Explanation Given information: The radial velocity component is 0 , angular velocity component is ω r and z-direction velocity component is 0 . Write the expression for θ component of Navier-Strokes equation. μ ( 1 r ∂ ∂ r ( r ∂ u θ ∂ r ) − u θ r 2 + 1 r 2 ∂ 2 u θ ∂ θ 2 − 2 r 2 ∂ u r ∂ θ + ∂ 2 u θ ∂ z 2 ) ...... (I) Here, radial velocity component u r , angular velocity component is u θ and z-direction velocity component is u z . Write the expression for vorticity along z component in cylindrical coordinate. ζ z = 1 r ( ∂ ( r u θ ) ∂ r − ∂ u r ∂ θ ) ...... (II) Calculation: Substitute 0 for u r , ω r for u θ and 0 for u z in Equation (I). μ ( 1 r ∂ ∂ r ( r ∂ ( ω r ) ∂ r ) − ω r r 2 + 1 r 2 ∂ 2 ( ω r ) ∂ θ 2 − 2 r 2 ∂ ( 0 ) ∂ θ + ∂ 2 ( ω r ) ∂ z 2 ) = μ (

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ISBN: 9781266016042

Author: CENGEL

Publisher: MCG CUSTOM

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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

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Chapter 10, Problem 107P

To determine

The viscous term of the θ component of the Navier-stroke equation

The z-component of vorticity.

The nature of flow.

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Chapter 10, Problem 106CP

Chapter 10, Problem 108P

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The viscous term of the θ component of the Navier-stroke equation The z-component of vorticity. The nature of flow.

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