/ THE INSTITUTION OF ENGINEERS, SRI LANKA IESL ENGINEERING COURSE PART 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 0.57m 3 /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 = C i B.j2gH Z h, 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. Page 10'5
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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.