flo! condition to be laminar. (3) 25. (a) Classif# positi&e displacement pumps. 8:plain t"e function of eac" one of t"em !it" a neat sketc". (/) (b) An air6lift pump raises !ater from a !ell of 120 m deep t"rou" a pipe of @ = 100 mm at t"e rate of 50 m$?"r. @etermine t"e efficienc# of pump. ater le&el is 4- m belo! t"e surface. Air consumption = 400 m $?"r of free air compressed to 500 k?m2B ratio of specific "eats of air ( γ ) = 1.4. (/) >r $0. (a) Compare bet!een centrifual and reciprocatin pumps. (/) (b) rite briefl# t"e c"aracteristic features and applications of fans* blo!ers and compressors. (/)
4HE Fluid Mechanics - October 1998 Part A 6 (20 X 2 = 40 marks) 1.
@ifferentiate bet!een e!tonian and on6e!tonian fluids.
2.
rite t"e unit for surface tension coefficient.
$.
"at are t"e t!o important c"aracteristics of potential flo!J
4.
@efine 9mass &elocit#9 of fluid t"rou" a c"annel.
-.
"at is ac" numberJ @efine t"e ac" number for an ideal as.
/.
@efine 9;oundar# +a#er9.
.
rite 8run9s e'uation for pressure drop t"rou" a packed bed.
3.
Classif# positi&e displacement pumps.
5.
rite an e:pression for "ead loss due to sudden e:pansion of t"e fluid.
10. rite t"e p"#sical sinificance of Froude9s number. 11. rite fe! industrial applications of fluidiGed beds. 12. nclined manometer is used for ____________. 1$. @efine 9anometric efficienc#9 in centrifual pump. 14. rite t"e principle of Pitot tube. 1-. "# is rotameter called an area meterJ 1/. "at is 9"at ammer9J 1. "at is PriminJ 13. "at is t"e function of &olute in a centrifual pumpJ 15. rite t!o differences bet!een compressors and blo!ers. 20. @efine 9Form dra9 and 97kin dra9. Part ; 6 (- X 12 = /0 marks) 21. (a) it" t"e "elp of s"ear stress6s"ear rate diaram* e:plain t"e classification of non6e!tonian fluids. @iscuss t"eir important c"aracteristics. (3) (b)A simple <6tube manometer is installed across an orifice meter. ,"e manometer is filled !it" mercur# (sp.r = 1$./) and t"e li'uid abo&e t"e mercur# is carbon tetra c"loride (sp.r = 1./). ,"e manometer reads $00 mm. "at is t"e pressure difference o&er t"e manometer in e!tons per s'uare meterJ (4) >r 22. (a) @efine 7imilitude. 8:plain t"e different t#pes of similarities in fluid flo! processes. (4) (b) Pressure drop of a "omoeneous fluid in a strai"t smoot" pipe ( ∆P) is a function of t"e pipe eometr# (diameter d* and lent" l)* t"e p" #sical properties of t"e fluid (densit# ρ and &iscosit# µ) as !ell as its &elocit# &.
∆P = f (d* l* ρ, µ, &)
2$. (a) Assumin one dimensional fluid flo!* !rite t"e continuit#* momentum and mec"anical ener# e'uations for an incompressible fluid. (/) (b) @iscuss t"e &elocit# profiles for laminar and turbulent fluid flo! t"rou" a pipe. "at is t"e relations"ip bet!een skin friction and !all s"ear in a pipeJ (/) >r 24. (a) @iscuss t"e &arious Gones for de&elopment of turbulent boundar# la#er on a flat plate. (4) (b) ;rine is to be pumped t"rou" a 2- m of smoot" copper tube "a&in an inside diameter of 2.- cm. Flo! rate of brine is 100 litre?min. Calculate t"e follo!in (i)Pressure drop from friction in k?m 2 (ii)Po!er re'uired to o&ercome friction. @ata 7pecific ra&it# of brine = 1.1iscosit# of brine = 2.- cp Friction factor f = 0.001- I 0.12-e60.$$ (3) 2-. (a) 8:plain t"e principle* construction and !orkin of an orifice meter !it" t"e "elp of a neat sketc". (/) (b) @iscuss t"e principle and applications of @oppler effect in flo! measurement. (/) >r 2/. (a) Compare bet!een an orifice meter and &enturi meter. (4) (b) An oil of specific ra&it# 0.3 is flo!in t"rou" a &enturi meter "a&in inlet diameter 20 cm and t"roat diameter 10 cm. ,"e mercur# differential manometer s"o!s a readin of 2- cm. Calculate t"e disc"are of oil t"rou" t"e "oriGontal &enturi meter. ,ake C d = 0.53 (3) 2. (a) it" t"e "elp of a neat sketc"* e:plain t"e flo! of fluid t"rou" ranular solids. (/) (b) @eri&e Carman6%oGne# e'uation for pressure drop t"rou" a packed bed. (/) >r 23. (a) 8:plain t"e different t#pes of fluidiGation and state t"eir conditions. 7tate commercial applications of fluidiGed bed. (/) (b) @ifferentiate bet!een +oadin and Floodin. o! !ill #ou estimate t"e floodin &elocit# in a packed to!erJ (/) 25. (a) Classif# pumps. it" t"e "elp of a neat sketc"* e:plain t"e operation of a centrifual pump. (/) (b) 7tate t"e principle and applications of air lift and diap"ram pumps. (/) >r $0. (a) 8:plain t"e principle of operation for fans* blo!ers and compressors. (/)
(b) A centrifual fan is used to take flue as at rest and at a pressure of 00 mm and a temperature of 50oC and disc"ares it at a pressure of /- mm and a &elocit# of 4- m?s. Calculate t"e po!er re'uired to mo&e 13000 m$?"r of as. 8fficienc# of t"e fan is /-K. olecular !ei"t of t"e as = $2. (/)
4HE Fluid Mechanics April - 1999 Part 6 A (Ans!er A++ 'uestions.) 20 : 2 = 40 arks 1.
@efine e!tonian fluid.
2.
"at is E&apour pressureE.
$.
@efine kinematic &iscosit#.
4.
rite t"e unit of po!er in .+.,. s#stem.
-.
@efine 9stream tube9.
/.
"at is 9form dra9J
.
7tate t"e use of e#nolds number in fluid flo!.
3.
ndicate a possible &elocit# profile in E,urbulent flo!E.
5.
@efine t"e term 9ac" number9.
10. 7tate 8uler9s e'uation for ideal fluid flo!. 11. "# t"e lent" of di&erent section of a &enturimeter is muc" loner t"an its con&erent section. 12. @efine t"e term ECoefficient of ContractionE. 1$. rite t"e e:pression for disc"are t"rou" a 6notc" !it" an included anle of θ 14. "at are t"e t#pes of ot6!ire anemometer used in practiceJ 1-. 7uest a flo! meter for measurin slurr# flo! in a closed pipeline. 1/. @efine t"e term EFluidiGationE. 1. ame an# t!o t#pes of positi&e displacement pump. 13. ame an# t"ree applications for continuous fluidiGation. 15. @efine t"e term Es"ut off "eadE of a centrifual pump. 20. "ic" fan produce a "i" static pressure rise* a back!ard cur&ed fan or a for!ard cur&ed fan.
Part 6 ; 21. (a) (i) @eri&e an e:pression for capillar# rise of !ater in a small tube. (-) (ii) ater "as a surface tension of 0.4 ?m. n a $ mm diameter &ertical tube if t"e li'uid rises / mm abo&e t"e li'uid outside t"e tube* calculate t"e contact anle. () >r (b) (i) @efine Heometric and %inematic similarit#. (4) (ii) A < 6 tube differential mercur# manometer is connected bet!een t!o pipes X and D. Pipe X contains carbon tetra c"loride (7p.r. 1.-5) under a pressure of 10$ k?m 2 and pipe D contains oil (7p.r. 0.3) under a pressure of 12 k?m2. Pipe X is 2.- m abo&e pipe D. ercur# le&el in t"e limb connected to pipe X is 1.- m belo! t"e centerline of pipe D. Find t"e manometer readin as s"o!n b# a centimeter scale attac"ed to it. (3) 22. (a) (i) 8:plain t"e concept &elocit# potential and stream function.(4) (ii) ater flo!s t"rou" a "oriGontal conical pipe. ,"e diameter at larer end is 1.$ m and t"at at smaller end is 0. m. ,"e pressure "ead at t"e smaller end is - m of !ater and disc"are is $.- m $?sec. Calculate t"e &elocities at t"e t!o ends and pressure "ead at larer end. (3) >r (b) (i) 8:plain t"e met"od of reducin skin friction dra. (4) (ii) A medium lubricatin oil of sp.r. 0.3/ is pumped t"rou" $00 m "oriGontal pipe of diameter -0 mm at a rate of 1.24 lit?sec. f t"e pressure drop is 0.2 Pa find t"e absolute &iscosit# of oil. (3) 2$. (a) @eri&e an e:pression for coefficient of disc"are of a &enturimeter. >r (b) it" a neat sketc" e:plain t"e !orkin principle of a ot6film anemometer. 24. (a) @escribe t"e met"ods of estimatin pressure drop t"rou" a packed bed. >r (b) @escribe t"e eneral properties of fluidiGed bed. 2-. (a) @escribe t"e !orkin principle of an# one t#pe rotar# pump !it" a neat sketc". >r (b) (i) 8:plain t"e &arious performance cur&es of a centrifual pump. (ii) ;riefl# e:plain t"e met"od of selectin a pump for a i&en application.
4HE Fluid Mechanics - October 1999
Part A (20 : 2 = 40 marks) 1.
@efine t"e term 97tatic "ead9.
2.
7tate ;ernoulli e'uation. rite dimensions for eac" term in&ol&ed.
$.
@ifferentiate bet!een absolute &iscosit# and kinematic &iscosit#. rite t"e units.
4.
,"e coefficient of disc"are for a i&en orifice is a function of ___________and ___________.
-.
@efine 98'ui&alent diameter9 for fluid flo! t"rou" ducts of noncircular diameter.
/.
rite t"e p"#sical sinificance of ac" number.
.
"at is meant b# 9skin friction9J
3.
8:plain t"e terms ma:imum &elocit# and a&erae &elocit# for a flo! of fluid in a circular pipe.
5.
rite ;lake6Plummer e'uation for packed beds.
10. 7tate @arc#9s la!. 11. ,"e &elocit# radient* be#ond t"e boundar# la#er is e'ual to _________. 12. ame t!o t#pes of fluidiGation and i&e t!o important industrial application. 1$. o! !ill #ou calculate t"e "ead de&eloped b# a pumpJ 14. rite an# four important ad&antaes of multistae compressors. 1-. Pump siGe is determined on t"e basis of __________and_____________. 1/. @etermine t"e densit# of air under a &acuum of 44- mm at 4-oC. 1. rite t"e !orkin principles of ultrasonic flo! meters. 13. "at is meant b# loadin in a packed to!erJ 15. rite a s"ort note on positi&e displacement pumps. 20. rite momentum e'uation for compressible flo!. Part ; (- : 12 = /0 marks) 21. (a) @e&elop a differential form of e:pression for t"e estimation of pressure filed !it"in a static fluid. (/) (b) @eri&e an e:pression for t"e estimation of pressure drop in a centrifue. (4) (c ) 7tate e!ton9s la!. Hi&e an# four e:amples of non6e!tonian fluids. (2)
>r 22. (a) Calculate t"e "#draulic mean diameter of t"e annular space bet!een a 4 cm and / cm tubes. (4) (b) A stream of droplets of li'uid formed rapidl# at an orifice submered in a second immiscible fluid. t !as found t"at t"e mean siGe of t"e droplets !as influenced b# t"e orifice diameter* &elocit# of li'uid* interfacial tension* &iscosit# of t"e dispersed p"ase* densit# of bot" dispersed and continuous p"ases and t"e acceleration due to ra&it#. r 24. (a) For a circular pipe of circular cross section* from t"e first principles pro&e t"at <:?r 2/. (a) A rotameter "as a tube of 0.$ m lon* !"ic" "as an internal diameter of 2- mm at t"e top and 20 mm at t"e bottom. ,"e diameter of t"e float is 20 mm and t"e specific ra&it# is 4.3 and its &olume is /./ cc. f t"e coefficient of disc"are is 0.2* at !"at "ei"t !ill t"e float be !"en meterin !ater at 100 cc?sec. (3) (b) "at is meant b# @oppler9s effectJ o! is it used in t"e flo! measurementsJ (4) 2. (a) ;riefl# discuss t"e follo!in (4) 1.
Particulate fluidiGation
2.
Areati&e fluidiGation
(b) From t"e first principles deri&e 8run9s e'uation* for t"e determination of pressure drop in a packed to!er and briefl# discuss t"e application. (3)
>r 23. (a)
anometric "ead
2.
anometric effficienc# >r
$0. (a) A centrifual pump is to be used to e:tract !ater from a condenser in !"ic" t"e &acuum is /40 mm of . At t"e rated disc"are t"e net positi&e suction "ead must be at least $ meter abo&e t"e ca&itation &apor pressure of 10 mm . f losses in a suction pipe account for a "ead of 1.- m* !"at must be t"e least "ei"t of li'uid le&el in t"e condenser abo&e t"e pump inlet. (3) (b) it" a neat sketc"* briefl# discuss t"e !orkin principles of a diap"ram pump. Hi&e an# t!o important applications. (4).
4HE Fluid Mechanics April 2000 Part A (20 : 2 = 40) 1.
"at is e!ton9s la! of &iscosit#J
2.
7tate t"e similarit# la!s
$.
"at is potential flo!J
4.
7tate t"e t#pe of fluid in t"e follo!in cases (a) ubber late: (b) ;entonite cla#
-.
@efine e'ui&alent diameter of pipe
/.
@istinuis" bet!een form dra and skin dra
.
@efine ac" number
3.
"at is t"e relation bet!een ma:imum &elocit# and a&erae &elocit# in laminar flo! and turbulent flo!
5.
@ra! &elocit# profile for laminar flo! in a circular pipe
10. Compare and contrast &enturi meter and orifice meter 11. "at is t"e principle of !orkin of pitot tubeJ 12. Hi&e e:amples of area and "ead flo! meters 1$. @efine porosit# and minimum fluidiGation &elocit# 14. @ra! t"e dra cur&es for reular solids 1-. 7tate 8run9s e'uation and its application 1/. @efine boundar# la#er 1. "at is meant b# P7J 13. Compare centrifual pump !it" reciprocatin pump 15. +ist t"e &arious losses occurrin in centrifual pump 20. rite t"e filed of application of &arious flo! meters Part ; (- : 12 = /0) 21. n a c"emical reactor of 10 m tall* t"e densit# of fluid mi:ture &aries !it" t"e distance 9#9 in meters from t"e top of t"e reactor as
ρ = 1000N 1 I #?-0 I (#?100)2O Assumin t"e mi:ture to be effecti&el# stationar#* determine t"e pressure difference bet!een t"e top and bottom of t"e reactor. >r 22. ,"e performance of an oil ri consumin a disc"are of oil depends on t"e internal diameter d of t"e ri* t"e rotational speed of t"e s"aft* t"e mass densit# ρ* t"e d#namic &iscosit# µ* t"e surface tension σ and t"e specific !ei"t ω of t"e oil. 7"o! b# dimensional anal#sis
2$. 7tate and pro&e t"e ;ernoulli9s t"eorem for incompressible fluid and indicate t"e corrections necessar# for its application >r 24. ater at /0oC is pumped from a reser&oir to t"e top of a mountain t"rou" a 1- cm pipe at a &elocit# of $.m?s. ,"e pipe disc"ares into t"e atmosp"ere at a le&el of 1000 m abo&e t"e le&el in t"e reser&oir. ,"e pipe itself is 1-00 m lon. f t"e o&erall efficienc# of t"e pump is /-K* calculate t"e po!er re'uirement. 2-. An orifice meter "a&in an inside diameter of 2.- cm is located in a 3 cm pipe. ater is flo!in t"rou" t"e line and t"e mercur# manometer measures t"e differential pressure o&er t"e instrument. ,"e leads are filled !it" !ater. "en t"e manometer readin is $- cm* !"at is t"e flo! rate of !ater per minuteJ >r 2/. (a) 8:plain t"e !orkin of a rotameter !it" a neat sketc". (/) (b) 8:plain t"e met"od of functionin of a manetic flo! meter. (/) 2. @eri&e 8run9s e'uation and state its usefulness. >r 23. "at is continuous fluidiGationJ 8:plain "o! and !"ere it is appliedJ ;riefl# state t"e desin steps for a s#stem usin continuous fluidiGation. 25. (a) @iscuss t"e factors to be considered for selectin a pump for an operation. (-) (b) it" a neat sketc" e:plain t"e !orkin of a centrifual pump. () >r $0. rite s"ort notes on (a) Compressors and blo!ers (b) Fans (c) @iap"ram pumps
4HE Fluid Mechanics October 2000 Part A (20 : 2 = 40 arks) 1.
@ifferentiate bet!een barometric pressure and absolute pressure.
2.
"at is meant b# pressure of a li'uid columnJ
$.
@#namic pressure is t"e difference bet!een ________ and ________.
4.
@efine t"e term 97lip &elocit#9.
-.
Hi&e t!o important industrial applications of fluidiGed bed.
/.
rite t"e principle of otameter.
.
Hi&e t"e relations"ip bet!een @ra coefficient and e#nolds number in (a) e!ton9s rane of operation (b) ntermediate rane of operation
3.
rite t"e p"#sical sinificance of Arc"imedes number.
5.
8:plain t"e term 9@arc# friction factor9.
10. "at is meant b# compressible fluidsJ Hi&e t!o e:amples. 11. rite %oGen#6Carman e'uation for packed beds. 12. @efine t"e term >rifice coefficient. 1$. @efine (a) 7tatic suction lift (b) 7tatic suction "ead. 14. Hi&e an# four important criteria in&ol&ed in t"e selection of pumps. 1-. "at is meant b# boundar# la#er t"icknessJ 1/. @ifferentiate bet!een fans and blo!ers. 1. rite t"e continuit# e'uation for compressible flo!. 13. "at is meant b# floodin in packed to!ersJ 15. 8:plain 9Ca&itation9 in pumps. 20. @efine t"e term "indered settlin. Part ; (- : 12 = /0 arks) 21. (a) From first principles* de&elop an e'uation for relatin pressure and "ei"t* in a static fluid. Hi&e t"e restrictions for t"e relation. (/) (b) @iscuss briefl# about on6e!tonian fluids. Hi&e e:amples. (4) (c) 7tate ;uckin"am π t"eorem. (2) >r 22. (a) o! fluids are classifiedJ 8:plain briefl# t"e principles and application of an inclined manometer. (/) (b) An open tank "olds certain amount of li'uid !"ose relati&e densit# is 1.2-. ,"e tank is fitted !it" manometer at a point of t"e !all and it s"o!s a pressure of P aue = 0.$- atm. "at is t"e "ei"t of t"e li'uid le&el in t"e tank from t"e point of connection of t"e manometerJ (/) 2$. (a) "at is meant b# potential flo!J (2) (b) @eri&e ;ernoulli9s e'uation and briefl# discuss t"e components in&ol&ed in t"e e'uation. (3) (c) rite an# four applications of ;ernoulli e'uation. (2)
>r 24. (a) 8:plain t"e term 9skin factor9 and 9form factor9. (4) (b) o! skin friction is related to pressure dropJ (4) (c) @iscuss briefl# about t"e friction factor in flo! t"rou" c"annels of noncircular cross section. (4) 2-. (a) ;riefl# discuss about t"e important flo! meters used in industr#. "at are t"e ad&antaes and disad&antaes o&er eac" ot"erJ (/) (b) 7ulfuric acid of specific ra&it# 1.2- is flo!in t"rou" a pipe of 4.- cm i.d. A t"in ripped orifice of 1.0 cm is fitted in t"e pipe and t"e differential pressure s"o!n b# t"e mercur# manometer is 10 cm. Assumin t"at t"e leads of t"e manometer are filled !it" acid* calculate t"e !ei"t of acid flo!in per "our. Assume Co = 0./ (/) >r 2/. rite s"ort notes on t"e follo!in (4 : $ = 12) (a) et as meters (b) ot film anemometers (c) anetic flo! meters (d) Pitot tube 2. (a) ;riefl# discuss about t"e fluidiGation processes. "at are t"e different t#pes used in industr#J (4) (b) @iscuss about t"e follo!in (4) (i) Porosit# of static bed and porosit# of fluidiGed bed (ii) inimum pressure drop and bed pressure drop in fluidiGed process. (c) @ifferentiate bet!een t"e follo!in in a fluidiGed bed reactor. (4) (i) orkin &elocit# (ii) Actual &elocit# >r 23. (a) "at is meant b# loadin in a packed bed reactorJ (2) (b) @eri&e 8run9s e'uation. 8:tend t"e e'uation for bot" laminar and turbulent conditions of packed to!er operation. (10) 25. (a) /0K 7ulfuric acid is to be pumped at t"e rate of 4000 cm$?sec t"rou" a lead pipe 2.- cm diameter and raised to a "ei"t of 2- cm. ,"e pipe is $0 m lon and includes t!o ri"t anled bends. Calculate t"e t"eoretical "orse po!er re'uired. ,"e specific ra&it# of t"e acid is 1.-$ and its kinematic &iscosit# is 0.42cm2?sec. ,"e densit# of !ater ma# be taken as 1000 k?m $. Assume a &alue of rou"ness factor as 0.0- and ? ρu2 = 0.004- eac". ,"e &elocit# "ead loss coefficient for flo! t"rou" 50o bend is 0.3. f necessar#* make assumptions and mention clearl#. (10) (b) @efine t"e term 9P79. (2) >r $0. (a) Compare t"e !orkin principles and c"aracteristics of centrifual pumps !it" t"at of reciprocatin pumps. (/) (b) @iscuss briefl# about positi&e displacement pumps. 8:plain its function !it" a neat sketc". (/)
eri!ations - Fluid Mechanics "uestions 1.
@eri&e a eneral e'uation for t"e &ariation of pressure due to ra&it# from point to point in a static fluid.
2.
@eri&e an e:pression for t"e pressure difference across t!o limbs of a differential manometer containin t!o aue fluids* mutuall# immissible. "at factors influence t"e sensiti&it#J
$.
@eri&e t"e e'uation of continuit# for an incompressible flo!. 7tate t"e importance of t"e e'uation.
4.
;# appl#in momentum balance to t"e stead# flo! of a fluid inside a pipeline* obtain t"e ;ernoulli9s e'uation. ndicate t"e corrections necessar# to t"e e'uation for application to real situations.
-.
@eri&e 8uler9s e'uation of motion alon a streamline in differential form and obtain ;ernoulli9s e'uation in t"e interal form for t"e flo! of an incompressible fluid.
/.
@eri&e t"e aen6Poiseuille e'uation for laminar flo! t"rou" a circular pipe. 7tate t"e limitations of t"e e'uation.
.
7"o! t"at t"e a&erae &elocit# of t"e fluid flo!in t"rou" a circular pipe under laminar conditions is "alf t"at of t"e ma:imum &elocit#.
3.
Consider t"e flo! of a e!tonian fluid in a pipe "a&in rou"ness 9k9. ;# dimensional anal#sis* de&elop an e'uation relatin t"e frictional pressure drop in terms of t"e follo!in
ρ 6 densit# of fluid µ 6 &iscosit# of fluid & 6 &elocit# of fluid @ 6 diameter of pipe + 6 lent" of pipe k 6 rou"ness
escriptions - Fluid Mechanics "uestions 1.
"at is ;uckin"am Pi6t"eoremJ 8:plain its application briefl#.
2.
8nlist t"e important dimensionless roups in&ol&ed in t"e stud# of fluid mec"anics and e:plain t"eir p"#sical sinificance.
$.
8:plain t"e terms (i) Heometric (ii) %inematic and (iii) @#namic similarities.
4.
@escribe t"e met"ods emplo#ed for flo! measurements in open c"annels.
-.
8:plain t"e conditions on !"ic" t"e c"oice of t"e follo!in meters !ould depend (i)>rifice meter (ii) enturi meter (iii) Pitot tube.
/.
@ra! t"e c"aracteristic cur&es for a centrifual pump.
.
"at is a positi&e displacement pumpJ @escribe t"e !orkin of an# one t#pe !it" neat sketc".
3.
@escribe t"e !orkin of an Airlift pump and e:plain on !"at factors its efficienc# dependent.
#hort $otes - Fluid Mechanics "uestions 1.
nclined manometer.
2.
Flo! of fluid in ;oundar# la#er.
$.
;oundar# la#er separation.
4.
9#draulicall# smoot"9 pipes.
-.
8:pansion and contraction losses.
/.
8'ui&alent lent" of fittins.
.
Flo! in non6circular conduits.
3.
Pneumatic transport.
5.
7team Met eMectors.
10. 7election of pumps for "andlin of li'uids. 11. ater "ammer. 12. et positi&e suction "ead. 1$. "at is ca&itation and "o! it can be eliminated for a centrifual pumpJ
%o&parisons - Fluid Mechanics "uestions 1.
@istinuis" bet!een compressible and incompressible fluids.
2.
@istinuis" bet!een e!tonian and non6e!tonian fluids.
$.
ndicate t"e difference bet!een skin friction and form friction.
4.
@ifferentiate bet!een packed and fluidiGed beds.
-.
@ifferentiate bet!een loadin and floodin &elocities in a packed absorption column.
/.
@ifferentiate bet!een aressi&e and particulate fluidiGation.
.
o! do &ariable "ead meters differ from &ariable area meters for t"e measurement of fluid flo!J
3.
Compare t"e ad&antaes and disad&antaes of centrifual pump reciprocatin pump.
5.
@istinuis" bet!een Fans and ;lo!ers and Compressors.
Fluid Mechanics - 'roble&s ($)* -)
1.
A differential manometer is used to measure t"e pressure drop in a pipeline con&e#in met"ane as at 20 oC and 1 atm pressure. ,"e t!o li'uids in t"e differential manometer are kerosene (specific ra&it# 0.32) and !ater. ,"e inside diameter of t"e reser&oirs and t"e <6tube manometer are -cm and 0.-cm respecti&el#. f t"e readin in t"e manometer is 1-cm* calculate t"e pressure difference indicated* !"en t"e c"ane in le&els in t"e reser&oir (i) is nelected and (ii) is taken into account.
2.
A eometricall# similar model of an air duct is built 1$0 scale and tested !it" !ater !"ic" is -0 times more &iscous and 300 times more dense t"an air. "en tested under d#namicall# similar conditions* t"e pressure drop is 2.2- atm in t"e model. Find t"e correspondin pressure drop in t"e full6scale protot#pe.
$.
An inclined manometer is installed across a pipeline carr#in !ater to measure t"e pressure drop due to friction. ,"e manometer is filled !it" oranic li'uid of specific ra&it# 1./ and its readins is - cm. ,"e anle bet!een t"e &ertical and inclined limbs is /0 o. Calculate t"e pressure drop.
4.
A centrifue bo!l $0 cm in .@. is rotatin at a speed of /0 re&olutions per second. t contains a - cm la#er of a li'uid of specific ra&it# 1./. f t"e s#stem is open to atmosp"ere* estimate t"e aue pressure e:erted at t"e !alls of t"e centrifue bo!l.
-.
ater at 20oC (&iscosit# = 1 cp) flo!s t"rou" a smoot" strai"t pipe A of inside diameter 4 cm at an a&erae &elocit# of -0 cm?sec. >il flo!s t"rou" anot"er pipe ; of inside diameter 10 cm. Assumin similarities* calculate t"e &elocit# of oil t"rou" pipe ;. 7pecific ra&it# of oil is 0.3 and its &iscosit# is 2 cp.
/.
A <6tube manometer filled !it" mercur# is connected bet!een t!o points in a pipeline. f t"e manometer readin is 2/ mm of * calculate t"e pressure difference bet!een t"e points !"en (a) !ater is flo!in t"rou" t"e pipe (b) air at atmosp"eric pressure and 20 oC is flo!in in t"e pipe.
@ensit# of mercur# = 1$./ m?cc @ensit# of !ater = 1 m?cc olecular !ei"t of air = 23.3
($)* -))
.
ater flo!s t"rou" a 106cm . @. pipeline at an a&erae &elocit# of 2m?s. @o!nstream t"e pipeline di&ides into a 10cm main and a 2.- cm. b#pass. ,"e lent" of 106cm. main pipeline in t"e b#passed section is 3 m. and t"e e'ui&alent lent" of t"e b#pass is 10 m. electin entrance and e:it losses* estimate t"e fraction of t"e total !ater flo!in t"rou" t"e b#pass* if t"e flo! is turbulent.
3.
Calculate t"e po!er re'uired per meter !idt" of t"e stream to force lubricatin oil at a rate of 100 m $?"r per meter !idt" t"rou" t"e space bet!een t!o "oriGontal flat parallel plates. ,"e plates are $ m lon and separated b# a distance of / mm. ,"e oil "as a densit# of 0.5 m?cc and a &elocit# of 2- cP. ake necessar# assumptions.
5.
ater is pumped from a reser&oir to a "ei"t of 1000 m from t"e reser&oir le&el* t"rou" a pipe of 1- cm .@. at an a&erae &elocit# of 4 m?s. f t"e pipeline alon !it" t"e fittins is e'ui&alent to 2000 m lon and t"e o&erall efficienc# is 0K* !"at is t"e ener# re'uired for pumpinJ Friction factor f = 0.04/ e 60.2.
10. Calculate t"e po!er re'uired and t"e pressure !"ic" s"ould be de&eloped b# a pump of efficienc# 30K to pump /0 liters? min. of 53K sulfuric acid at 2-oC from an open tank at round le&el to a closed o&er"ead tank at a aue pressure of 2 atm kept $m abo&e t"e round. ,"e densit# of t"e acid is 13-0k?m $ and t"e &iscosit# is 2- centipoises. elect frictional losses. 11. A "oriGontal annulus is 10 m lon !it" an inner diameter of 2.- cm and an outer diameter of -./ cm. A suar solution of densit# 1$00 k?m $ and a &iscosit# of /0 cP is flo!in t"rou" t"e annulus at 20oC. Calculate t"e &olumetric flo! rate !"en t"e impressed pressure drop is 40 k?m2. 12. ,"e pressures at t!o sections of a "oriGontal pipe are 0.$ kf?cm2 and 0./ kf?cm2 and t"e diameters are .cm* and 1- cm respecti&el#. @etermine t"e direction of flo! if !ater flo!s at a rate of 3.- k?sec. 7tate #our assumptions. 1$. ater flo!s t"rou" a 0.20$ m diameter pipe* !it" an a&erae &elocit# of $./ m?sec. ,"ere is a sudden enlarement to 0.40/ m diameter pipe. "at is t"e po!er loss due to t"e sudden enlarementJ 14. A capillar# tube 0.2 cm in diameter and 10 cm lon disc"are one liter of a li'uid in ten minutes under a pressure difference of - cm mercur#. Find t"e &iscosit# of t"e li'uid usin t"e follo!in data 1-. 2.1/ m$?" !ater at $20 % is pumped t"rou" a 40 mm .@. pipe t"rou" a lent" of 1-0 m in a "oriGontal direction and up t"rou" a &ertical "ei"t of 12 m. n t"e pipe t"ere are fittins e'ui&alent to 2/0 pipe diameters. "at po!er must be supplied to t"e pump if it is /0K efficientJ ,ake t"e &alue of fannin friction factor as 0.003. ater &iscosit# is 0./- cp* and densit# = 1 m?cc. 1/. A reaction &essel is pro&ided !it" a burstin disc and t"e ases are &ented to t"e atmosp"ere t"rou" a stack pipe "a&in a cross sectional area of 0.0 m2. ,"e rupture disc "as a flo! area of 4000 mm 2 and t"e ases e:pand to t"e full area of t"e stack pipe in a di&erent section. f t"e as in t"e &essel is at a pressure of 10 ?m2 and a temperature of -00 %. Calculate t"e initial rate of disc"are of as. 1. ater flo!s t"rou" a 100 mm steel pipe at an a&erae &elocit# of 2 m?s. @o!nstream t"e pipe di&ides into a 100 mm main and a 2- mm b #pass. ,"e e'ui&alent lent" of t"e b#pass is 10 mB t"e lent" of t"e 100 mm pipe in t"e b#passed section is 3 m. electin entrance and e:it losses* calculate t"e fraction of t"e total !ater t"at passes t"rou" t"e b#pass.
($)* -)))
13. Calculate t"e pressure drop of air flo!in at $0oC and 1 atm pressure t"rou" a bed of 1.2- cm diameter sp"eres* at a rate of /0 k?min. ,"e bed is 12- cm diameter and 2-0 cm "ei"t. ,"e porosit# of t"e bed is 0.$3. ,"e &iscosit# of air is 0.0132 cP and t"e densit# is 0.0011-/ m?cc.
15. f a sp"erical particle of - mm diameter and specific ra&it# $.0 falls at a rate of 2 m?s t"rou" an oil of specific ra&it# 0.33* determine t"e &iscosit# of t"e oil. 20. A bed containin $2*00 k of 100 mes" s"arp sand is to be fluidiGed !it" air at 400oC and 1 atm abs in a c#lindrical &essel $.- m in diameter. ,"e ultimate densit# of t"e sand particle is 2/50 k?m $. ,"e &iscosit# of air at operatin conditions is 0.0$2 cp. Calculate
(a)t"e minimum "ei"t of fluidiGed bed (b)t"e pressure drop across t"e bed at t"e minimum porosit# condition (c)t"e critical superficial air &elocit#* i&en minimum porosit# = 0.--* diameter of 100 mes" particle siGe = 0.14 mm. 21. A mi:ture of &apors pass t"rou" a packed bed of lass sp"eres "a&in densit# 2.4 ?cc eac" of diameter 0.- cm. ,"e pressure drop due to t"e flo! is 40- kf?m 2. ,"e "ei"t of packed bed is 1.3- m. ,"e densit# and &iscosit# of t"e &apor mi:ture are $.3 : 10 6$ ?cc and 0.01- cP respecti&el#.
@ata Cross sectional area of t"e packed column tube = 0.05 m 2 ;ed porosit# = 0.4 Find t"e mass flo! rate of t"e &apor mi:ture. s t"e bed fluidiGedJ 22. A reenerati&e "eater is packed !it" a bed of / mm cubes. ,"e cubes are poured into t"e c#lindrical s"ell of t"e reenerator to a dept" of $.- m suc" t"at t"e bed porosit# !as 0.44. f air flo!s t"rou" t"is bed enterin at 2-oC and atm abs and lea&in at 200 oC* calculate t"e pressure drop across t"e bed !"en t"e flo! rate is -00 k?"r per s'uare meter of empt# bed cross section. Assume a&erae &iscosit# as 0.02- cP and densit# as /.3 k?m$. 2$. A smoot" flat plate is pulled t"rou" a pool of stanant !ater at a &elocit# of / m?s. ,"e plate "as a !idt" of $ m and a lent" of $0 m. 8stimate t"e total dra force actin on one side of t"e plate. 24. 000 k?"r of air* at a pressure of atm and a temperature of 12oC is to be passed t"rou" a c#lindrical to!er packed !it" 2.- cm ;erl saddles. ,"e "ei"t of t"e bed is / m. "at minimum to!er diameter is re'uired* if t"e pressure drop t"rou" t"e bed is not to e:ceed -00 mm of mercur#J
For ;erl saddles* ∆ p = (1./- : 105 s1.32 ρ 1.3- )?@ p1.4 !"ere ∆ p is t"e pressure drop in kf?cm 2* is t"e bed "ei"t in meter* ρ is t"e densit# in ?cc* @ p is nominal diameter of ;erl saddles* s is t"e superficial linear &elocit# in m?sec.
($)* -)+
2-. A "oriGontal &enturi meter "a&in a t"roat diameter of 4 cm is set in a 10 cm .@. pipeline. ater flo!s t"rou" t"e s#stem and t"e pressure differential across t"e &enturi meter is measured b# means of a simple <6tube manometer filled !it" mercur#. 8stimate t"e flo! rate !"en t"e manometer readin is $0 cm. Assume C& = 0.53. f 10K of t"e pressure differential is permanentl# lost* calculate t"e po!er consumption of t"e meter.
2/. ,"e rate of flo! of !ater in a 1-0 mm diameter pipe is measured !it" a &enturi meter of -0 mm diameter t"roat. "en t"e pressure drop o&er t"e con&erin section is 100 mm of !ater* t"e flo! rate is 2. k?sec. "at is t"e coefficient of t"e meterJ 2. ater is flo!in t"rou" a .- cm .@. pipe. ,"e corner taps of a $ cm s'uare eded orifice in t"e pipe are connected to a manometer containin met"#l benGoate (sp.ra&it# = 1.10). t"e difference in li'uid le&els in t"e manometer is $0 cm. Find t"e flo! rate. 23. ;rine of specific ra&it# 1.2 is flo!in t"rou" a 10 cm .@. pipeline at a ma:imum flo! rate of 1200 liters?min. A s"arp eded orifice connected to a simple <6tube mercur# manometer is to be installed for t"e purpose of measurements. ,"e ma:imum readin of t"e manometer is limited to 40 cm. Assumin t"e orifice coefficient to be 0./2* calculate t"e siGe of t"e orifice re'uired. 25. ater is flo!in t"rou" a smoot" pipe of 10 cm .@. to !"ic" a "oriGontal &enturi meter "a&in a t"roat diameter of 4 cm is attac"ed. A mercur# <6tube manometer connected to t"e meter s"o!s a readin of 2cm. Calculate t"e flo! rate. $0. A e!tonian fluid "a&in a &iscosit# of 1.2$ poise* and a densit# of 0.35$ m?cm$* is flo!in t"rou" a strai"t* circular pipe "a&in an inside diameter of - cm. A pitot tube is installed on t"e pipeline !it" its impact tube located at t"e center of t"e pipe cross section. At a certain flo! rate* t"e pitot tube indicates a readin of 3 cm of mercur#. @etermine t"e &olumetric flo! rate of t"e fluid. $1. ,"e rate of disc"are of !ater from a tank is measured b# means of a notc"* for !"ic" t"e flo! rate is directl# proportional to t"e "ei"t of t"e li'uid abo&e t"e bottom of t"e notc". Calculate and plot t"e profile of t"e notc" if t"e flo! rate is $0 m $?"r* !"en t"e li'uid le&el is 1- cm abo&e t"e bottom of t"e notc". $2. A rotameter calibrated for meterin "as a scale ranin from 0.014 m$?min to 0.14 m$?min. t is intended to use t"is meter for meterin a as of densit# 1.$ k?m $ !it" in a flo! rane of 0.23 m $?min to 2.3 m$?min. "at s"ould be t"e densit# of t"e ne! float if t"e oriinal one "as a densit# of 1500 k?m $J ;ot" t"e floats can be assumed to "a&e t"e same &olume and s"ape.
($)* -+
$$. A double actin reciprocatin pump "as a c#linder of 1- cm in diameter and an a&erae stroke of 20 cm. ,"e piston rod is 2.2- cm in diameter. ,"e pump runs at a rate of /0 strokes per minute and disc"ares into a calibration tank of 1.2 m diameter. ,"e pump disc"ares suc" t"at t"e !ater le&el in t"e tank rose b# 1.$0 m in a period of 2 minutes. Calculate t"e !ater6end efficienc# of t"e pump. $4. A centrifual pump is re'uired to deli&er 0 liters per second of !ater at room temperature aainst a "ead of 100 meters !"en runnin at 14-0 rpm. Find t"e number of staes for best efficienc#. $-. ,"e impeller of a centrifual pump "as an e:ternal diameter of 4- cm and is - cm !ide at t"e outer perip"er#. ,"e impeller &anes are set at $-oC at t"is perip"er#. ,"e impeller &anes are set at $- o at t"is perip"er#. ,"e t"ickness of t"e &anes accounts for K of t"e flo! area. ,"e pump deli&ers at 200 liters?sec of !ater at /-0 rpm aainst a manometric "ead of 12 meters. "at is t"e manometric efficienc# of t"e pumpJ $/. Crude oil is pumped at a rate of 30 liters?sec from a "arbor to a refiner# at a distance of 10 km t"rou" a 0.$ m .@. pipeline. ,"e crude oil "as a densit# of 0.3 m?cc and a &iscosit# of - cP. Calculate t"e po!er ratin of t"e motor dri&in t"e pump* assumin an o&erall efficienc# of /0K at full capacit#.
$. Air is flo!in in a smoot" pipe "a&in 1 m diameter at a rate of $40 m$?min. ,"e lent" of t"e pipe is 2-0 m. ,"e air temperature is 20 oC. "at is t"e difference in ele&ation bet!een t"e inlet and outlet if t"e static pressure c"ane is GeroJ f a pump is to be installed keepin t"e pipe "oriGontal* !"ic" t#pe of pump s"ould be selected and !"at s"ould be its t"eoretical po!er re'uirementJ Assume t"at be"a&es an ideal as.
@ata %inematic &iscosit# of air = 1./ : 106- m2?sec. 7tatic pressure = 1 atm.
$3. A petroleum fraction is pumped 2 km from a distillation plant to a storae tank t"rou" a mild steel pipeline 1-0 mm in diameter at t"e rate of 0.04 m $?sec. "at is t"e pressure drop alon t"e pipe and t"e po!er supplied to t"e pumpin unit if it "as an efficienc# of -0KJ ,"e pump impeller is eroded and t"e pressure at its deli&er# falls to one "alf. ;# "o! muc" is t"e flo! rate reducedJ ρ = 0.0- ?cc µ = 0.- milli .s?m 2.
Fluid Mechanics - (nit 1 E,ercises 1. f an oil "as an absolute &iscosit# of -10 poises* !"at is its &iscosit# in 7.. unitsJ 2. "at is a e!tonian fluidJ Hi&e e:amples. $. Hi&e an e:ample for Pseudo plastic fluid.
4. A t#pical mud is 0 !ei"t percent sand and $0 !ei"t percent !ater. "at is its densit#J ,"e respecti&e densities are ρ
sand
= 140 lb?ft$ and ρ !ater = /2.$ lb?ft$
-. "at is t"e smallest diameter lass tube t"at !ill keep t"e cap illar# "ei"t6c"ane of t"e !ater at 20oC less t"an t"at of 0.5 mmJ /. Calculate t"e appro:imate depression of mercur# at 20oC in a capillar# tube of radius 1.mm
σ = 0.-14 ?m* ρ = 1$./ ?cc* θ = 140o . Air is introduced t"rou" a noGGle into a tank of !ater to form a stream of bubbles. f t"e streams are intended to "a&e a diameter of 2 mm* calculate b# "o! muc" t"e pressure of t"e air at t"e tip of t"e noGGle must e:ceed t"at of t"e surroundin !ater.
σ = 71.6€: 106$ ?m.
3. "# are specific ra&ities most often referred to t"e densit# of !ater at 4oC instead of at 0oCJ 5. ost s!immers find t"e pressure at a dept" of about 10 ft painful to ears. "at is t"e aue pressure at t"is dept"J 10. A ne! submarine can safel# resist an e:ternal pressure of 1000 psi. o! deep in t"e ocean can it safel# di&eJ 11. ,"e deepest point in t"e oceans of t"e !orld is belie&ed to be in t"e arianas ,renc"* sout"east of QapanB t"ere t"e dept" is about 11*000 m. "at is t"e pressure at t"at pointJ 12. >n a &er# cold da# at t"e 7out" Pole* t"e temperature of air is 6/0oF. Assumin t"at t"e air remains isot"ermal up to a 10*000 ft ele&ation and t"at t"e pressure at t"e sea le&el is 1 atm* calculate t"e pressure at 10*000 ft. 1$. n t"e "#draulic lift in Fi1* t"e total mass of car* rack* and piston is 1300 k. ,"e piston "as a cross6sectional area of 0.2 m2. "at is t"e pressure in t"e "#draulic fluid in t"e c#linder if t"e car is not mo&inJ.
Fi.1 14. t is proposed to build a raft of pine los to carr# a caro on a ri&er. ,"e caro !ill !ei" -00 k* and it must be kept entirel# abo&e t"e !ater le&el. o! man# kilorams of pine los must !e use to make t"e raft* if t"e los ma# be entirel# submered and t"e# "a&e sp.r = 0.3J 1-. ,"e fluid in t"e manometer of Fi2 is et"#l iodide !it" sp.r = 1.5$. ,"e manometeric fluid "ei"t difference is -0 in. "at is t"e aue pressure in t"e tankJ "at is t"e absolute pressure in t"e tankJ
Fi.2 1/. A furnace "as a stack 100 ft "i". ,"e ases in t"e stack "a&e = 23?mol and , = $00oF. ,"e outside air "as = 25 ?mol. f t"e pressures of t"e air and t"e as in t"e stack are e'ual at t"e top of t"e stack* !"at is t"e pressure difference at t"e bottom o f t"e stackJ 1. A natural as !ell contains met"ane ( = 1/ ?mol)* !"ic" is practicall# a perfect as. ,"e pressure at t"e surface is 1000 psi. "at is t"e pressure at a dept" of 10*000 ftJ o! muc" error !ould be made b# assumin t"at met"ane !ere a constant densit# fluidJ Assume t"e temperature is constant at 0oF. 13. For lo! pressure differences* t"e inclined manometer s"o!n in Fi$ is often used. f t"e scale is set to read Gero lent" at P A = P; and t"e manometer fluid is colored !ater* !"at !ill t"e readin be at PA 6 P; = 0.1 lbf?in2J "at !ould be readin of an ordinar# manometer !it" &ertical les for t"is pressure differenceJ
Fi.$ 15. Calculate t"e pressure in t"e ocean at a dept" of 2000 m assumin t"at salt !ater is
a) ncompressible !it" a constant densit# of 1002 k?m$ b) compressible !it" a bulk modulus of 2.0- : 105 ?m2 and a densit# at t"e surface of 1002 k?m$ 20. ,"e &iscosit# of an oil is 10 cP and its specific ra&it# is 0.3. ee:press bot" of t"ese in bot" lbm* ft* sec s#stem and in 7.. units. 21. 7a# ,rue or False.
a. Absolute pressures and temperatures must be emplo#ed !"en usin t"e ideal as la!. b. ,o con&ert t"e pressure from aue to absolute* add appro:imatel# 1.01 Pa. c. t is possible to "a&e aue pressures t"at are as lo! as 620 psi. d. A &ertical pipe full of !ater* $4 ft "i" and open at t"e top* !ill enerate a pressure of about one atmosp"ere (aue) at its base.
ome R .7ubramanian* +ecturer* C"emical 8n* 7C8* 7riperumbudur 6 /0210-* ,amil adu* @A
(nit-2 E,cercises Mass alance. /Euation o %ontinuit3
1.
A !ater tank "as an inflo! line 1 ft in diameter and t!o 1?2 ft diameter outflo! lines. ,"e &elocit# in t"e inflo! line is - ft?sec. ,"e mass of !ater in t"e tank is not c"anin !it" time. "at are t"e &olumetric flo! rate* mass flo! rate* and t"e &elocit# in t"e ot"er outflo! lineJ Answer: 2.55 ft3/sec, 159 lb/sec, 13 ft/sec.
2.
A lake "as a surface area of 100 km2. >ne ri&er is brinin !ater into t"e lake at a rate of 10*000 m $?s* !"ile anot"er is takin !ater out at 3000m $?s. 8&aporation and seepae are neliible. o! fast is t"e le&el of t"e lake risin or fallinJ Answer: 72mm/h
$.
A &acuum c"amber "as a &olume of 10 ft$. "en t"e &acuum pump is runnin* t"e stead#6state pressure in t"e c"amber is 0.1 lbf?in 2. ,"e pump is s"ut off* and t"e follo!in pressure6time data are obser&ed 4. Time after shutoff, min 5. 0 0.1 6. 10 1.1 7. 20 2.1 8. 30 3.1
Pressure, psia
Calculate t"e rate of air leakae into t"e &acuum c"amber !"en t"e pump is runnin. Air ma# be assumed to be a perfect as. ,"e air temperature ma# be assumed constant at 0 oF. Answer: 0.0051 lb/min. Ener alance. /ernoulli5s euation3
1.
,"e tank in fi1 is c#lindrical and "as a &ertical a:is. ts "oriGontal cross6sectional area is 100 ft 2. ,"e "ole in t"e bottom "as a cross6sectional area of 1 ft 2. ,"e interface bet!een t"e asoline and t"e !ater remains perfectl# "oriGontal at all times. ,"e interface is no! 10 ft abo&e t"e bottom. o! soon !ill asoline start to flo! out t"e bottomJ Assume frictionless flo!. 7p.r of asoline0.2 . Answer: 36.5 sec.
Fi1 2.
n t"e &essel in fi2 !ater is flo!in steadil# in frictionless flo! under t"e barrier. "at is t"e &elocit# of t"e !ater flo! under t"e barrierJ Answer: 11.3 ft/sec.
Fi2 $.
n t"e tank in fi$ !ater is under a la#er of compressed air* !"ic" is at a pressure of 20 psi. ,"e !ater is flo!in out t"rou" a frictionless noGGle* !"ic" is - ft belo! t"e !ater surface. "at is t"e &elocit# of t"e !aterJ Answer: 57.4 ft/sec.
Fi$ )nco&pressible One-di&ensional Frictional Flo.
1.
ater is flo!in t"rou" a "oriGontal tube !it" 1.00 in inside diameter. "at is t"e ma:imum a&erae &elocit# at !"ic" laminar flo! !ill be of stable flo! patternJ "at is t"e pressure drop per unit lent" at t"is &elocit#J Answer: 2.8 ft/sec; 2.08 X 104 !si/ft.
2.
A fluid is flo!in in a pipe. ,"e pressure drop is 10 lbf?(in2.1000 ft). e no! double t"e flo! rate* "oldin t"e diameter and fluid properties constant. "at is t"e pressure drop if t"e ne! e#nolds number (a) is 10 and (b) is 10 3J Answer: 20 !si !er 1000 ft; 35 t" 40 !si !er 1000 ft.
$.
,!o tanks are connected b# -00 ft of $ in pipe. ,"e tanks contain an oil !it" µ = 100 cP and ρ = 0.3- ?cc. ,"e le&el in t"e first tank is 20 ft abo&e t"e le&el in t"e second* and t"e pressure in t"e second is 10 psi reater t"an t"e pressure in t"e first. o! muc" oil is flo!in t"rou" t"e pipeJ "ic" !a# is it flo!inJ Answer: 40 #$l/min; fr"m the sec"n% t$n& t" the first t$n&.
4.
,!o lare !ater are connected b# a 10 ft piece of $ in pipe. ,"e le&els in t"e tank are e'ual. "en t"e pressure difference bet!een t"e tanks is $0 psi* !"at is t"e flo! rate t"rou" t"e pipeJ Answer: 1040 #$l/min.
-.
e are oin to la# a lent" of / in steel pipe for a lon distance and allo! !ater to flo! t"rou" it b# ra&it#. f !e !ant a flo! rate of -00 al?min* "o! muc" must !e slope t"e pipe (i.e.* b# "o! man# feet of drop per foot of pipe lent")J Answer: .0166 ft/ft.
4HE - Fluid Mechanics
Test - 1 (22-Jan-2001)
Maximum Marks : 60
Duration : 90 min
Part A (12 : 2 = 24 arks)
1. What is a Newtonian ui!" #i$e two exam%&es' Fluid which obeys the Newton's law of viscosity:
τ = µ du/dy are said to be Newtonian fluids. Examples: water, air, erosene. !. #i$e suita&e exam%&es or (a) *in+ham %&asti, ui! () Thixotro%i, ui! "a# $in%ham plastic fluid: &ooth paste, %els, sewa%e slud%e "b# &hixotropic fluid: paint
.' The $is,osit/ o an oi& is 10 ,' eex%ress in oth & t se, s/stem an! in '3' units'
lbftsec units: 1( c) * 1( x 1( + %/m.sec * (.(1 x !.!(+/"+.!1 x 1# lb/ft.sec * 6.713 lb/ft.sec -.: 1( c) * 0.01 kg/m.sec . De4ne *u&k mo!u&us' Write !own its units' $ul modulus "0# * "chan%e in pressure# / "volumetric strain# olumetric strain is the chan%e in volume divided by the ori%inal volume. &herefore, "chan%e in volume# / "ori%inal volume# * "chan%e in pressure# / "bul modulus# i.e., d/ * dp/0 Ne%ative si%n for d indicates the volume decreases as pressure increases. n the limit, as dp tends to (, 0 * dp/d n terms of density, 0 * ρdp/dρ $ul modulus has the units of pressure2 N/m !.
5' a&,u&ate the a%%roximate !e%ression o mer,ur/ at 20o in a ,a%i&&ar/ tue o ra!ius 1'5 mm σ 7 0'518 Nm ρ 7 1.'6 +,, θ 7 180o h * σcos"θ#/"ρ%d# h * x (.31 x cos"1(#/"1+.4 x 1((( x 5.1! x + x 1( +# i.e., h * 3.93 mm
6' tate the as,a&s &aw o %ressure at a %oint in a ui!' )ressure at a point is same in all directions. &his is )ascal's law. &his applies to fluid at rest
' 3t is im%ossi&e to ha$e +au+e %ressures that are as &ow as -20 %si+' Justi/ this statement' !( psi% * !( 6 1.7 * 3.+ psia. &he minimum possible pressure is only ( psia. &herefore, the %iven %au%e pressure is an impossible one.
;' The ui! in the manometer (shown in 4+ure) is eth/& io!i!e with s%'+r 7 1'9.' The manometeri, ui! hei+ht !i
11' (a) Determine whether the $e&o,it/ ,om%onents +i$en e&ow satis/ the e=uation o ,ontinuit/:
u 7 2x2 > ?/ $ 7 -2x/ > ./ 2 > .?/ w 7 -1'5?2 - 2x? - 6/?' where u $ an! w are $e&o,it/ ,om%onents in x / an! ? !ire,tions res%e,ti$e&/' ∂u/∂x * x ∂v/∂y * !x 6 4y 6 +8 ∂w/∂8 * +8 !x 4y
∂u/∂x 6 ∂v/∂y 6 ∂w/∂8 * (. &herefore, continuity euation is satisfied. 1!.
Write *ernou&&is e=uation' tate its assum%tions'
Flow is steady, inviscid and incompressible. &here are no addition of ener%y in between the the sections considered. Part ; ($ : 12 = $/ arks)
1.' Deri$e ex%ressions or the $ariation o %ressure with a&titu!e (i) or a!iaati, atmos%here (ii) or the atmos%here in whi,h the tem%erature !e,reases with a&titu!e at a ,onstant rate' "i# ariation of pressure with distance is %iven by, dp/d8 * ρ%
; 1
For adiabatic atmosphere, p γ * constant i.e.,
p/ργ * constant
p/ργ * p1/ρ1γ
ρ * ρ1"p/p1#γ * $ pγ
; !
where $ is a constant * ρ1/p1γ -ubstitutin% from eun.! in eun.1, dp/d8 * $ p γ %
-eparatin% the varaiables and inte%ratin%, dp/pγ * $% d8 <1/" γ 1#= pγ 61 * $%8 6 > where > is a constant. &he constant > can be eliminated by substitutin% the initial conditions2 that when 8 * 8 1, p * p1 > * <1/"γ 1#= p1γ 61 $%8 1 &herefore, <1/" γ 1#= pγ 61 * $%8 6 <1/" γ 1#= p1γ 61 $%81 "ii# For the atmosphere in which the temperature decreases with height at a constant rate , & * & o >8 where &o is the temperature at the %round level2 and > is the rate of chan%e of temperature with hei%ht"8#. dp/d8 * ρ% * "p?/9&#% * p?/<9"& o 6 >8#= where ? is the molecular wei%ht of air. -eparatin% the variables, dp/p * ?/<9"& o 6 >8#= d8 ln p * ?/"9># ln "&o 6 >8# 6 @ where @ is a constant2 &he constant @ can be eliminated from the substitution of initial conditions, p * p 1 when 8 * 8 1 @ * ln p1 6 ?/"9># ln "&o 6 >81# &herefore, ln p/p 1 * ?/"9># ln <"&o 6 >81#/"&o 6 >8#= >r
18' @n a $er/ ,o&! !a/ at the New De&hi the tem%erature o air is 5o' Assumin+ that the air remains isotherma& u% to a 10000 t e&e$ation an! that the %ressure at the sea &e$e& is 1 atm ,a&,u&ate the %ressure at 10000 t' ariation of pressure with distance is %iven by, dp/d8 * ρ%
; 1
Assumin% that air is followin% ideal %as relationship, ρ3 p. -ubstitutin% for ρ in Eun.1, dp/p * 1.!33 x 1( 3 x 5.1! d8 nte%ratin% between the limits: "8 1 * (, p1 * 1 atm * 1.(1+!3 x 1( 3N/m!2 and when 8! * 1(,((( ft * +( m, p ! * B# ln "p!/p1# * 1.!33 x 1( 3 x 5.1! x "8 ! 81# i.e., p!/1.(1+!3 x 1( 3 * e(.+73+ * (.47 &herefore, p ! * (.454! x 1( 3 N/m! * 0.687 atm (a).
15' (i) Deri$e an ex%ression or the %ressure !ir
14. A ,&ose!-B-tue manometer 4&&e! with mer,ur/ is atta,he! to the un!ersi!e o a &ine ,arr/in+ water as shown in 4+ure' At a %oint !ire,t&/ ao$e the ,&ose!-B-tue manometer ta% the u%stream ta% o an in$erte! B tue is &o,ate!' The in$erte!-B-tue manometer is 4&&e! with a &i=ui! o s%e,i4, +ra$it/ 0'5' What are % 1 an! %2 in %sia"
$alance for the mercury manometer: ( x 1+.4 * p 1 6 "3 6 !# x 1 p 1 * ( x 1+.4 4( inch water * 1!.!5 m water * 17.485 psia $alance for the inverted manometer: p1 +5 x 1 * p ! 1 x 1 !3 x (.3 p1 p! * !3 x 1 !3 x (.3 * 1!.3 inch water * (.+173 m water * (.(+(7 atm * (.3! psi. &herefore, p ! * 17.3 (.3! * 17.006 psia.
1' A si%hon ,onsistin+ o a . ,m !iameter tue is use! to !rain water rom a tank' The out&et en! o the tue is 2 m e&ow the water sura,e in the tank' Water is at 25o' (i) Ne+&e,tin+ ri,tion ,a&,u&ate the !is,har+e' (ii) 3 the %eak %oint o the si%hon is 1'8 m ao$e the water sura,e in the tank estimate the %ressure o ui! at the %oint o si%hon' (iii) Cstimate the maximum !istan,e etween water sura,e an! the %eak %oint o si%hon so that the ow is not +ettin+ !isture!'
($a%or %ressure o water at 25o 7 .16'6 Nm 2) &he %iven problem is shown as a dia%ram: $ernoulli's euation for frictionless flow is:
"a# Applyin% $ernoulli's euation for the points 1 and +, " i.e. comparin% the ener%y levels for the fluid in the tan surface and at the dischar%e point of tube# p1 * ( N/m!"%# p+ * ( N/m!"%# 81 * ( m 8+ * ! m -ince the rate of fall of liuid level in the tan is almost ne%li%ible, v1 * ( m/sec. &herefore, ( 6 ( 6 ( * ( 6 "v +! / !%# ! v+ * "! x !%# (.3 * 4.!43 m/sec @ischar%e C * "π/#@! v * "π/# x (.(+ ! x 4.!43 * (.((+ m +/sec * 15.94 m3 /hr "b# Applyin% $ernoulli's euation for the points 1 and !, " i.e. comparin% the ener%y levels for the fluid at the tan surface to the pea point of siphon#
p1 * ( N/m!"%# 8! * 1. m v! * v+ * 4.!43 m/sec "since the cross sectional area of sections ! and + are the same# ( 6 ( 6 ( * p ! / "ρ%# 6 4.!43! / "!%# 6 1. p! / "ρ%# * +. m p! * +. x 1((( x 5.1! N/m !"%# * +++4(. N/m !"%# Absolute pressure at point ! * 1(1+!3 +++4(. * 67964.2 N/m2(a) "c# ?aximum hei%ht is obtained by settin% p ! * +14.4 N/m !"a#: Applyin% $ernoulli's euation between points 1 and !, 1.(1+!3 x 1( 3/"1((( x 5.1!# 6 ( 6 ( * +14.4/"1((( x 5.1!# 6 4.!43 !/ "!%# 6 hmax &herefore, h max * 8.294 meter >r
1;' The o&&owin+ !ata were otaine! on a se,tion o %i%in+ throu+h whi,h an in,om%ressi&e $is,ous ui! is owin+ ( ee i+ure) Point 1
ressure 7 1'25 x 105 a ross-se,tiona& area 7 15 x 108 m2 &ui! Ee&o,it/ 7 1 ms Point 2
ressure 7 1'05 x 105 a ross-se,tiona& area 7 5 x 10-8 m2 C&e$ation ao$e %oint 1 7 . m >t"er @ata
Densit/ o ui! 7 1000 k+m. ower !e&i$ere! / the %um% 7 '5 W assume eF,ien,/ 7 100G) Predict !"et"er flo! is takin place from point 1 to 2 or from 2 to 1.
$y euation of continuity, A1v1 * A!v! &herefore, v ! * 13 x 1 / 3 * + m/sec. ?ass flow rate * ρ C * 1((( x 13 x 1( x 1 * 1.3 %/sec. )ump head * 7.3 / "1.3 x 5.1!# * (.31 m Assumin% flow is from 1 to !, we can write the $ernoulli euation between 1 and ! as,
where '' is the wor done by pump and 'w' is the wor done by the fluid, and h is the head loss by friction. -ubstitutin% for the nown uantites, 1.!3 x 1( 3/"1((( x 5.1!# 6 1 !/"! x 5.1!# * 1.(3 x 1( 3/"1((( x 5.1!# 6 + !/"! x 5.1!# 6 + 6 h 6 ( (.31 1!.7 6 (.(31 6 ( * 1(.7 6 (.35 6 + 6 h (.31 &herefore, h * (.3 m.
For a possible flow, h can not be ne%ative. &herefore, the assumed direction is not correct. Det us rewor for flow from ! to 1: &hen,
1.(3 x 1( 3/"1((( x 5.1!# 6 + !/"! x 5.1!# 6 + * 1.!3 x 1( 3/"1((( x 5.1!# 6 1!/"! x 5.1!# 6 h 6 ( (.31 1(.7 6 (.35 6 + * 1!.7 6 (.(31 6 ( 6 h (.31 &herefore, h * 1.15 m, which is a positive uantity2 therefore, fl! is frm 2 t 1.
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3NDCI
ast Mo!i4e! on: 062200; 12:5;:58 K M'uramanian e,turer hemi,a& Cn++ EC ri%erumu!ur - 602105 Tami& Na!u 3ND3A
msuuLs$,e'a,'in 4HE - Fluid Mechanics
,est 6 2 (arc"62001) a:imum arks /0 @uration 50 minutes Part A (12 : 2 = 24 arks)
1. it" a neat sketc"* compare t"e &elocit# profiles for laminar and turbulent flo! of a fluid in a pipeline. 2. ndicate t"e met"ods to reduce (i) skin frictional losses (ii) form frictional losses. $. Calculate t"e "#draulic radius for flo! of fluid t"rou" a rectanular duct of siGe 0.- m : 0.$ m.
4. it" a neat diaram* illustrate t"e relation bet!een friction factor and e#nolds number* for laminar and turbulent flo!s in circular ducts* indicatin t"e effect of rou"ness. -. ,"e relation bet!een frictional pressure drop (∆ p) and &olumetric flo! rate () for flo! t"rou" pipelines is i&en b#
∆ p = cn B !"ere c is a constant. "at is t"e &alue of 9n9 for (i) laminar flo! (ii) turbulent flo! t"rou" &er# smoot" pipe (iii) turbulent flo! t"rou" &er# rou" pipe /. @ra! t"e s"ape of noGGles* t"at is needed for acceleratin t"e flo! &elocit#* for t"e follo!in flo! conditions* indicatin t"e flo! direction (i) subsonic flo! to soinc flo! (ii) sonic to supersonic flo! (iii) subsonic to supersonic flo! . @ra! a neat sketc" s"o!in t"e de&elopment of boundar# la#er for laminar flo! in pipe* also indicate t"e s"ape of t"e &elocit# profiles at de&elopin and de&eloped sections. 3. o! does t"e pressure drop &ar# !it" t"e flo! rate in a rota6meter* and in orifice meterJ 5. ,"e pressure drop bet!een upstream and t"roat of &enturi meter is 100 cm of t"e flo!in fluid. "at is t"e pressure drop if t"e &olumetric flo! rate is doubledJ 10.Compare t"e manometer readins of orifice meter and &enturi meter for a flo!rate of t"rou" a pipe of diameter @* i&en t"at diameter of &enturi t"roat = diameter of orifice openin. 11.Hi&e t!o industrial applications of (i) packed beds (ii) fluidiGed beds
12.@ifferentiate bet!een areati&e and particulate fluidiGation. Part ; ($ : 12 = $/ arks) 1$.(a) ;# appl#in momentum balance to t"e stead# flo! of a fluid in a stream6 tube* deri&e 8ulers e'uation of motion. (3) (b) >btain ;ernoulli e'uation from 8uler e'uation b# makin necessar# assumptions. (4) Or
14.For laminar flo! of a e!tonian fluid in circular pipe* obtain t"e follo!in relations from first principles (i) Frictional pressure drop and !all s"ear stress (ii) elocit# distribution in t"e radial direction (iii) A&erae &elocit# and ma:imum &elocit# (i&) Pressure drop and a&erae &elocit# 1-.ater is pumped from a round le&el reser&oir to an o&er"ead tank t"rou" a .- cm @ pipe as s"o!n in t"e sketc"
(a) "at pressure is needed at t"e outlet of t"e pump to suppl# !ater to t"e tank at t"e rate of 100 ltr?minJ (b) "at is t"e po!er re'uired for t"e pump* if t"e pump is onl# /0K efficientJ
@ata µ = 1 cPB ρ = 1 ?ml. 8'ui&alent lent" of fittins (+ e?@) Hlobe &al&e (open) $00 4-o elbo! 1Fannin friction factor for turbulent flo! is i&en b# f = 0.05 (e) 60.2-
Or
1/.(a) A &enturi meter "as t"roat to upstream pipe cross6section ratio of 0.-. ,"e fluid flo!in is !ater. ,"e pressure at t"e entr# of con&erin cone section is 1$.5 k?m2(a). "at is t"e &elocit# at t"e t"roat !"ic" corresponds to a pressure of 0 k?m2(a) at t"e t"roatJ f t"e !ater is at 200 oF* !"at is t"e "i"est &elocit# possible at t"e t"roat at !"ic" !ater !ill boilJ @ata For !ater at 200oF* @ensit# = 530 k?m$. apor pressure = -.3 k?m2(a). (3) (b) A rotameter !it" a stainless steel float "as a ma:imum capacit# of 1.2 ltr?sec of !ater. "at !ill be t"e ma:imum capacit# for kerosene in ltr?sec for t"e same rotameter and floatJ Assume t"at t"e C d for t"e rotameter is not c"anin muc" !it" flo!rate. @ata 7pecific ra&it# of stainless steel = .52 7pecifc ra&it# of kerosene = 0.32 (4) 1.(a) @eri&e relations for e#nolds number and friction factor and establis" t"e 8run e'uation for sinle6p"ase flo! of fluid t"rou" packed bed. (3) (b) ;rin out t"e e'uation predictin minimum fluidiGation &elocit#. (4)
Or
13.A mi:ture of &apors pass t"rou" a packed bed of lass sp"eres "a&in densit# 2.4 ?cc eac" of diameter 0.- cm. ,"e pressure drop due to t"e flo! is 4000 ?m2. ,"e "ei"t of packed bed is 1.3- m. ,"e densit# and &iscosit# of t"e &apor mi:ture are $.3 : 106$ ?cc and 0.01- cP respecti&el#. @ata Cross sectional area of t"e packed column tube = 0.05 m 2 ;ed porosit# = 0.4 Find t"e mass flo! rate of t"e &apor mi:ture.
4HE - Fluid Mechanics
Test - 1
Maximum Marks : .0
Duration : 90 min
art - A (10 I 1 7 10 Marks) 1' What is a Newtonian ui!" #i$e exam%&es' 2' Aso&ute %ressures an! tem%eratures must e em%&o/e! when usin+ the i!ea& +as &aw'(Truea&se) .' To ,on$ert the %ressure rom +au+e to aso&ute a!! a%%roximate&/ 1'01 a'(Truea&se) 8' 3t is %ossi&e to ha$e +au+e %ressures that are as &ow as -20 %si+'(Truea&se) 5' A $erti,a& %i%e u&& o water .8 t hi+h an! o%en at the to% wi&& +enerate a %ressure o aout one atmos%here (+au+e) at its ase'(Truea&se) 6' Wh/ are s%e,i4, +ra$ities most oten reerre! to the !ensit/ o water at 8o instea! o at 0o" ' Most swimmers 4n! the %ressure at a !e%th o aout 10 t %ainu& to ears' What is the +au+e %ressure at this !e%th" ;' A new sumarine ,an sae&/ resist an externa& %ressure o 1000 %si+' How !ee% in the o,ean ,an it sae&/ !i$e" 9' #i$e suita&e exam%&es or (a) *in+ham %&asti, ui! () Thixotro%i, ui! 10'
#i$e the ,ontinuit/ e=uation or three !imensiona& ow art - * (2 I 10 7 20 Marks)
11' Deri$e an ex%ression or the %ressure !i
ui!s mutua&&/ immissi&e' What a,tors inuen,e the sensiti$it/" @r 12' A !i
K M'uramanian e,turer hemi,a& Cn++ EC ri%erumu!ur - 602105 Tami& Na!u 3ND3A
48 Fluid ec"anics 6 ,est 2 @uration 50 min. a:imum arks $0 Part A (10 : 1 = 10 marks)
1. Consider a duct of s'uare cross section of side 9b9. ,"e "#draulic radius is i&en b# (A) b?3 (;) b?4 (C) b?2 (@) b 2. @efine t"e term 9ac" number9 $. For an orifice meter* t"e pressure reco&er# is ________ t"an t"at for a &enturi meter. 4. ,"e e'uilibrium position of t"e float in a rotameter is determined b# t"e balance of t"ree forces. ,"ese are ___________* ___________ and ___________. -. A rotameter* t"rou" !"ic" air at room temperature and atmosp"eric pressure is flo!in* i&es a certain readin for a flo! rate of 100 cc?s. f "elium (olecular !ei"t 4) is used and t"e rotameter s"o!s t"e same readin* t"e flo! rate is (A) 2/ cc?s (;) 42 cc?s (C) 2/5 cc?s (@) $2- cc?s /. rite do!n t"e e'uation for flo! rate t"rou" a 6notc" . (i)"at is !all draJ (ii) "at is form draJ 3. @ifferentiate bet!een +oadin and Floodin 5. @ifferentiate bet!een bubblin and particulate fluidiGation 10."at is t"e t"eoretical ma:imum operable &elocit# for a fluidiGed bedJ Part ; (2 : 10 = 20 marks) 11.2.1/ m$?" !ater at $20 % is pumped t"rou" a 40 mm .@. pipe t"rou" a lent" of 1-0 m in a "oriGontal direction and up t"rou" a &ertical "ei"t of 12 m. n t"e pipe t"ere are fittins e'ui&alent to 2/0 pipe diameters. "at po!er must be supplied to t"e pump if it is /0K efficientJ ,ake t"e &alue of fannin friction factor as 0.003. ater &iscosit# is 0./- cp* and densit# = 1 m?cc. >r 12.(a) 8:plain t"e construction and !orkin principle of Pitot tube. (/)
