Hydraulic Structures: Fourth Edition

Worked examples

ForH1.50 m, H/Hd1.50/2.800.536; by interpolation between
0.578 (H/Hd0.05) and 0.75 (H/Hd1),Cd0.666 and

Q590.660.6661.53/2723 m^3 s^1.

The maximum head for no cavitation. Hmax1.65Hd1.652.8
4.62 m. For this condition, Cd0.81, and therefore

Qmax590.660.814.623/24757 m^3 s^1.

Worked Example 4.4

A long chute 2 m wide, of slope 0.25, and with n0.012 carries a discharge
of 7.5 m^3 s^1. Using various methods, estimate the average air concentra-
tion and the depth of the fully aerated uniform flow.

Solution

The discharge per unit width, q7.5/23.75 m^3 s^1 m^1.
The depth of the uniform non-aerated flow, y 0 fromqis

q

2/3

y 0 , 3.75

2/3

y 0.

By trial and error, y 0 0.259 m, Vq/y 0 14.48 m s^1 andR0.206 m.

FrV/(gR)1/210.19.

1. From equation (4.41),

yac 1 (q^2 /g)1/3, 0.361ya(m)0.418

for

C 11  1 y 0 /ya, 28C(%)38.

2. From equation (4.42),

0.1(0.2Fr^2 1)1/20.10.2 (^1) 
1/2

0.1(0.210.19^2 1)1/20.445,

0.445, ya0.374 m, C31%.

ya 0.259



0.259

V^2



gR

ya y 0



y 0

(0.25)1/2



0.012

2 y 0



2  2 y 0

S1/2



n

2 y 0



2  2 y 0