What is the velocity in feet per second in a 12-inch diameter pipe at a flow rate of 1200 gpm?

To determine the velocity of water flowing through a pipe, you can use the formula:

[ V = \frac{Q}{A} ]

where ( V ) is the velocity in feet per second, ( Q ) is the flow rate in cubic feet per second, and ( A ) is the cross-sectional area of the pipe in square feet.

First, convert the flow rate from gallons per minute (gpm) to cubic feet per second (cfs). The conversion factor is:

[ 1 \text{ gpm} = \frac{1}{448.831} \text{ cfs} ]

So, for a flow rate of 1200 gpm:

[ Q = 1200 \text{ gpm} \times \frac{1}{448.831} \approx 2.673 \text{ cfs} ]

Next, calculate the cross-sectional area ( A ) of a 12-inch diameter pipe. To find the area:

1. Convert the diameter from inches to feet:

[ 12 \text{ inches} = 1 \text{ foot} ]

2. Calculate the radius:

[ r = \frac{1}{