(a)
The Relationship for the torque transmitted by an MR clutch for N plates attached to the input shaft rotating at an angular speed of

Answer to Problem 129P
The Relationship for the torque transmitted by an MR clutch for N plates attached to the input shaft rotating at an angular speed of
Explanation of Solution
Given:
The shear stress used for the Herschel-Bulkley constitute model is
Write the expression for the velocity gradient.
Here, velocity is
Write the expression for shear stress.
Here, yield stress is is
Power index is
Substitute Equation in Equation (II).
Write the expression for the velocity of shaft.
Here, angular velocity is
Substitute Equation (IV) in Equation (III).
Write the expression for the force.
Here, area is
Substitute
Write the expression for the torque generated.
Substitute
Calculation:
Integrate both sides of the Equation (IX).
Write the expression for the torque generated by the both surfaces of the plate.
Write the expression for the torque generated by the
Conclusion:
The torque generated by the MR clutch is
(b)
Torque transmitted by the clutch.

Answer to Problem 129P
Torque transmitted by the clutch is
Explanation of Solution
Given information:
The number of plate clutch is
Write the expression for the angular speed of the shaft.
Here, speed of the shaft is
Write the expression for the torque generated.
Calculation:
Substitute
Substitute
Conclusion:
The torque generated is
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