wr-practice problem solutions

8/3/2019 Wr-practice Problem Solutions

1/18

Open Channel Flow1. The trapezoidal channel shown below has a depth of flow of 2.0 feet. Determine the wettedperimeter.

p~s '+-2.+3\~3>: : 'Ii: \ '6.u:; ~

2. Calculate the velocity and flow rate of storm flow in an 8-foot wide rectangular concretechannel (n=0.015) if the depth of flow is 2.4 feet. The channel slope is 0.01.n = c.O\St:: 0,0\A-: \.2..t-\..)t..z.A-4) = \9'.2.~.).:z.p o : 2d ~ ~ - = < '_Z ) (_2 .A-++) .d..8++) ~ \2 .s . . f .+a . . ~ A / V = ,9.2;'\-Yrz..~~+ __ 1.5 + +

j - ; f .'-L-----!L-J-18' l

'1 -: . , \ .~ ) ((?hff)2./3 01: : ~ . 4 - ~ . C > I ~ ) t I.? f+ - . J 1>." I

V '$ JI3,Ol ~p~ r~=vA

~ ( .. 1 '3 . 0'1 tps) ( I ' .2. ~ ...~ )G > " I :Z '4~. T C J c.~S I

' " - ' - - - . - ~ - - - _ H_ ~_ _~ _ _ __ _ _ __ __ ._ ___

I:\PE Prep\Water Resources\Practice Problems - t.doc 1


2/18

Flow in Closed Conduits1. Compute the head loss and pressure drop in 200 feet of horizontal 6-inch diameterasphalted cast iron pipe carrying water with a mean velocity of 6 fps. Use f = 0.02,temperature = 70 degrees F., nominal pipe size.A . Determine the Reynolds Number.~. Determine the Relative Roughness.

I+.A

6p: ht! . . (~ )Q '" t-'l,~ lb/ . . f . . \ .? ,-

Ap'" (4.+1)\


3/18

3. Assume the conduit shown in the figure has inside diameters of 12-inch and 18-inch atsections 1 and 2 respectively. If water is flowing in the conduit at a velocity of 16.6 fps atsection 2, find the (a) velocity at section 1, (b) volume flow rate at section 1, (c) volume flowrate at section 2.C D t)f) !=LOW _,__ . -

/ : t . \ ~ ift ; ,2. . - r r c . . _ 2 . /IL) ' ,- = = 0.19 + + " 2 -titb'Z.. 4At .. " '0 . 8 / 1 ? - 1 " 2 --::. \.11 + + "t -4-

@ A , V, .,..Az. Y . , _v , ' : : . ~ hi

- = ~:1i) :1'1

VI ~ = ? . 1 . 'Z. ~p~

@ ~ , - = '{AI=,31,2.)\0.1'9)

~ - = Z9.~ G.+ :>I .

~'2. "" \ / - z . . A . , _-::~L...-)\.\.11)

~ '2.:r. ~9.4- c. . ;s

4. Water flows through a 3-inch diameter pipe at a velocity of 10.0 fps. Find the volume flowrate in cfs and gpm.

~::. vA::::~o tp~)(c>.C>S + \ - 2 , }

L ' ? ' " 0.49 ~

L CeFR"", ~I.>.\


4/18

Hydrology1. A unit hydrograph for a drainage area is shown in the figure below. 12 hours after thebeginning of runoff, the discharge measured at a gaging station at the outlet of the drainagearea is 150 m 3/s . What is the peak discharge from the drainage area.

6 12 time (h)

q? ': P~A\C- D , ~C.\o4A t a . c . . . eC?'" = \-\"'b~"~("I.A.P\"", PEe . .. \\ . . b ls ~ " ,\ 't .'" ".qb - = l"v\E' ' ' ' 'SIACt- ? 1 1 ! . . . \ , - 'b\'$~~,~c...tiC( ~


5/18

Hydraulic Machines1. A pump station will be used to fill a tank on a hill above from a lake below. The flow rate is10,000 gallons per hour (gph) of 60F water. The atmospheric pressure is 14.7 psia. Thepump is 12 feet above the lake, and the tank surface level is 350 feet above the pump. The

discharge line is 4-inch diameter schedule 40 steel pipe. The equivalent length of the inletline between the lake and the pump is 300 feet. The total equivalent length between the lakeand the tank is 7000 feet, including all fittings, bends, screens, and valves. The cost ofelectricity is $0.04 per kW-hr. The overall efficiency of the pump and motor set is 70%.O c : . ~ c>.~3 < : : . + : sWhat is the flow rate in cubic feet per hour (Cfh)?/~ .. \O,c>cC>apn){( ~ .)..,., o.oc:.2.z.z,S 0::. 0.31 S r + ' 3 / - s ~, ( .. ..C> ,_ . . .

B.) ~~,t \!\~~~;~~~~,._:: : ~ 1 " ' 1 ? , )~ _ C? J lo.~"1 ~ l . -~ J ~) / 0 .0~84!\'\ ~~ '2.""'I; - = vA => Y - IA .:What is the Reynolds number?t2< "" ~ '"


6/18

Flow in Open Channels1. What is the hydraulic radius of a 24-inch RCP storm sewer when the depth of flow is 24inches? ," C " " " ~ ~ c . . ._ ' l .. t> ~ - \ .) ~ C>. " 2 . . S '- "> e . )

2. What is the hydraulic radius of a 24-inch RCP storm sewer when the depth of flow is 11inches?

):IPE PreplWater ResourceslPractice Problems - 1.doc

F~e."", l!.PP. $...Ad$ :: 0.4-


7/18

Groundwater1. Groundwater monitoring wells have beenconstructed on a site as shown in the figure. Thesite's hydrogeologic setting is characterized by an

unconfined aquifer with silty sand to a depth of 10m. The average hydraulic conductivity for theaquifer is 0.42 m id and the effective porosity is0.34. Groundwater elevation data for themonitoring wells are provided in the accompaniedtable.

Well Casing topelevation (m abovemean sea level)Groundwaterdepth belowcasing top (m)MW-1MW-2

MW-3MW-4MW-5MW-6MW-7

49.7749.7449.5949.6049.0949.3149.63

4.745.665.595.955.575.254.62

What is the direction of the groundwater gradient?(A) N 45 E(8) N 45 W(C) S 45 E(D) S 450W

I:IPE PreplWater ResourceslPractice Problems - 1.doc

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+onitoringwell

~W-3

. - : W - 7

~W-2

o 50I Iscale (m)'

7

north


8/18

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~ ~ ~ e > - v ? 1 1

'71,

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lIaM6ulJo~lUow~.

Z 9 " 1 7szsl SoSS6S6SoS99S1 7 l o 1 7

9 " 6 1 7~ 0 6 1 7

6 0 " 6 1 70 9 6 1 76 S " 6 1 71 7 l " 6 1 7a"6v

l-MW9-MWS-MWtrMW-MWZ-MW~-MW{ill} dO l Bu !seoMO l aq 4 ld ap. I91eMpunOJE>

< IaA91ea s uesu iaAoqe w) UO!IBAa ladOl6U!SBO

\"a lqBIp a!u edWO~OB a 4 } U ! p a P !A o Jd a ra s lla M OUPO IIUOWa lU .101 etep UO !lBA a la .Ia lBMpUnOJE> " v O OS ! A l!S OJo d 9 A!p aJJ9 a 4} p UB P /W Z v " O S ! . Ia J !n b sa 4I J0 1 A l!A !l~ np UOO 0 lln BJp A4 a 6S Ja A B a4.L Wo ~ J O 4 1d a p B O l pUBS A II!S 4 1!M J a J!n b s p su gu oo unUSA q p az pa }o eJ sljo S ! 6 um a s o !6 01 0a 6o Jp 1\4 S ta llSa4.L a Jn6!J a 4 } U ! U Mo4s S B a lls e uo pa pnJ1S UO Ouaaq aAB l! suaM 6uP01IUOW Ja lBMpunOJE> " ~

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9/18

Fluid Dynamics1. Water flows at 4.2 fps in a 2-inch diameter pipe that is connected through a reducer to a 1.5-inch diameter pipe. What is the flow velocity in the 1.5-inch diameter pipe?

(Because specific information regarding the type of pipe is not given, assume pipediameters given are actual inside diameters.)Neglect hIand minor losses. " \ :. 4.1. .t!ps

t) ,:: 7.;" =J p . . : : .\ \\)2. = \,S;n =; ~ "2 ::.

V :z . . . A ,vlb . . ' 2 .

~O"l.-a +4. ) \ .~ . '2 . ~~s)="Vz.:: 1.1 ~P$

Open Channel Flow

1. Determine the area of flow in the trapezoidal channel shown below. The depth of flow is 2.0feet.

A I ' : b .3:: ' I z . ( ( , , ) \ . -z .) -:.. (p . c + ~A"l. ~ ~+-~) \ . " l ,~4- ) = - \2.~z

I:\PE Prep\Water Resources\Practice Problems - 1.doc 8


10/18

Hydraulic Grade Line1. In some parts of its length, the storm sewer shown in the illustration flows full during extremerainfall events. At what manhole, if any, does the storm water overflow through the manholeonto the street surface?

Location Pipe Pipe Watercenterline centerline pressurede~th {tt} elevation {tt l {~si}MHA 8 . 2 1 0 0 0MHB 1 0 . 5 8 6 4 . 2MHC 1 2 . 4 7 1 6 . 8MHD 6 . 8 5 4 3 . 1MHE 6 . 2 4 3 1 . 2MH =manhole .

'd= depth below gradez= elevationnotto scale

c/\

0 ~ h f>

~-L-D-E_ -

A - 6-:--2.4- :: = C : : >~ - c..o~.~ ~ '-'2..~ -::. "'.1 +~G- c::, '1~.2.. '" ( ,,"2 ..",\ ': \S.1 + \ -t > - 44 c . . . " \- - 7


11/18

Culvert1. A 1 m high, 27 m long box culvert placed at a 2% slope sees an upstream water surfaceelevation of 1202.83 m and a downstream water surface elevation of 1202.38 m. The invertelevation of the culvert outlet is 1201.17 m. What is the culvert flow classification?

(hint: draw the figure)

. . J j nsz,S?....1 2 . ( >' 2 . .. ,I ,..... "V 12.02.~ ~ ""- r o e 0E p,p :: 12..0"2..."",i "2. (> ' . " "1 1 " " )!

J J . < - - < _____:2~1 1'1 _ - - - - - ; l o r N . 12.01. rt 1'1::

I:\PE Prep\Water Resources\Practice Problems - 1.doc 10


12/18

Hydrology1. A 500-foot by 1,500 foot site is presentlycovered with woodlands. Development will

change 50% of the site to single familyresidential and 25% to multi-familyresidential land use.

The figure relates rainfall intensity andstorm duration. Appropriate values of runoffcoefficients for various land use activitiesare listed in the table.

The velocity of overland water flow isestimated to be 1.0 fps before developmentand 3.0 fps after development. The directionof flow is parallel to the 1,500 footdimension of the site.

Runoff CoefficientsLand Use Runoff CWoodlands 0.15Single Family 0.40Multi-Family 0.50

!. r I" ' o J40 so so . ~o' ., ~ 1 . 9 0 110 no '1~ HO t , . , 'J6Q ria ~8!

o Storm Duration (mini

(A) Calculate the peak storm water runoffrate from a 1O-year design storm for pre-development and post-development landuse conditions.

)( ' I )( O I M . ;' Jf c, "'" (L IV / ( . . .OseG.)

A-=-~S:>O.f+){lc;b'" ~ + - ) - : . l7~,o($o ++~)( Y 45,5("0 ) .,,_ ,.1 .z :z ..Ac ..I .) ('(l~ d C'::Vi!l..O p,....~,.JT

G ~t'.. ~ l !CS~o f.+) l 1.0 +p~ ) (tk~)-: Z 5 " " . - P1= - 4 " 0 / -e ...., "" " tz-AT ,(;). . . t - = 7 .: '5 ,. ., ;, . 0 ct>L..'- uP._'"h .04- ENTelL .. I> \') I...A '"" I:):,_________::::.43;7


13/18

Open Channel Flow1. A 4-foot diameter concrete interceptor sewer (n = 0.013, slope = 0.02) carries wastewater ata depth of 1.5 feet. What is the velocity of flow? (assume n varies with depth)

~~b,",- b.pp_ \9.(.AT OfD: o.3~

\.S4- ~ c.~~,0

p ._?? \f .s>~A ~ f"~~ ~.1-c: : .< . . I ) \4 .c) " "0-%3v : (_4.yb.O\~) \.o. 2 . + + + " 2 -

Q: vA: < . . . \.49/n)tR) '2.1~-is (A)= ( _ , . b t ; 9 /o0\'3)( I.2 . S f+)'Z./:,~z..)( zA + - + ~ )

.. ~__ \45 ....(:'::).I:\PE PreplWater ResourceslPractice Problems - 1.doc 12


14/18

Hydraulic Machines1. A sanitary sewer lift station must ultimately pump 1,080 gpm. The total static head is 24 feet.The operating point for this system with an 8-inch pump having the characteristic curve datais 34 feet of head.

Discharge(gpm)o175260363449

Head (ft)424038343444053063028207

(A) Draw the characteristic curve, locate the beginning point of the system curve and theoperating point.

(B) What is the flow rate at the operating point for the 8-inch pump?

(C) What diameter pump of the same type and manufacturer as the 8-inch pump isrequired for a single pump installation to Q = 1,080 gpm?u"S e p",-'"" P:;,\~\'-A'\2-'"\-(E~\.Ab.'\c>~~

Q\ ( . ( "2 - \ ) ~ = 1'5"2.4. . .'":> , b " : >D, 2- t > : : Q:'34 'n -= : :> U';}E \Z--,~\4. 91.- ' ." ' - ' f lz .q.,

..t).'5;:.;. 0.02.0 ),,-S}? ----.--.------ - ----------------------.-.- .--- ---------.-.- .z,

I:IPE PreplWater ResourceslPractice Problems -1.doc 13


15/18

Hydrology1. Frequency-intensity-duration curves for a watershed ate presented in the illustration. What isthe frequency of the 60 min duration and 5.8 in/hr intensity storm?

tOO'(~-:: SD'ta,2 . .

~ . IF'

4'1,\ '/,

180

\CO"(n.. '. >'frequency c~rve 'Ifrequency c U r v e 2.fni~ql!ency curveS ~.freqo~ricy curve 4freqi~nf;y.curve 5

- - - =4- 50%10%.,4%


16/18

Fluid Dynamics1. Water is flowing in a schedule-40 steel pipe as shown. The characteristics of each pipe are

summarized in the table. The flow rate in pipe A is 0.76 cfs. What is the velocity in pipe B?(Neglect hf A-B)

PipeAB

A A . . 1T

A~ -z :

Pressure(psig)

: . . . . . .

pipe B

Nominaldiameter(in)

2 . 51.5 100 '" 14;d r - .: .90 II.\~:

. _elevation head is equal\4,~O f ~ +\'?.,'1(,,~ f'S~

(2.5A z . ) ' ::~, , - < : . . 5 / . 1 . ) " '-e4

C ( = vA " - 4/A.1l. o. . , e , c . . : i ; . s -.:. 2.:l..~S~p: ; )::.';'; A - = O.c>:A- + + " 2 -PA 0 0- + - 7 ; , t + , , " 2 - ~ ~~ Vf!,7-fA. A~ = . . .I 1) -. 0 2.~\c;:\OD "2-'" (,f-2..3S) \ ' 2 . . '1",,0 V 7-v-:aA . . . . l -+ ~,"\-.4 -"2.1- L . .A - . +

z-ss.S~ ::: 2..o1.~9 " " V~-z . .( , . , . ' " .~V~ " 2 --:. : 508~c.,.4~V~2. -= Iq~_\CV~ ~ ~.(p ~~~

I:\PE Prep\Waler Resources\Praclice Problems -1_doc 15


17/18

Open Channel Flow1. An 8-foot wide rectangular channel has been observed to carry storm water at a depth of 2.4feet. What is the hydraulic radius?

- - - - - j - - - - - I t----_._----- j_'----------------~

Ap\9.2 ~+

I :\PE Prep\Water Resources\Practice Problems - t.doc 16


18/18

Hydraulic Jump1. Water flows at a rate of 500 cfs through a rectangular section 10-feet wide from a "steep"

slope to a "mild" slope creating a hydraulic jump, in the manner illustrated in the figure. Theupstream depth of flow (d 1) is 3.1 feet. Find the (a) upstream and downstream velocities (b)

:d0.wnstream depth.q ':'Soc c : . t ~a, -: - 5 , \ t . - \ -A= '-\O++)(3.'~~) ~ '3\~+z..~':'vAy;: 5: _I A

.~.::..~~..d'2..:: - 1/2. ;d I + d'-

-:. - \.SS + - J So.S~ -+ 2.4~: - \.SS -\- 1.'2..2-

< 3 ' Z . . -e, 5.1 f+

I :IPE PreplWater ResourceslPractice Problems - 1.doc 17

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