/THE INSTITUTION OF ENGINEERS, SRI LANKA

IESL ENGINEERING COURSEPART 11/ EXAMINATION - OCTOBER/NOVEMBER 2012

304 WATER ENGINEERING

Answer five (05) questions. Time allowed: 3 hours

Question 1

(a) In subcritical flow in an open channel, the wave speed is greater than the flow speed (Froude

number is less than one) and the disturbance is propagated upstream. Hence, it is necessary to

trace the surface profile towards upstream from the point of disturbance. Standard Step

Method and Direct Step Method are the most widely used methods to trace the water surface

profile in open channels. Briefly describe these two methods showing how they are applied.

(b) The normal depth of flow in a 1.2m wide rectangular channel is 0.6m when the discharge is

0.57m3/s. The bed slope is 1 in 1600. At a sluice gate constructed across the channel, flow

depth increases to 0.9 m. How far upstream will the depth be 0.75 m?

Question 2

(a) By applying the Bernoulli equation or otherwise, show that the flow rate through a sharp

crested rectangular weir can be expressed as,

Q = CiB.j2gHZh, where C discharge coefficient, B crest width, H weir head and g

acceleration due to gravity.

(b) A sharp crested weir is used to measure the flow rate of water in a 5m wide horizontal open

channel. The height of the weir (hw) is 0.60 m. Calculate the flow rate when the water depth at

the weir is 1.5m. Discharge coefficient for this weir is given by the empirical formula,

C = 0.598 + 0.0897 !!...., (in SI units) where H is the weir head.hw

(c) Compare the use of rectangular weirs and throated flumes in measuring the flow rates in open

channels highlighting the advantages and disadvantages of each method.

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Question 3

(a) List the factors that affect the rate of infiltration.

(b) Horton's model [f (t)=Ic + (fo - fJe-kt] and ¢ index method are the most widely used methods

to estimate the amount of infiltration. Compare the two methods emphasizing their

applicability under different conditions.

(c) Direct runoff due to a 12 hour storm (described in Table Q3) is 100 mm. Calculate the

average infiltration rate during the same 12 hours period.

Table Q3

Time (hours) Rainfall (mm)

0:00 -2:00 35.0

2:00 -4:00 60.0

4:00 -6:00 27.0

6:00 -8:00 15.0

8:00 -10:00 5.0

10:00 -12:00 2.0

Question 4

(a) List three assumptions on which the unit hydro graph concept is based on.

(b) Discuss how a unit hydro graph is developed. Clearly state the data needed and how the

assumptions that listed in the answer for Question 4 (a) are applied.

(c) The six-hour unit hydro graph of a watershed having a drainage area of 393 km2 is given in

Table Q4.

Table Q4

Time (hr) 0 6 12 18 24 30 . 36 42

Unit hydro graph (rrr'(s) (for 0 1.8 30.9 85.6 41.8 14.6 5.5 1.8

a one centimeter of rainfall)

For a storm over the watershed having an excess rainfall of 5cm for the first six hours and

15cm for the next six hours, compute the stream flow hydro graph, assuming a constant base

flow of 100 m3Is.

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Question 5

(a) In extreme value analysis, it is very important to know to which probability distribution

function that the data set belongs to. Briefly explain how it can be decided that a record of

annual maximum rainfalls belongs to extreme value distribution type I, II or III.

(b) Flood frequency computations for a river at a proposed dam site using the Gumbel's method

resulted in flood peaks 1200 m3/s and 1800 m3/s for 25-year and 50-year return periods. If the

flood peak (XT) with return period T, is given by Xr = O"n-l Yr + X - YnO"n-1 , calculate the floodSn Sn

peak with 100-year return period. YT is the reduced variate and given by Yr = -In(ln~) .T-l

Other notations have their usual meanings.

Question 6

(a) There is a system of subsurface, perforated, parallel pipes connected to a pumping stationconstructed to drain excess water in a rectangular playground. If the steady state unconfmedgroundwater flow with a recharge R is governed by,

Ei h2 + 82h2 = _ 2R (with usual notations), propose a simple field test to determine the

(}x 2 ay2 Khydraulic conductivity, K of the unconfined aquifer under the playground. Assume the pipesare laid on the top surface of the horizontal impermeable bed rock.

(b) At a steady state, the pumping rate Q of a well in an unconfmed aquifer is given by,

Q = 7rK (~2- hJ) (with usual notations). Explain why this equation gives only an approximate1 rln. r.

value for the hydraulic conductivity K, if the observation wells (where hI and hz are measured)

are very close to the pumping well.

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Question 7

(a) Small amplitude wave theory is the simplest form of wave theories used to explain ocean wave

characteristics. However, it is applicable only under certain conditions. List the conditions that

should be satisfied so that the small amplitude wave theory can express the wave

characteristics with a reasonable accuracy.

(b) A wave train is propagating normally towards the coast over a sea bed with straight and shore

parallel depth contours. The deep water wave length and height are 300m and 2m respectively.

What are the wave length and height at a depth of 30m? For small amplitude waves, the wave

length L, wave period T and the depth h are related to each other according to the equation,

L - gT2 t h 2rrh-- an -.2rr L

(c) What is the wave height at 30m depth, if the deep water wave crests are oriented at 60° to the

depth contours? Ifnecessary, use the wave table provided with the question paper.

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Table ofWaveFunctions

h hkh ~nOc%c- - tanh(kh) sinh( kh) cosh(kh) n

Ln L0.00010 0.00399 0.02507 0.02506 0.02507 1.0003 0.9998 4.46680.00050 0.00893 0.05611 0.05605 0.05614 1.0016 0.9990 2.98830.00100 0.01263 ('.07936 0.07919 0.07944 1.0032 0.9979 2.51540.00150 0.01548 0.09726 0.09696 0.09742 1.0047 0.9969 2.27440.00200 0.01788 0.11234 0.11187 0.11258 1.0063 0.9958 2.11850.00250 0.02000 0.12566 0.12501 0.12599 1.0079 0.9948 2.00520.00300 0.02192 0.13773 0.13686 0.13816 1.0095 0.9937 1.91740.00350 0.02369 0.14885 0.14776 0.14940 1.0111 0.9927 1.84630.00400 0.02534 0.15922 0.15788 0.15989 1.0127 0.9916 1.78710.00450 0.02689 0.16895 0.16737 0.16976 1.0143 0.9906 1.73660.00500 0.02836 0.17819 0.17633 0.17914 1.0159 0.9896 1.69280.00550 0.02976 0.18699 0.18484 0.18808 1.0175 0.9885 1.65420.00600 0.03110 0.19541 0.19296 0.19665 1.0192 0.9875 1.61990.00650 0.03238 0.20345 0.20069 0.20486 1.0208 0.9865 1.58920.00700 0.03362 0.21124 0.20815 0.21282 1.0224 0.9854 1.56130.00750 0.03482 0.21878 0.21536 0.22053 1.0240 0.9844 1.53580.00800 0.03598 0.22607 0.22229 0.22800 1.0257 0.9834 1.51240.00850 0.03711 0.23317 0.22903 0.23529 1.0273 0.9823 1.49080.00900 0.03821 0.24008 0.23557 0.24239 1.0290 0.9813 1.47070.00950 0.03928 0.24680 0.24191 0.24932 1.0306 0.9803 1.45210.01000 0.04032 0.25334 0.24805 0.25606 1.0323 0.9792 1.43470.01100 0.04233 0.26597 U.25987 U.26911 1.0306 0.9772 1.40320.Ot200 0.04426 0.27809 0.27114 0.28169 1.0389 0.9751 1.37520.01300 0.04612 0.28978 0.28193 0.29385 1.0423 0.9731 1.35000.01400 0.04791 0.30103 0.29225 0.30559 1.0457 0.9710 1.32740.01500 0.04964 0.31190 0.30216 0.31698 1.0490 0.9690 1.30680.01600 0.05132 0.32245 0.31172 0.32807 1.0524 0.9670 1.28790.01700 0.05296 0.33276 0.32100 0.33893 1.0559 0.9649 1.27050.01800 0.05455 0.34275 0.32993 0.34950 1.0593 0.9629 1.25450.01900 0.05611 0.35255 0.33863 0.35990 1.0628 0.9609 1.23960.02000 0.05763 0.36210 0.34706 0.37006 1.0663 0.9588 1.22580.03000 0.07135 0.44831 0.42050 0.46347 1.1022 0.9388 1.12540.04000 0.08329 0.52333 0.48026 0.54754 1.1401 0.9192 1.06430.05000 0.09416 0.59162 0.53106 0.62675 1.1802 0.8999 1.02280.06000 0.10430 0.65534 0.57525 0.70326 1.2225 0.8811 0.99320.07000 0.11394 0.71591 0.61437 0.77865 1.2674 0.8627 0.97130.08000 0.12321 0.77415 0.64934 0.85383 1.3149 0.8448 0.95470.09000 0.13220 0.83064 0.68082 0.92950 1.3653 0.8273 0.94220.10000 0.14098 0.88580 0.70931 1.00627 1.4187 0.8103 0.93270.15000 0.18330 1.15171 0.81832 1.42375 1.7398 0.7325 0.91330.20000 0.22512 1.41447 0.88844 1.93563 2.1787 0.6677 0.91810.25000 0.26788 1.68314 0.93327 2.59832 2.7841 0.6163 0.93230.30000 0.31212 1.96111 0.96117 3.48325 3.6239 0.5777 0.94890.35000 0.35789 2.24869 0.97797 4.68488 4.7904 0.5501 0.96410.40000 0.40496 2.54444 0.98775 6.32878 6.4073 0.5314 0.97600.45000 0.45304 2.84653 0.99328 8.58496 8.6430 0.5192 0.98470.50000 0.50183 3.15309 0.99636 11.68279 11.7255 0.5115 0.99050.55000 0.55108 3.46254 0.99804 15.93324 15.9646 0.5068 0.99420.60000 0.60063 3.77387 0.99895 21.76265 21.7856 0.5040 0.99660.65000 0.65037 4.08640 0.99944 29.75407 29.7709 0.5023 0.99800.70000 0.70021 4.39955 0.99970 40.70094 40.7132 0.5013 0.99880.75000 0.75012 4.71314 0.99984 55.69638 55.7054 0.5008 0.99930.80000 0.80007 5.02699 0.99991 76.23326 76.2398 0.5004 0.99960.85000 0.85004 5.34096 0.99995 104.35397 104.3588 0.5002 0.99980.90000 0.90002 5.65499 0.99998 142.85541 142.8589 0.5001 0.99990.95000 0.95001 5.96909 0.99999 195.57328 195.5758 0.5001 0.99991.00000 1.00001 6.28325 0.99999 267.76172 267.7636 0.5000 1.0000

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