ch06solutions

ch06solutions - Problem 6.1 [2] Given: Velocity field Find:...

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Unformatted text preview: Problem 6.1 [2] Given: Velocity field Find: Acceleration of particle and pressure gradient at (1,1) Solution: NOTE: Units of B are s-1 not ft-1 s-1 Basic equations For this flow u x y , ( ) A y 2 x 2 ( ) B x = v x y , ( ) 2 A x y B y + = a x u x u v y u + = A y 2 x 2 ( ) B x x A y 2 x 2 ( ) B x 2 A x y B y + ( ) y A y 2 x 2 ( ) B x + = a x B 2 A x + ( ) A x 2 B x + A y 2 + ( ) = a y u x v v y v + = A y 2 x 2 ( ) B x x 2 A x y B y + ( ) 2 A x y B y + ( ) y 2 A x y B y + ( ) + = a y B 2 A x + ( ) B y 2 A x y + ( ) 2 A y B x A x 2 y 2 ( ) + = Hence at (1,1) a x 1 2 1 1 + ( ) 1 s 1 1 2 1 1 + 1 1 2 + ( ) ft s = a x 9 ft s 2 = a y 1 2 1 1 + ( ) 1 s 1 1 2 1 1 1 + ( ) ft s 2 1 1 1 s 1 1 1 1 2 1 2 ( ) + ft s = a y 7 ft s 2 = a a x 2 a y 2 + = atan a y a x = a 11.4 ft s 2 = 37.9 deg = For the pressure gradient x p g x a x = 2 slug ft 3 9 ft s 2 lbf s 2 slug ft = x p 18 lbf ft 2 ft = 0.125 psi ft = y p g y a y = 2 slug ft 3 32.2 7 ( ) ft s 2 lbf s 2 slug ft = y p 78.4 lbf ft 2 ft = 0.544 psi ft = Problem 6.2 [2] Given: Velocity field Find: Acceleration of particle and pressure gradient at (0.7,2) Solution: Basic equations For this flow u x y , ( ) A x B y = v x y , ( ) A y = a x u x u v y u + = A x B y ( ) x A x B y ( ) A y ( ) y A x B y ( ) + = a x A 2 x = a y u x v v y v + = A x B y ( ) x A y ( ) A y ( ) y A y ( ) + = a y A 2 y = Hence at (0.7,2) a x 1 s 2 0.7 m = a x 0.7 m s 2 = a y 1 s 2 2 m = a y 2 m s 2 = a a x 2 a y 2 + = atan a y a x = a 2.12 m s 2 = 70.7 deg = For the pressure gradient x p g x a x = 1000 kg m 3 0.7 m s 2 N s 2 kg m = x p 700 Pa m = 0.7 kPa m = y p g y a y = 1000 kg m 3 9.81 2 ( ) m s 2 N s 2 kg m = y p 11800 Pa m = 11.8 kPa m = Problem 6.3 [2] Problem 6.4 [2] Problem 6.5 [2] Given: Velocity field Find: Acceleration of particle and pressure gradient at (1,1) Solution: Basic equations For this flow u x y , ( ) A x 2 y 2 ( )...
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This note was uploaded on 03/09/2010 for the course ME 309 taught by Professor Merkle during the Spring '08 term at Purdue.

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ch06solutions - Problem 6.1 [2] Given: Velocity field Find:...

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