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:

$A=\frac{\pi D^2}{4}$

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:

$8.000cm\times\frac{1m}{100cm}=0.080m$

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

$A=\frac{\pi(0.080m)^2}{4}$

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:

$R=(0.005m^2)(49.0\frac{m}{\min })$

Solving the operations:

$R=0.246\frac{m^3}{min}$

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