Question

Water flows through a cylindrical pipe of varying cross-section. The velocity is 3.0 m/s at a point where the pipe diameter is 1.0 cm. What is the flow rate R

Answer 1

The flow rate is
`R =2.357 *10^(-4) \ m^3/s`

Step-by-step explanation:

From the question we are told that

The velocity is
`v = 3.0 \ m/s`

The diameter of the pipe is
`d = 1.0 \ cm = 0.01 \ m`

The radius of the pipe is mathematically represented as

`r = (d)/(2)`

substituting values

`r = (0.01)/(2)`

`r = 0.005 \ m`

The flow rate is mathematically represented as

`R = v * A`

Where is the cross-sectional area of the pipe which is mathematically evaluated as

`A = \pi r^2`

substituting values

`A = 3.142 * (0.005)^2`

`A = 7.855 * 10^(-5) \ m^2`

So

`R = 3.0 * 7.855 *10^(-5)`

`R = 2.357*10^(-4) \ m^3 /s`