Result and Discussion of Bernoulli Theorem fluid mechanics

Results

Flowrate (Q) = 10L / 0.7665min = 2.175 x 104 m³/s Cross section  I

Usin sing Bernoul oulli equation

h* = h8

hi



mm 217.0

mm 20!.0

m/s 0."!6

mm2 5"0.!"

m/s 0.40!

% #0.0"2

$  '  F

215.0 21".0 210.0 20&.0 206.0

1!5.0 142.0 17&.0 1&".0 1!0.0

0.626 1.1&0 0.7!2 0.700 0.560

"66.44 201.06 "14.16 "&0.1" 5"0.!"

0.5!4 1.0&1 0.6!2 0.572 0.40!

0.052 0.0!" 0.145 0.224 0."6!

Vib Vib = √   2 x g x (h –hi)

Using sing continuit uity equation  Ai = Vic= πDi²/4 Qαν  /Ai

 Difference

(Vib - Vic)/  Vic Vic

Flowrate Flowrate (Q) = 10L 10L / 0.6107min 0.6107min = 2.72! 2.72! x 10 4 m³/s Cross section  I

Usin sing Bernoul oulli equation

h* = h8

hi

 $  '  F

mm 246.0 242.0 240.0 2"".0 2"2.0 2"0.0

mm 2"0.0 20!.0 11!.0 1&1.0 1!1.0 201.0

Vib Vib = √   2 x g x (h –hi) m/s 0.560 0.&05 1.541 1.010 0.&!7 0.754

Using sing continuit uity equation  Ai = Vic= πDi²/4 Qαν  /Ai

mm2 5"0.!" "66.44 201.06 "14.16 "&0.1" 5"0.!"

m/s 0.514 0.745 1."57 0.&6! 0.71& 0.514

 Difference

(Vib - Vic)/  Vic Vic % 0.0&! 0.0&1 0.1"" 0.162 0.24! 0.467

Flow rate (Q) = 10L/0.462&min = ".601 x 10 4 m³/s Cross section  I

Using Bernoulli equation

h* = h8

hi

 $  '  F

m 2&5.0 2&4.0 27!.0 27&.0 27&.0 26&.0

mm 260.0 22!.0 &5.0 1&4.0 20".0 222.0

Vib = √   2 x g x (h –hi) m/s 0.700 1.0"! 1.!50 1."5& 1.21" 0.!50

Using continuity equation  Ai = Vic= πDi²/4 Qαν  /Ai

mm2 5"0.!" "66.44 201.06 "14.16 "&0.1" 5"0.!"

m/s 0.67& 0.!&" 1.7!1 1.146 0.!47 0.67&

*+ere, ross se-tion

'istan-e (mm)

 $  '  F

60.0 &".0 105.0 14&.6 166.4 215.0

'iameter o -ross se-tion (mm) 26.0 21.6 16.0 20.0 22.0 26.0

+e istan-e is rom t+e e3innin3 ti to t+e rese-tie tain3s

 Difference

(Vib - Vic)/  Vic % 0.0"2 0.056 0.0&! 0.1&5 0.2&0 0.401

Discussion

$ase on t+e exeriment t+e reslts a-+iee t+e o8e-tie. +e o8e-tie o oin3 t+is exeriment is to etermine t+e li elo-it9 sin3 t+e $ernolli:s t+eorem an t+e -ontinit9 e;ations. *+en t+e inlet low -ontrol ale oen rom t+e small an reeate rom ste 1#12 or  anot+er two ierent lowrate an it otain t+e lowrate o t+e irst trial is 10L / 0.7665min se-on trial 10L / 0.6107min an t+e last trial is 10L / 0.462&min.it was -al-late elow

al-lation or lowrate (Q) onert,

= 45.!!se- < 1min / 60se-

Flowrate

= 10L / 0.7665min

+is exeriment was reeate aot t+ree times to 3et a--rate reslts. ter 3et t+e lowrate t+e $ernolli:s e;ation an ontinit9:s e;ation was se as a met+o to ine t+e elo-it9 t+at -an 3ie two ierent reain3s. s a reslts t+e elo-it9 t+at s+ows t+e +i3+est elo-it9 is t+e aster lowrate 10L / 0.7665min t+at elo-it9 or $ernolli e;ation are =0."!6 $=0.626 =1.1&0 '=0.7!2 =0.700 F=0.560 an or -ontinit9 e;ation t+e elo-it9 are =0.40! $=0.5!4 =1.0&1 '=0.6!2 =0.572 F= 0.40! w+ile t+e slowest lowrate 10L / 0.462&min 3ie t+e lowest elo-it9 w+i-+ or $ernolli e;ation are =0.700 $=1.0"! =1.!50 '=1."5& =1.21" F=0.!50 an or ontinit9 e;ation t+e elo-it9 are =0.67& $=0.!&" =1.7!1 '=1.146 =0.!47 F= 0.67& . t -al-late 9 elow

$ernolli:s e;ation, V iB =√   2 x g x (h –hi) *+ere, >rait9 3 = !.&1 m/s2  +i = t+e total +ea + = ressre +ea

?i$ =√ 2 x !.&1m/s2 x (21 @20-m)  

=0."!6

ontinit9:s e;ation, Vic= Qαν  /Ai *+ere, Qαν = low rate aera3e i = area o -ross se-tion ?i-= Qαν/i = 2.175 < 10#4 m" /s (5"0.!" < 10#")#2 = 2.175 < 10#4 m" /s (5"0.!" < 10#6) = 0.40! m/s 'ieren-e (Vib-Vic)/ Viv *+ere, ?i- = -ontinit9:s e;ation ?i = $ernolli:s e;ation = (0."!6 @ 0.40!) / 0.40! = #0.0"2 From t+e reslt o exeriment we Anow t+at we -an -al-late elo-it9 9 sin3 $ernolli:s e;ation an -ontinit9 e;ation. *e -an see t+e elo-it9 is rela9in3 on t+e lowrate. +at mean +i3+ lowrate -an 3ie +i3+ elo-it9. ter we -al-late t+e elo-it9 sin3 $ernolli:s e;ation an -ontinit9 e;ation t+ere +ae a i3 ieren-e o reain3s. Bo t+e +9ot+esis was -orre-t roen t+at sin3 $ernolli:s e;ation is etter t+an -ontinit9 e;ation e-ase t+e reslt 3ien 9 $ernolli:s e;ation is smaller t+an -ontinit9 e;ation.

+ere are seeral ossiilities w+9 t+e reslt oes not ere-t t+at mst e aoie rin3 t+e exeriment. Firstl9 t+e air les still in t+e manometers. t -an istr t+e reslt otaine as t+e reslt is ina--rate. $esies t+e arallax error is t+e one o t+e a-t w+9 t+e reslt is ina--rate. t +aens w+en ro-ess o manometer reain3 t+at t+e reain3 was taAen in-orre-t wa9 w+en t+e menis-s o li was not stailiCe 9et or still moin3.

Table 1: Manometer Reading Vs Velocity

MANOMETER READING (H) 217 215 213 210 208 206

Man

VELOCITY (M/S) 0.36 0.626 1.18 0.792 0.7 0.56

Table 2: Manometer Reading Vs Velocity

MANOMETER READING (H) 26 22 20 233 232 230

VELOCITY (M/S) 0.56 0.85 1.51 1.01 0.897 0.75

MA

Ma

Table 3: Manometer Reading vs Velocity MANOMETER READING (H) 285 28 279 278 278 268

MANOMETE

Manometer Reading (

VELOCITY (M/S) 0.7 1.039 1.95 1.299 1.213 0.95