A frustum-shaped body is rotating at a constant angular speed of 200 rad/s in a container filled with SAE 10W oil at 20°C (
The torque required to rotate the inner cylinder at constant speed.
And the torque required for motion at
Answer to Problem 85P
The torque required to rotate the inner cylinder at constant speed is
And the torque required for motion at
Explanation of Solution
Given information:
The dynamic viscosity of oil at
Write the expression for shear stress on the surface of frustum.
The wall shear is
Substitute
Here, angular velocity of the container is
Write the expression for shear force.
Here, area of the frustum is
Substitute
Write the expression for torque developed.
Here, torque developed is
Substitute
Write the expression for torque by integrating Equation (V).
Write the expression for shaft power developed.
Here, developed shaft power is
Substitute
Write the expression for shaft power for the top surface.
Substitute
Substitute
Here, diameter of frustum at the top is
Substitute
Here, diameter of frustum at the bottom is
Substitute
Substitute
Here, shaft power for the side surface is
Write the expression to obtain value of
Differentiate
Substitute
Write the expression for total shaft power.
Substitute
Write the expression for power required to maintain the motion at
Here, viscosity at
Write the expression for reduction in power input required when the oil pressure rise at
Here, total shaft power at
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The torque required to rotate the inner cylinder at constant speed is
And the torque required for motion at
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Chapter 2 Solutions
Fluid Mechanics: Fundamentals and Applications
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