Explanation Given: The damping torque relation is T d a m p i n g = C ω . Constant C is 0.5 π μ ( 1 a + 1 b ) R 4 . Velocity profiles are linear on both sides. The tip effects are neglected. Write the expression for the shear stress. τ = μ d u d y ...... (I) Here, shear stress is τ , dynamic viscosity is μ and velocity gradient is d u d y . Velocity is u and thickness of the film is y . Write the expression for the velocity of the disk. V = r ω ...... (II) Here, velocity is V , radius of the disk is r and angular velocity is ω . Write the expression for the shear force. d F = τ d A ...... (III) Here, shear force is d F and area is d A . Write the expression for the area of disk. A = 2 π r d r ...... (IV) Here, radius of the disk is r . Write the expression for the torque generated. d T = r d F ...... (V) Here, torque is T . Write the expression for the total torque or damping torque. T d a m p i n g = T t o p + T b o t t o m ...... (VI) Substitute y for d y and r ω for the V in Equation (I). τ = μ r ω y ...... (VII) Substitute Equation (VII) in Equation (III). d F = μ r ω y d A ...... (VIII) Substitute Equation (VIII) in Equation (V). d T = r ( μ r ω y d A ) = μ ω r 2 y ( 2 π r d r ) Integrating above Equation with respect to r

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ISBN: 8220103676205

Author: CENGEL

Publisher: YUZU

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Chapter 2, Problem 131P

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To prove:

That damping torque is proportional to angular speed with relation Tdamping=Cω.

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Chapter 2, Problem 130P

Chapter 2, Problem 132P

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To prove: That damping torque is proportional to angular speed with relation T d a m p i n g = C ω .

Solution Summary: The author demonstrates that damping torque is proportional to angular speed with relation T_damping=Comega .

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To prove:

That damping torque is proportional to angular speed with relation Tdamping=Cω.

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Chapter 2 Solutions

To prove: That damping torque is proportional to angular speed with relation T d a m p i n g = C ω .

Solution Summary: The author demonstrates that damping torque is proportional to angular speed with relation T_damping=Comega .

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To prove: That damping torque is proportional to angular speed with relation Tdamping=Cω.

Want to see the full answer?

Chapter 2 Solutions

To prove:

That damping torque is proportional to angular speed with relation Tdamping=Cω.