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 45hp at 100 rpm, what must the diameter be in order to transmit 60hp at 150rpm?

Respuesta :

The the diameter of the shaft is  to be in order to transmit 60 hp at 150 rpm 1.88 inch.

Explain the term horsepower?

  • Power is measured in hp, which is the standard abbreviation for horsepower.
  • The rate of job completion can be used to describe power in this context.
  • Most frequently, the term "horsepower" is used to describe an engine or motor's output.

We must first obtain the formula for calculating horsepower.

The phrase to use is as follows:

hp = k  × v  × d³ ......eq(1)

Where:

  • hp is horsepower
  • v is speed (in rpm)
  • d is diameter
  • k is constant of horsepower.

Since k is a constant, it will always have the same value when the shaft is transferring 60 horsepower at 150 rpm.

Therefore, using the first set of information, we can determine the value of k and subsequently the diameter.

When we solve for k in (1), we get:

k = hp / (v × d³)

Put the values;

k = 45 / (100  × 3³)

k = 0.02

Put the value of k and solve for diameter.

d = ∛hp / (k   × v)

d = ∛60 / (150 × 0.06)

d = 1.88 inch

Thus, the the diameter of the shaft is  to be in order to transmit 60 hp at 150 rpm 1.88 inch.

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