LABORATORY WORK IN HYDROLOGY
KANCHAN KASWAN KASWAN
KANISHKA SAHNI
KAPIL DEV BANSAL
KARAN PREET SINGH K. S. HARI PRASAD
DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY TECHNOLOGY ROORKEE-247667 FEBRUARY 2012 C!"#!"$
Page No. 1. Determination of Average Rainfall over a Catchment
3
…………………. Kapil Dev Bansal 2. Determination of Insit! "oil #$%rological Properties
1&
…………………. Kanish'a "ahni 3. Determination of Infiltration Parameters (ith Do!)le Ring Infiltrometer
1*
…………………. Kanchan Kas(an +. ,eas!rement of Discharge in an -pen Channel (ith C!rrent ,eter
1
…………………. Karanpreet "ingh *. Determ Determina inatio tion n of of #$%ra! #$%ra!lic lic Con%!c Con%!ctiv tivit$ it$ (ith (ith Cons Constan tantt #ea% #ea% Permea Permeamet meter er
2+
…………………. K. ". #ari Prasa%
R Reeferences
2
2
C%&'"#( 1 D#"#()*!&"*! + A,#(&# R&*!+& ,#( & C&"/%)#!" A*)
/o %etermine average rainfall over a catchment )$ 0i Arithmetic Average ,etho% 0ii /hiessn pol$gon metho% an% 0iii Isoh$etal ,etho% A''&(&"$ R#*(#3 /hematic map of the catchment (ith location of rainga!ge stations
Planimeter /racing an% 4raph "heets "!rfer soft(are T%#(
/he average rainfall over a catchment is nee%e% in the anal$sis an% %esign of several h$%rological process s!ch stream flo( estimation floo% anal$sis an% i%entification of areas v!lnera)le %!ring heav$ rains. /he rainfall recor%e% at a rainga!ge station represents onl$ point a small part of the catchment. #o(ever the rainfall %istri)!tion ma$ not )e !niform over the entire catchment an% necessitates the nee% for arriving at an average val!e for the entire catchment. /he rainfall %istri)!tion over a catchment %epen%s primaril$ on the nat!re of the catchment 0plain or hill$ area an% one has to %evise an acc!rate of (a$ of %eterimining the average rainfall for in%ivi%!al catchment. /he commonl$ !se% metho%s for the %etermination of average rainfall in a catchment area are 0i Arithmetic Average ,etho% 0ii /hiessn pol$gon metho% an% 0iii Isoh$etal ,etho% Arithmetic Average Method: 5hen the rainfall meas!re% at vario!s rainga!ge stations in a catchment sho( little variation the average precipitation over the catchment is %etermine% as the arithmetic mean of the rainfall val!es recor%e% at each of the stations. If P 1 , P 2 ,……, P N are the rainfall val!es recor%e% at N rainga!ge station in the catchment the average rainfall P ave is comp!te% as the arithmetic average6 P ave
=
P 1
+ P + .... + P i + ..... + P N 2
N
=
1
N
∑ P
N i =1
i
01.1 /his metho% is ver$ simple an% can )e !se% for ver$ small catchments (hich are plain. "ince the metho%s %oes not ta'e into acco!nt the terrain characteristics of the catchment it is rarel$ !se% in case of large catchments.
3
T%*#$$#! P! M#"%3
In /heissen pol$gon metho% 0"!)raman$a 2&&7 each rainga!ge station is given (eight on the )asis of the area closest to that station. 8ig 1.1 sho(s a catchment (ith five rain ga!ge stations. Among these one rain ga!ge station is o!tsi%e the catchment.
F* 1.1 T%*#$$#! P! M#"%3
/he rainga!ge stations are 9oine% (ith one another to form a net(or' of triangles. Perpen%ic!lar )isectors for each si%e of these triangles are %ra(n as sho(n in 8ig. 1.1. /hese )isectors form pol$gons aro!n% each rainga!ge station an% are calle% :/hiessen Pol$gons;. /hese pol$gons have the propert$ that ever$ point (ithin the pol$gon (ill )e closest to the
4
rain ga!ge station representing that pol$gon. In case of rain ga!ges locate% o!t si%e the catchment the intersection of the )isectors (ith the catchment )o!n%ar$ is consi%ere% as the pol$gon representing that station "tation D in fig. 1.1. /he areas of the pol$gons are %etermine% either (ith a planimeter or !sing an overla$ gri%. If P 1 , P 2 ,……, P N are the rainfall recor%e% at N rainga!ge station in the catchment an% A1 , A2 ,……, A N are the correspon%ing /hiessen pol$gons the average rainfall P ave over the catchment is %etermine% as N
P ave
=
+ P A + .... + P i Ai + ..... + P N A N = A + A + .... + Ai + ...... + A N
P 1 A1
2
1
2
2
∑= P A i
i
i
1
N
∑= A
01.2
i
i
1
/his metho% gives ver$ goo% res!lts for plain catchments. #o(ever it is not ver$ m!ch s!ita)le for mo!ntaino!s catchments.
I$%#"& M#"%3
Isoh$etal metho% !ses isoh$ets to %etermine the average rainfall over a catchment. An isoh$e is a line 9oining points of eR. 8ig. 1.2 sho(s the plotting of isoh$ets for a catchment having 13 rain ga!ge stations. #aving %ra(n the conto!rs the area )et(een the a%9acent isoh$ets are %etermine% (ith planimeter. If the isoh$ets go o!t of the catchment the catchment )o!n%ar$ is !se% as the )o!n%ing line. . If P 1 , P 2 ,……, P N are the val!es of the isoh$ets an% A1 , A2 ,……, A N-1 are the correspon%ing interisoh$ets then the mean precipitation of the catchment is %etermine% as
P + P + A P + P + ...... + A P N − + P N N − 2 2 2 A + A + ..... + A N −
A1 P ave =
1
2
2
3
1
2
1
1
2
1
01.3 Isoh$etal metho% is the )est among all the metho%s of %etermining the average precipitation of a catchment.
5
F*.5.2 P""*! + I$%#"$
P(/#3(# &!3 C)'"&"*!$
Arithmetic Average Method:
1. Kno(ing the rainfall at the rainga!ge stations comp!te Pave !sing e
Thiessen Polygon Method.
6
1.
Plot the location of rain ga!ges on the )ase map (ith a pencil.
2.
Connect a%9acent points (ith %ashe% lines !sing a straight e%ge an% pencil.
3.
Constr!ct perpen%ic!lar )isectors across the %ashe% )o!n%ar$ lines.
+.
Connect the )isector lines to o!tline pol$gons )elonging to each station or region.
*.
Co!nt s
@. =se e
T.1 T%*#$$#! P! M#"%3 S"&"*!
T%#*$$#! A(#& Ai 8
R&*!+& P i 8
Ai x P i
i
L28
L8
L58
Isohyetal Method: Dra(ing Isoh$ets !sing "!rfer .& 1. -pen "!rfer .& 2. Press Ctrl5 3. In the first col!mn give hea%ing val!es an% enter val!es in the s!)se
@. In the plot (in%o( choose the G(*3 E D&"& comman% or clic' the
)!tton in the gri%
tool)ar . /he O'#! D&"& %ialog is %ispla$e%. F. In the O'#! D&"& %ialog clic' the file /=/-R5".DA/ 0locate% in S(+#(;$ "A,PG>" fol%er. /he name appears in the File name )o )elo( the list of %ata files.
7
7. Clic' the !en )!tton an% the 4ri% Data %ialog is %ispla$e%. Alternativel$ $o! can %o!)leclic' the %ata file name to %ispla$ the G(*3 D&"& %ialog. . /he G(*3 D&"& %ialog allo(s $o! to control the gri%%ing parameters. /a'e a moment to loo' over the vario!s options in the %ialog. Do not ma'e changes at this time as the %efa!lt parameters create an accepta)le gri% file. 1&. Clic' the " )!tton. In the stat!s )ar at the )ottom of the (in%o( a %ispla$ in%icates the progress of the gri%%ing proce%!re. B$ accepting the %efa!lts the gri% file !ses the same path an% file name as the %ata file )!t the gri% file has a H.4RD etension. 11. B$ %efa!lt a S(+#( %ialog appears after gri%%ing the %ata (ith the f!ll path name of the gri% file that (as create%. Clic' the " )!tton in the S(+#( %ialog. /he /!tor5".4RD gri% file is create%. 12. If #rid $e!ort (as chec'e% in the G(*3 D&"& %ialog a report is %ispla$e%. o! can minimi?e or close this report. 13. Choose the M&' E N#9 : C!"( M&' comman% or clic' the
)!tton in the map
tool)ar . 1+. /he O'#! G(*3 %ialog is %ispla$e%. /he gri% file $o! create% in Gesson 2 0/=/-R5".4RD is a!tomaticall$ entere% in the File name )o. If the file %oes not appear in the File name )o select it from the file list. 1*. Clic' the !en )!tton to create a conto!r map. 1@. /he map is create% !sing the %efa!lt conto!r map properties. 1F. If $o! (ant the conto!r map to fill the (in%o( choose the Jie( E 8it to 5in%o( comman% or clic' the )!tton. Alternativel$ if $o! have a (heel mo!se roll the (heel for(ar% to ?oom in on the conto!r map. Clic' an% hol% the (heel )!tton straight %o(n (hile $o! move the mo!se to pan aro!n% the screen. 17. #aving plotte% the isoh$ets %etermine the area )et(een the a%9acent isoh$ets an% fill in /a)le 1.2. 1. =se e
8
T.2 I$%#"& M#"%3 I$%#"$
A,#(&# ,&# + P P i 8
A(#& Ai 8
Ai x P i
I
L8
L28
L58
9
C%&'"#( 2 D#"#()*!&"*! + I!-$*" S* H3(*/& P('#("*#$ A*)
/o %etermine an% compare the insit! soil h$%rological properties !sing Core C!tter an% /ime Domain Reflectometr$ A''&(&"$ R#*(#3
C$lin%rical Core C!tter /ime Domain Reflectometer "teel Rammer
"teel Doll$
Containers Balance sensitive to &.&1 gms "pa%e /ro(el /rimming Knife an% -ven T%#(
Determination of soil h$%rological properties is important in the anal$sis of man$ h$%rological processes s!ch as infiltration percolation s!rface r!noff an% in soil science an% irrigation engineering. /he soil is a three phase s$stem comprising soli% particles (ater an% air. /he (ater an% air are present in the voi%s )et(een soli% particles. /hese pores ma$ )e fille% !p (ith onl$ (ater onl$ air or (ith (ater an% air. Correspon%ingl$ the soil ma$ )e sat!rate% %r$ or partiall$ sat!rate% 0!nsat!rate%. %e&initions: Get J )e the vol!me of a soil sample J s )e he vol!me of soli% particles J v is the vol!me of voi%s 0pores J( )e the vol!me of (ater an% J a )e the vol!me of air in the soil sample respectivel$. /he porosit$ 0 φ is %efine% as the vol!me of voi%s per !nit soil vol!me6 φ =
' v '
02.1 /he vol!metric moist!re content 0 θ is %efine% as the vol!me of (ater per !nit soil vol!me6
θ =
' (
'
02.2
Degree of sat!ration 0) is %efine% as the ratio of vol!me of (ater an% the vol!me of voi%s6 ) =
' (
' v
8rom e
10
02.3
θ
) φ
=
02.+ In la)orator$ soil samples are collecte% an% the soil moist!re is %etermine% gravimetricall$ )$ (eighting the (et an% %r$ soil samples an% is reporte% as percentage of %r$ (eight of the soil. 8ig. 2.1 sho(s the core c!tter assem)l$ !se% for collecting the insit! soil samples nee%e% for the gravimetric anal$sis. /he %r$ (eight moist!re fraction 0* is %efine% as 05al'er an% "'oger)oe 17F6 * =
)am!le (et (eight − )am!le dry (eight )am!le dry (eight
=
* ( * d
02.* 5here * ( is the (eight of (ater an% * d is the %r$ (eight of the soil sample. As the h$%rologists an% irrigation engineers re
ρ + ρ (
*
02.@
5here ρ + is the %r$ mass %ensit$ of the soil sample an% ρ ( is the mass %ensit$ of soil (ater.
11
F*. 2.1 C(# /""#( &$$#) +( (&,*)#"(*/ &!&$*$
/he techniC of the soil. /he B>C is a f!nction of the vol!metric moist!re content. #ence the time ta'en for the p!lse to travel along the metal ro%s %epen%s on the moist!re content. /he time ta'en )$ the p!lse is converte% to the correspon%ing vol!metric moist!re content thro!gh cali)ration (hich (o!l% )e recor%e% %igitall$.
F*. 2.2 T*)# D)&*! R#+#/")#"#(
P(/#3(#
1.5eigh the core c!tter an% meas!re its inner %imensions an% calc!late its vol!me. 2. P!sh the c$lin%rical c!tter into the soil to its f!ll %epth )$ gentl$ ramming it. 3. Gift the c!tter !p caref!ll$ (ith the help of a tro(el. +. /rim the top an% )ottom s!rface caref!ll$. *. Near)$ the site (here the core c!tter (as inserte% meas!re the vol!metric moist!re Content !sing /DR @. /a'e the empt$ pans an% (eigh them. F. Determine the (eight of the soil insi%e the c!tter )$ placing the soil in the pan. 7. /a'e the soil mass in the pan an% place it in the oven for a perio% of a)o!t 2+ ho!rs. After oven %r$ing again note %o(n the (eight of the pan in or%er to %etermine the %r$ (eight of the soil mass.
12
O$#(,&"*!$ &!3 C&/&"*!$
Diameter of the core c!tter 0G L
#eight of the core c!tter 0G L
Jol!me of the core c!tter 0 V 0G3 L T&# 2.1 C)'&(*$! + ,)#"(*/ )*$"(# $*! (&,*)#"(*/ &!&$*$ &!3 TDR P&!
W". +
N.
E)'" '&! P&! w18 M8
W". + W". + W". + W". + W". + D( 9#" $*
9*"% 9#" $* w28 M8
w2-w18 M8
'&!
3(
9*"%
$*
3( $* w38
9&"#(
)*. w2-w38
w3-w18 M8
M8
13
9".
M8
+(&/. W 8
ρ + <
θ <
(3 − (1
ρ +
'
ρ (
M=L58
θ
*
TDR
P(#/&"*!$
"teel %oll$ sho!l% )e place% on the top of the c!tter )efore ramming it %o(n into the gro!n%. Core c!tter sho!l% not )e !se% for gravels )o!l%ers or an$ har% gro!n%. Before removing the c!tter soil sho!l% )e remove% aro!n% the c!tter to minimi?e the %ist!r)ances. 5hile lifting the c!tter no soil sho!l% %rop %o(n /he /DR rea%ings sho!l% )e ta'en caref!ll$.
14
C%&'"#( 5 D#"#()*!&"*! + I!+*"(&"*! P&(&)#"#($ 9*"% D# R*! I!+*"()#"#( A*)
/o con%!ct infiltration test !sing a floo%ing t$pe %o!)le ring infiltrometer an% %etermination infiltration parameters A''&(&"$ R#*(#3
Do!)le ring infiltrometer (oo%en hammer Pointer 4a!ge (ith Jernier "cale "top(atch an% B!c'et T%#(
Infiltration is the process (ater entering from the gro!n% s!rface into the soil. /he infiltration rate %epen%s on man$ factors s!ch as soil t$pe tet!re vegetative cover soil properties s!ch as h$%ra!lic con%!ctivit$ an% porosit$ an% the antece%ent moist!re con%ition. /he infiltration rate & 0 T is the rate at (hich (ater enters the soil at the s!rface an% is !s!all$ epresse% in cmMhr. D!ring infiltration the infiltration rate & varies (ith time an% man$ empirical relationships are propose% to %escri)e the infiltration phenomenon. 0#orton133 4reen an% Ampt 111 Philip 1@. Among these #ortons infiltration e
+ ( & − & c ) e − / t
&
03.1
In e
15
t$pe. /he parameter & c is essentiall$ the h$%ra!lic con%!ctivit$ of the soil. /he infiltration parameters are %etermine% in the file% either (ith 0i "ingle ring infiltrometer or 0ii %o!)le ring infiltromter. /he ma9or %ra()ac' of single ring infiltrometer is that (ater infiltrates laterall$ at the )ottom of the ring an% as s!ch %oes not acc!ratel$ represent the vertical infiltration phenomenon an% is rarel$ !se% in the fiel%. #ence the %o!)lering infiltrometer is most commonl$ !se% for meas!ring infiltration rate an% %etermination of infiltration parameters. D# (*! *!+*"()#"#(
/he %o!)le ring infiltrometer consists of t(o concentric hollo( c$lin%ers of length 2* cm ma%e of cast iron as sho(n in 8ig. 3.1. /he %iameters of the inner an% o!ter c$lin%ers are a)o!t 3& cm an% @& cm respectivel$.
F*. 5.1 D# R*! I!+*"()#"#(
D!ring an infiltration test the fiel% is first levelle% an% the infiltrometer is %riven to a %epth of 1* cm into the soil (ith a (oo%en hammer. /hen 5ater is applie% initiall$ to the o!ter ring an% (ater is applie% to the inner rings after some time. /he p!rpose of the o!ter ring to is to restrict the later flo( of (ater from the inner c$lin%er (hich ens!res vertical movement of (ater at the centre of the infiltrometer. /he rate of %o(n(ar% movement of (ater at the centre is meas!re% (ith a pointer ga!ge (ith Jernier scale. P(/#3(#
1. Gevel the file% at (hich infiltration test is )eing carrie% o!t 2. #ammer the %o!)le ring infiltrometer at least 1* cm into the soil. =se the tim)er to protect the ring from %amage %!ring hammering. >ns!re that the infiltrometer is %riven verticall$ an% approimatel$ a)o!t 12 cm of the infiltrometer is a)ove thr gro!n%. 3. "tart the test )$ po!ring (ater into the o!ter ring first. A%% (ater into the inner ring !p to the same level as in the o!ter ring. +.
"tart the stop (atch an% recor% the (ater level (ith a pointer ga!ge
*.
Keep recor%ing the (ater levels at reg!lar intervals
@. /he fre
16
F. Contin!e the recor%ing of (ater levels !ntil the rate of fall of (ater level )ecomes constant. O$#(,&"*!$ &!3 C)'"&"*!$
Gease Co!nt of Pointer 4a!ge L T&# 5.1 C&/&"*!$ T*)# T 8
P*!"#( &# R#&3*! L8
D(' *! 9&"#( #,# L8
I!+*"(&"*! f - f c (&"# f L/T 8 L=T8
ln(f –f c8
1. Plot & vMs t on a normal graph sheet an% %ra( the )est fitting c!rve for the %ata points. 8rom the graph 8in% the val!e of & c as the limiting 0as$mptotic val!e of & at large time. 2. =se the val!e of f so o)taine% to comp!te ln0& & c in /a)le 3.1 3. Plot ln0& & c vMs t an% %ra( a )est fitting line thro!gh the %ata points an% o)tain the slope of the line an% the yintercept. /he $ intercept gives the val!e of ln0& & c 4. /he slope gives the %eca$ constant / 5. Kno(ing ln0& & c from step 3 an% & c from step 1 & can )e %etermine% P(#/&"*!$
1. 5ater is to )e first fille% in the o!ter ring so that (ater in the inner ring moves verticall$ %o(n(ar%s 2. Presence of vegetation ma$ effect o)servations. 3. /he (ater %epth in inner an% o!ter ring m!st )e same %!ring the o)servation perio%.
S(/#$ + #(((
1. ,eas!rement of Jernier scale !pto &.1mm 2. "tra$ points on the c!rve ma$ )e %!e to loose fiing of pointer ga!ge !se%.
C%&'"#( 4 17
M#&$(#)#!" + D*$/%&(# *! &! O'#! C%&!!# 9*"% C((#!" M#"#( A*)
/o meas!re %ischarge in an open channel !sing c!rrent meter an% hec' its acc!rac$. A''&(&"$- C!rrent ,eter "cale "top (atch T%#(
,eas!rement of %ischarge in rivers (i%e open channels is essential to assess the s!rface (ater potential to meet %omestic agric!lt!ral an% in%!strial nee%s. /he %ischarge in a river or a canal can )e meas!re% )$ emplo$ing either %irect or in%irect metho%s 0"!)raman$a 2&&7. Among the %irect metho%s AreaJelocit$ metho% is the most commonl$ !se% techni
=
v ave =
v &.@ d
&or de!th o& &lo( < 3 m
( v&.2 d + v &.7d ) 2
&or de!th o& &lo( > 3 m
0+.1
0+.2
5here d is the %epth of flo( v &.2 d v &.@ d and v &.7 d are the velocities at %epths &.2d &.@d an% &.7d from the (ater s!rface respectivel$. 67rrent Meter: C!rrent meters are the most commonl$ !se% instr!ments !se% to meas!re velocit$ at a point in rivers an% open channels. It essentiall$ consists of a rotating element (hich rotates %!e to the reaction of the stream c!rrent (ith an ang!lar velocit$ proportional to the velocit$. C!rrent meters are commerciall$ availa)le in t(o t$pes 0a verticalais meters an% 0) hori?ontalais meters as sho(n in 8ig. +.1. Jerticalais c!rrent meter consists of a series of
18
conical c!ps mo!nte% aro!n% a vertical ais. /he hori?ontalais c!rrent meter consists of a propeller mo!nte% at the en% of hori?ontal shaft.
/o meas!re the velocit$ at a point in a riverM canal the c!rrent meter is hel% against the c!rrent. D!e to the stream velocit$ the propeller or conical c!ps rotate the n!m)er of revol!tions )eing proportional to the velocit$ at that point. A f!nctional relationship is %evelope% relating the n!m)er of revol!tions to the stream velocit$ )$ cali)ration. A t$pical relationship is of the form v = a N s + +
0+.3
5here v is the stream velocit$ N s is the n!m)er of revol!tions per secon% an% a an% + are cali)ration constants. P(/#3(#
1. -pen the s!ppl$ valve. A%9!st the %ischarge an% the tail gate to get a s!ita)le %epth of flo( in the channel. 2. 5ait !ntil the flo( )ecomes !niform. 3. "elect a s!ita)le section in the mi%%le portion of the channel +. /a'e the pointer ga!ge rea%ing at the mi%%le of the section to get the %epth of flo( *. Divi%e the cross sectional area into three or fo!r vertical s!)sections @. Place the c!rrent meter at &.@d from the (ater s!rface at the mi%%le of each s!)section an% recor% the n!m)er of revol!tions F. ,eas!re also the pointer ga!ge rea%ing of the sharp creste% (eir at the %Ms of the channel to compare the %ischarge meas!re% )$ c!rrent meter. 7. Repeat the steps 1 to F for three or fo!r %ischarges. . Recor% the pointer ga!ge rea%ing at the (eir crest level.
19
O$#(,&"*!$ &!3 C)'"&"*!$
C!rrent meter cali)ration constants a L
b L
T&# 4.1 M#&$(#)#!" + 3*$/%&(# $*! /((#!" )#"#(
R!n No
1
Pointer ga!ge rea%ing at (ater s!rface h1 0G Pointer ga!ge rea%ing at )e% h2 0G Depth of flo( y 0h1 h2 0G 5i%th of s!)section 1 0+1 0G Area of s!)section 1 A1 0+1 8 y C!rrent meter revol!tions per secon% N s1 8lo( velocit$ in s!)section 1 0 v
1
= a N s1 + +
0GM/ Discharge in s!)section 291 0 v1 A1 0GM/3 5i%th of s!)section 2 0+2 0G Area of s!)section 2 A2 0+2 8 y C!rrent meter revol!tions per secon% N s2 8lo( velocit$ in s!)section 2 0 v
2
= a N s 2 + +
0GM/ Discharge in s!)section 2 92 0 v2 A2 0GM/3 5i%th of s!)section 3 0+3 0G Area of s!)section 3 A3 0+1 8 y C!rrent meter revol!tions per secon% N s3 8lo( velocit$ in s!)section 3 0 v
3
= a N s 3 + +
0GM/ Discharge in s!)section 3 93 0 v3 A3 0GM/3
/otal Discharge 9 91 ; 92 ; 93 0GM/3 5i%th of )roa% creste% (eir < 0G L
20
2
3
+
Pointer ga!ge rea%ing at the crest of )roa% creste% (eir yc 0G T&# 4.2 M#&$(#)#!" + 3*$/%&(# $*! $%&(' /(#$"#3 9#*(
R!n No
1
Pointer ga!ge rea%ing at (ater s!rface y( 0G #ea% over the (ier = 0 y( yc 0G Coefficient
of
6 d = &.@11 + &&F*
Discharge 9 =
2 3
%ischarge
= <
6 d <
2 g =
3M 2
0G3M/
21
2
3
+
C%&'"#( > D#"#()*!&"*! + H3(&*/ C!3/"*,*" 9*"% C!$"&!" H#&3 P#()#&)#"#( A*)
/o %etermine the sat!rate% h$%ra!lic con%!ctivit$ of a soil !sing constant hea% permeameter. A''&(&"$
Constant hea% permeameter stop (atch scale T%#(
/he f!n%amental la( (hich is !se% to %escri)e flo( of (ater in soils is Darc$s la( 0Ragh!nath . Darc$ con%!cte% several eperiments on (ater flo( thro!gh pipes fille% (ith soil. 5ater (as allo(e% to enter at one en% an% pass thro!gh a circ!lar pipe of cross section A fille% (ith san% an% pair of manometers. /he (ater (as collecte% at the other en%. /he (ater (as allo(e% !ntil s!ch time as all the pores (ere fille% (ith (ater an% the inflo( rate 9 is e
A∆h ,
∆h
or
an% inversel$ proportional to the length of the pipe i.e. 9 A
∝
∆h
,
or ' ∝
∆h
,
0*.1 5here ' is the Darc$ velocit$. Intro%!cing a constant of proportionalit$ " >
=
" i
0*.2 5here " is calle% the h$%ra!lic con%!ctivit$ an%
i =
∆h
,
is the h$%ra!lic gra%ient. >
0*.2 is pop!larl$ 'no(n as Darc$s Ga(. Darc$s la( is vali% (hen inertial forces are less
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%ominant as compare% to visco!s forces. In general the la( is consi%ere% as vali% (hen the Re$nol%s n!m)er 0%efine% as 'd Mν (here d is the average %iameter of the soil grains an% ν is the 'inematic viscosit$ of (ater is less than !nit$. Be$on% Darc$s range 0i.e.
Re$nol%s n!m)er greater than !nit$ the mean velocit$ is given )$ ' = / i
n
0*.3
5here is n an eponent greater than !nit$. If velocit$ an% h$%ra!lic gra%ient are meas!re% in Darc$s range 0 i.e. Re$nol%s n!m)er less than !nit$ an% plotte% on a loglog graph paper the res!lting plot (ill )e a straight line incline% at an angle of +* & 0i.e. slope e
8ig. *.1 sho(s the constant hea% permemaeter commonl$ !se% in la)oratoeis for %etermination of
h$%ra!lic con%!ctivit$.
0approimate si?e 1&&m
It consists of a s
× 1&&mm or 1*&mm %ia. ma%e of Perspe sheet. /he col!mn is
a)o!t 1.* m long an% is fille% (ith san% grains of !niform si?e 0 a)o!t 2 mm %iameter. Press!re taps are provi%e% on one si%e of the col!mn. /hese press!re taps are connecte% to pie?ometer t!)es. /he s!ppl$ pipe is connecte% to the lo(er en% of the col!mn. -!tlet pipe is connecte% to the !pper en% of the col!mn. Preca!tionar$ meas!res are ta'en to prevent the migration of san% grains along (ith the flo(ing (ater. P(/#3(#
1.
Chec' that there is no air )!))le in the pie?ometer t!)es.
2.
Note the %istances of vario!s press!re taps from a reference point.
3.
-pen the s!ppl$ valve an% let the flo( )ecome stea%$.
+.
/a'e %o(n the pie?ometer rea%ings.
*.
,eas!re the %ischarge !sing collecting tan' an% stop (atch.
@.
Jar$ the %ischarge an% repeat steps 0+ an% 0* to collect more sets of o)servations.
23
F*. >.1 C!$"&!" H#&3 P#()#&)#"#( A''&(&"$
24
O$#(,&"*! &!3 C)'"&"*!$
Kinematic viscosit$ ν 0G2M/ L
Average grain %iameter d 0G L
Cross sectional area of permeameter A 0G2 L T&# >.1 3#"#()*!&"*! + H3(&*/ C!3/"*,*" R! N.
V. + 9&"#( /#/"#3 S L58
T*)# T&?#! +(
V#/*" '
C#/"*! " T8
P*#@)#"#( R#&3*!$
) =
L8
t A
H3(&*/ H3(&*/ (&3*#!" /!3/"*,*" i
L=T8
K L=T8
D*$"&!/# + '*#@)#"#($ +() 3&")
25
1. Plot the pie?ometer rea%ings 0on $ais vMs %istance of the correspon%ing press!re tap from the selecte% reference %at!m for each of the r!ns ta'en. 8itin a straight line for each of these r!ns an% fin% the slope of each of these lines. /hese are the mean val!es of h$%ra!lic gra%ient i
= h & I,
for %ifferent r!ns. >nter these val!es of i in the
correspon%ing col!mn of the o)servation an% comp!tations ta)le. Also calc!late the velocit$ ' for all these r!ns. 2. Plot ' vMs i 0 (ith i on ais on a loglog graph paper. 8itin a straight line having a !nit slope to %ata points for relativel$ lo( velocit$. 8or higher velocit$ %ata points fitin another straight line an% meas!re its slope. 3. Determine the val!e of n in >
26
