Yy13 Explanation Given information: The Cartesian velocity components ( u , v ) is ( C y ( x 2 + y 2 ) , − C x ( x 2 + y 2 ) , ) . Write the expression for the radial distance from the origin. r = x 2 + y 2 r 2 = x 2 + y 2 ........... (I) Here, x is Cartesian co-ordinate and y is Cartesian coordinate. Write the expression for the x-coordinate. x = r cos θ ...... (II) Here, the radial distance from the origin is r and angle of given point projected at center from the x-axis is θ . Write the expression for the y-coordinate. y = r sin θ ...... (III) Write the expression for the u r component of velocity. u r = u cos θ + v sin θ ........... (IV) Substitute C y ( x 2 + y 2 ) for u and − C x ( x 2 + y 2 ) for v in the Equation (IV). u r = C y ( x 2 + y 2 ) cos θ − C x ( x 2 + y 2 ) sin θ ........... (V) Write the expression for the u θ component of velocity. u θ = − u sin θ + v sin θ ........... (VI) Substitute C y ( x 2 + y 2 ) for u and − C x ( x 2 + y 2 ) for v in the Equation (VI)

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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 9, Problem 13P

Yy13

To determine

The cylindrical velocity components ur, and uθ of the fluid at the given point.

The nature of the flow.

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Chapter 9, Problem 12P

Chapter 9, Problem 15EP

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The cylindrical velocity components u r , and u θ of the fluid at the given point. The nature of the flow.

Solution Summary: The author explains the cylindrical velocity components u_r, and the radial distance from the origin.

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The cylindrical velocity components ur, and uθ of the fluid at the given point.

The nature of the flow.

Want to see the full answer?

Chapter 9 Solutions

The cylindrical velocity components u r , and u θ of the fluid at the given point. The nature of the flow.

Solution Summary: The author explains the cylindrical velocity components u_r, and the radial distance from the origin.

Concept explainers

Videos

The cylindrical velocity components ur, and uθ of the fluid at the given point. The nature of the flow.

Want to see the full answer?

Chapter 9 Solutions

The cylindrical velocity components ur, and uθ of the fluid at the given point.

The nature of the flow.