Question

1. consider the pipe shown below. the average speed of water flowing through the 6-inch-diameter pipe is 3 ft/s. what is the volume flow rate of water in the pipe? express the volume flow rate in ft³/s. (5 points)

Explanation:

Step1: Convert diameter to feet

The diameter of the pipe is 6 inches. Since 1 foot = 12 inches, we convert inches to feet: $d = \frac{6}{12} = 0.5$ ft. The radius $r$ is half of the diameter, so $r=\frac{0.5}{2}= 0.25$ ft.

Step2: Calculate the cross - sectional area of the pipe

The pipe is circular, so the cross - sectional area $A$ is given by the formula for the area of a circle $A=\pi r^{2}$. Substituting $r = 0.25$ ft, we get $A=\pi(0.25)^{2}=\pi\times0.0625\approx0.19635$ $ft^{2}$.

Step3: Calculate the volume flow rate

The volume flow rate $Q$ is given by the product of the cross - sectional area $A$ and the average velocity $v$. The formula is $Q = A\times v$. We know that $A\approx0.19635$ $ft^{2}$ and $v = 3$ ft/s. So $Q=0.19635\times3\approx0.589$ $ft^{3}/s$ (or using the exact formula $Q=\pi r^{2}v=\pi\times(0.25)^{2}\times3=\frac{3\pi}{16}\approx0.589$ $ft^{3}/s$).

Answer:

The volume flow rate of water in the pipe is approximately $\boldsymbol{0.589}$ $ft^{3}/s$ (or $\frac{3\pi}{16}\approx0.589$ $ft^{3}/s$).