Question

Water is flowing through a channel that is 12m wide with a

speedof 0.75m/s. the water then flows into four identical channels
thathave a width of 4.0 m. the depth of the water does not change
as itflows into the four channels. What is the speed of the water
in oneof the smaller channels?

Answer 1

a) 0.56m/s

Step-by-step explanation:

`A_(1)` = 12m

`A_(2)` = 4.0m

`v_(1)` = 0.75m/s

area= w×h

`Q_(1)` = 4
`Q_(2)`

`A_(1)`×
`v_(1)` = 4
`A_(2)`×
`v_(2)`

`v_(2)` =
`(A_(1)v_(1) )/(4A_(2) )` =
`(12*0.75*h)/(4*4.0*h)`

`v_(2)` = 0.56m/s

⇒ the speed of the water in one of the channels is 0.56m/s

Answer 2

Velocity from second channel will be 1.6875 m/sec

Step-by-step explanation:

We have given width of the channel , that is diameter of the channel 1
`d_1` = 12 m

So radius
`r_1=(d_1)/(2)=(12)/(2)=6m`

Speed through the channel 1
`v_1=0.75m/sec`

Width , that is diameter of the channel 2
`d_2=4m`

So
`r_2=2m`

From continuity equation

`A_1v_1=A_2v_2`

`\pi * 12^2* 0.75=4* \pi*  4^2* v_2`

`v_2=1.6875m/sec`

So velocity from smaller channel will be 1.6875 m /sec