221k views
4 votes
Water flows through a pipe diameter of 8.000 cm at 49.0 m/min. Find the flow rate in m3/min

User Fried Rice
by
7.6k points

1 Answer

3 votes

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.

User Pengdu
by
6.7k points