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:
[tex]R=Av[/tex]Where:
[tex]\begin{gathered} R=\text{ volumetric flow rate} \\ A=\text{ cross-area of the pipe} \\ v=\text{ velocity of the flow} \end{gathered}[/tex]The cross-area of the pipe is the area of a circle and is given by:
[tex]A=\frac{\pi D^2}{4}[/tex]Where:
[tex]\begin{gathered} A=\text{ cross-area} \\ D=\text{ diameter} \end{gathered}[/tex]Before we determine the area we will convert the diameter from cm to meters using the following conversion factor:
[tex]100cm=1m[/tex]Multiplying by the conversion factor we get:
[tex]8.000cm\times\frac{1m}{100cm}=0.080m[/tex]Now, we plug in the value in the formula for the area:
[tex]A=\frac{\pi(0.080m)^2}{4}[/tex]Solving the operations:
[tex]A=0.005m^2[/tex]Now, we plug in the values of area and velocity in the formula or the volumetric flow rate:
[tex]R=(0.005m^2)(49.0\frac{m}{\min })[/tex]Solving the operations:
[tex]R=0.246\frac{m^3}{min}[/tex]Therefore, the flow rate is 0.246 cubic meters per minute.
