Answer:
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 data:
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
