Problem 5. Water 1os from a lake into a steep rectangular channel over a concret
ID: 1844801 • Letter: P
Question
Problem 5. Water 1os from a lake into a steep rectangular channel over a concrete broad-crested weir which is X feet below the lake level., the channel bed starts 2 feet below the crest of the weir. Assuming the flow is supercritical just below the crest and at the channel inlet: a Find the average flow velocity, water depth, and the Froude number at the channel inlet assuming no pressure drop over the weir, b. Accounting for discharge coefficient, determine the flow rate over the weir for a weir length of 20 feet and compare the results with part (a) flow rate and calculate percent of error in Part (a) in flow rate calculation.Explanation / Answer
steep rectangular channel over a concrete braod crested weir = 8ft (below from lake level)
the flow is supercritical and channel bed starts at 2 feet
area of rectangular section,A = width x legnth
20 x 8 = 160 ft sq
area = 160ft sq
volumetric flow rate = (lxA) / initial velocity
= 20 x 160 / 2
=3200/2
= 1600m/s
volumetric flow rate,V = 1600m/s
average flow velocity ,v = V/A (V=volumetric flow rate , A = area of section )
v = 1600/160
v= 10
a. average flow velocity 10m/s
water depth = (area x depth of channel section) / legnth of sectin
= 1600 x 2 / 20
= 3200/20
= 160 ft
water depth = 160 ft
froude number at the channel section = v/gl.(1/2)
= 10 / (9.81 x 2)(1/2)
10 / 9.81 = 1.01
the froudes number for the chennel section assuming no water pressure drop over the weir = 1.01
b. flow rate over the weir for the weir legnth 20 feet
flow rate ,q =2/3 cbd (2g)1/2 x h3/2
q= 2/3 x 2 x 160 ( 2x9.81 )1/2 x (2)3/2
q=0.6 x 320 ( 9.81 ) x 4
q = 1883.52 x 4
q = 7534
flow rate = 7534m/s
flow rate of part A = 1600m/s
the percentage of error in part A in as flow calculation = (7534/1600)
= 4.70 %
so the error percentage in flow rate on part A = 4.70 %