The horsepower (hp) that a shaft can safety transmit varies jointly with its speed (in revolutions per minute, or rpm) and the cube of the diameter. If a shaft of a certain material 2 in in diameter can transmit 36 hp at 75 rpm, what diameter must the shaft have in order to transmit 150 hp at 20 rpm?

Answer 1

just plug and chug:

hp = k*s*d^3

36 = k * 75 * 2^3

k = 36/(75 * 8) = 36/600

now, for the unknown d

150 = k * 20 * d^3
150 = 36/600 * 20 * d^3

150 * 600/36 * 1/20 = d^3

125 = d^3