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

Answer

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

$F_r = \dfrac{Q}{A\sqrt{gD}}$

Where D is the hydraulic radius

 $D = \dfrac{A}{P}$

$F_r = \dfrac{Q}{A\sqrt{g\times \dfrac{A}{P}}}$

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,

$F_r = \dfrac{Q}{A\sqrt{g\times \dfrac{A}{P}}}$

$F_r = \dfrac{250}{27\sqrt{32.2\times \dfrac{27}{13}}}$

 F_r = 1.087

 F_r > 1

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