Question

At a certain depth (h) which is one-tenth of its bottom width (h = b/10), a rectangular channel has a velocity of 2 m/s. What will be the velocity in this channel when the depth is doubled?

Answer 1

The velocity when depth becomes double will be 2.82 m/s

Step-by-step explanation:

At initial condition

velocity V= 2 m/s

h=b/10

We know that velocity if given as follows for rectangular channel

`V=√(2gh)`

Now by putting the values in the above formula

`2=√(2*9.81* h)`

h=0.203 m

Now when depth is doubled ,it means that new h=2 x 0.203 m

So our new h will be h=0.406 m

Now again by using formula

`V=√(2gh)`

`V=√(2*9.81* 0.406)`

V=2.82 m/s

So the velocity when depth becomes double will be 2.82 m/s