Final answer:
To calculate the pipe diameter from the given flow rate and velocity, we find the cross-sectional area and then use the area to determine the diameter. The pipe's diameter comes out to be 24 inches.
Step-by-step explanation:
The student is asking about the relationship between flow rate, cross-sectional area, and velocity in a pipe, which involves the use of the continuity equation from fluid mechanics, a topic in physics. The flow rate (Q) through a pipeline is given, and we know the velocity (v) of the water. The cross-sectional area (A) of the pipe can then be found using the equation Q = A * v. To find the area, rearrange the equation to A = Q / v: A = 8 ft³/s / 2.55 ft/s = 3.137 ft² To find the diameter of the pipe, we need to relate the area to the diameter using the area of a circle formula, A = π * (d/2)^2. Solving for d gives: d = 2 * sqrt(A / π) d = 2 * sqrt(3.137 ft² / 3.14159) d ≈ 2 ft Since 1 foot = 12 inches, the diameter in inches is 2 ft * 12 inches/ft = 24 inches.