Question

A trapezoidal channel with 6.0 ft bed width, 3 ft water depth and 1:1 side slope, carries a discharge of 250 ft3/s. Determine whether the flow is supercritical or subcritical.

Answer 1

given,

width of trapezoidal channel, b = 6 ft

depth of water, d = 3 ft

discharge,Q = 250 ft³/s

now, we have to calculate Froude number

`F_r = (Q)/(A√(gD))`

Where D is the hydraulic radius

`D = (A)/(P)`

`F_r = \frac{Q}{A\sqrt{g* (A)/(P)}}`

P is the width of the channel

P = b + 2 z d

P = 6 + 2 x 1 x 3

P = 13 ft

A = d(b + z d) = 3 (6 + 3) = 27 ft²

g = 32.2 ft/s²

now,

`F_r = \frac{Q}{A\sqrt{g* (A)/(P)}}`

`F_r = \frac{250}{27\sqrt{32.2* (27)/(13)}}`

F_r = 1.087

F_r > 1

Froude number is greater than 1 so, the flow is Super critical flow.