In a 5 {m} wide rectangular channel, the velocity \mu distribution in the vertical direction y is given by u=1.25 y^{\frac{1}{6}}. The distance y is measured from the channel bed. If the flow depth is 2 {m}, the discharge per unit width of the channel is

GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 64 of 65

Marks: +1, -0

In a

5 {m}

wide rectangular channel, the velocity

µ

distribution in the vertical direction

y

is given by

u=1.25 y^{\;{1}/{6}}

. The distance

y

is measured from the channel bed. If the flow depth is

2 {m}

, the discharge per unit width of the channel is

Solution:

U_{y}=1.25 y^{1 / 6}

Consider an element dy at distance y from channel bed.

d q=U_{y} d A

d q=1.25 y^{1{/}6} d y

q \to

Discharge per unit width

q \;\; =∫↙{0}↖{2} 1.25 y^{1{/}6} d y

\;\; =1.25(\;{y^{7{/} 6}}/{7 {/} 6})_{0}^{2}

\;\; =1.25 × \;{6}/{7} × 2^{7{/}6}=2.4 {m}^{3}{/}{m}{/}{s}

Go to Question:

Prev Question

Next Question