Question

The horsepower (hp) that a shaft can safely transmit varies jointly with its speed, in revolutions per minute (rpm), and the cube of the diameter. If the shaft of a certain material 3 inches in diameter can transmit 46 hp at 100 rpm, what must the diameter be in order to transmit 74 hp at 175 rpm?

Answer 1

Answer:

diameter ≅  3 inches

Explanation:

$HP=k*s*d^{3}$

Use a constant factor, k

Let Hp = horsepower

Let s = speed in rpm

Let d = diameter in inches

to find constant k, using

Hp=46

S=100

d=3 in

$46=k*100*3^{3} \\\\46=k*100*27\\46=2700k\\k=\frac{46}{2700} \\k=0.017$

 

To find diameter when;

Hp=74

S=175

k=0.017

d=d inches

$74=0.017*175*d^{3} \\\\74=2.975*d^3\\d^3=\frac{74}{2.975} \\d=\sqrt[3]{24.87} \\d=2.9 inches$  d≅ 3 inches