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

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