Explanation Given information: The Cartesian co-ordinate ( x , y ) is ( 0.4 m,0 .20 m ) and velocity component ( u , v ) is ( 10.3 m / s , − 5.6 m / s ) . Write the expression for the radial distance from the origin. r = x 2 + y 2 ........... (I) Here, x and y are Cartesian co-ordinate. Write the expression for the angle measured from the x-axis. θ = tan − 1 ( y x ) ...... (II) Write the expression for the u r component of the velocity. u r = u cos θ + v sin θ ........... (III) Write the expression for the u θ component of the velocity. u θ = − u sin θ + v sin θ ........... (IV) Calculation: Substitute 0.4 m for x , 0.2 m for y in the Equation (I). r = ( 0.4 m ) 2 + ( 0.2 m ) 2 = ( 0.2 m ) 2 = 0.447 m Substitute 0.4 m for x , 0.2 m for y in the Equation (II). θ = tan − 1 ( 0.2 m 0.4 m ) = tan − 1 ( 0

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Chapter 9, Problem 12P

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The cylindrical coordinates r, θ, ur, and uθ of the fluid at the given point.

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The cylindrical coordinates r , θ , u r , and u θ of the fluid at the given point.

Solution Summary: The author explains the cylindrical coordinates of the fluid at the given point.

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The cylindrical coordinates r, θ, ur, and uθ of the fluid at the given point.

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