While performing a fire hazard survey on a structure in a non-hydrant area you need to estimate the water supply capacity of a stream adjacent to the structure as a possible drafting site. The stream is 5' wide and the average depth is 12". You observe that a leaf floating on the surface travels 10 feet in 30 seconds from the current. What is the approximate flow rate in gallons per minute (GPM) of the stream?
To estimate the flow rate of the stream, we use the formula for flow rate: Q = A * V, where Q is the flow rate, A is the cross-sectional area of the stream, and V is the velocity of the water. First, calculate the area. The stream's width is 5 feet, and the average depth is 12 inches, which is 1 foot, so the cross-sectional area (A) is 5 feet * 1 foot = 5 square feet. Next, calculate the velocity (V). A leaf floats 10 feet in 30 seconds, so the velocity is 10 feet / 30 seconds = 0.33 feet per second. To find the flow rate in cubic feet per second, multiply the area by the velocity: 5 square feet * 0.33 feet per second = 1.65 cubic feet per second. Convert cubic feet per second to gallons per minute by multiplying by 448.831 (since 1 cubic foot per second is approximately 448.831 GPM): 1.65 * 448.831 ≈ 740.56 GPM. Therefore, the approximate flow rate of the stream is closest to 750 GPM.
I keep coming up with 750. 7.481 gallons per cubic foot x 5 feet x 20 feet in one minute = 748