The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute, rpm) and the cube of its diameter. If a shaft of a certain material 2 inches in diameter can transmit 36 hp at 75 rpm, what diameter must the shaft have in order to transmit 375 hp at 50 rpm?

d = 5 inch

Explanation:

First to all we need to get the expression to calculate the horsepower.

The expression to use is the following:

hp = k * v * d³ (1)

Where:

hp: horsepower

v: speed (in rpm)

d: diameter

k: constant of horsepower.

The value of k, because is a constant, will be the same when the shaft is transmiting 375 hp at 50 rpm. So, with the first data, we can calculate the value of k, and then, the value of the diameter

Solving for k in (1) we have:

k = hp / v * d³

replacing the dа ta:

k = 36 / 75 * 2³

k = 0.06

With this value, we can solve for d and we have:

d = ∛hp / k * v

d = ∛375 / 50 * 0.06

d = 5 inch