Question

Water flows through a pipe diameter of 8.000 cm at 49.0 m/min. Find the flow rate in m3/min

Answer 1

We are asked to determine the volumetric flow rate through a pipe of diameter 8.000 cm. To do that we will use the following formula:

`R=Av`

Where:

`\begin{gathered} R=\text{ volumetric flow rate} \\ A=\text{ cross-area of the pipe} \\ v=\text{ velocity of the flow} \end{gathered}`

The cross-area of the pipe is the area of a circle and is given by:

`A=(\pi D^2)/(4)`

Where:

`\begin{gathered} A=\text{ cross-area} \\ D=\text{ diameter} \end{gathered}`

Before we determine the area we will convert the diameter from cm to meters using the following conversion factor:

`100cm=1m`

Multiplying by the conversion factor we get:

`8.000cm*(1m)/(100cm)=0.080m`

Now, we plug in the value in the formula for the area:

`A=(\pi(0.080m)^2)/(4)`

Solving the operations:

`A=0.005m^2`

Now, we plug in the values of area and velocity in the formula or the volumetric flow rate:

`R=(0.005m^2)(49.0(m)/(\min ))`

Solving the operations:

`R=0.246(m^3)/(min)`

Therefore, the flow rate is 0.246 cubic meters per minute.