Question

The maximum flow of water in a pipe is modeled by the formula Q=Av, where A is the cross-sectional area of the pipe and V is the velocity of the water. Find the diameter of a pipe that allows a maximum flow of 50ft^3/min of water flowing at a velocity of 600ft/min

Answer 1

For this case we have the following equation:
 Q = Av
 Where the area is given by:
 A = pi * r ^ 2
 A = pi * (d / 2) ^ 2
 A = (pi / 4) * d ^ 2
 Substituting we have:
 Q = ((pi / 4) * d ^ 2) v
 From here, we clear the diameter:
 d = root ((4 / pi) * (Q / v))
 Substituting values we have:
 d = root ((4 / pi) * (50/600))
 d = 0.36 feet
 Answer:
 The diameter of a pipe that allows a maximum flow of 50ft ^ 3 / min of water flowing at a velocity of 600ft / min is:
 d = 0.36 feet