Question

A steel tube having an outer diameter of 2.5 in. is used to transmit 9 hp when turning at 27 rev/min. 1 hp = 550 ft?lb/s. Determine the inner diameter d of the tube if the allowable shear stress is ?allow = 10ksi . it is a hollow tube.

Answer 1

Concepts and reason

Angular velocity:

The rate at which the angular position of a turning object changes with respect to time is referred as angular velocity. It is denoted by and its unit is.

Power:

Power is defined as the rate of doing work per unit time. It is denoted by and its unit is Watts.

Torque:

Torque is referred as the turning force which makes the object to turn about an axis. It is denoted by and its unit is.

Allowable shear stress:

Allowable shear stress is the ratio between the yield stress and the safety factor. It is also referred as the quantity of shear stress that the material can withstand without failure.

Fundamentals

The formula for calculating the angular velocity is as follows:

Here, rotating speed is in .

The formula for calculating the power is as follows:

Here, power is and torque is .

The polar moment of inertia is expressed as follows:

Here, diameter of the cylinder is .

Calculate the angular velocity.

Here, turning speed of the steel tube is.

Substitute for.

Calculate the torque produced by the steel tube.

Substitute for and for.

Calculate the polar moment of inertia.

Here, allowable shear stress is, outer radius of the tube is and polar moment of inertia is.

Substitute for, for and for.

Calculate the inner diameter of the tube using the formula of the polar moment of inertia.

Here, outer diameter of the tube is and inner diameter of the tube is.

Substitute for and for.

Ans:

The inner diameter of the tube is.