308-22-25 - NCSU MAE308 22. Assuming frictionless,...

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NCSU MAE308 22. Assuming frictionless, incompressible, one-dimensional flow of water through the horizontal tee connection sketched below, estimate values of the x and y components of the force exerted by the tee on the water. The flowrate in Section 3 is 10 m 3 /s. The velocity and pressure in Section 1 are 6 m/s and 200 kPaG, respectively. Each pipe has an inside diameter of 1 m. Section (1) Section (2) Section (3) x y z Horizontal z 1 = z 2 = z 3 73 . 12 ) 1 ( 4 π 10 A Q v 2 3 3 3 = = = m/s Conservation of Mass Q 1 + Q 2 = Q 3 →v 1 A 1 + v 2 A 2 = v 3 A 3 v 2 =v 3 -v 1 =12.73-6=6.73 m/s BE for fluid particle flowing from (1) to (3) 13 f 13 s 3 2 3 3 1 2 1 1 w w gz v 2 1 ρ p gz v 2 1 ρ p + + + + = + + 137037 ) 73 . 12 6 ( 2 999 200000 ) v v ( 2 ρ p p 2 2 2 3 2 1 1 3 = - + = - + = PaG BE for fluid particle flowing from (2) to (3) 23 f 23 s 3 2 3 3 2 2 2 2 w w gz v 2 1 ρ p gz v 2 1 ρ p + + + + = + + Note that the work terms in each BE are different. 195358 ) 73 . 6 73 . 12 ( 2 999 137037 ) v v ( 2 ρ p p 2 2 2 2 2 3 3 2 = - + = - + = PaG Conservation of Momentum ∫ ∫ = cs n dA v ρ F v (1): v x =-v 1 , v y =0, v n =-v 1 (2): v x =0, v y =-v 2 , v n =-v 2 (3): v x =0, v y =-v 3 , v n =+v 3 x-momentum
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This note was uploaded on 08/01/2008 for the course MAE 308 taught by Professor Danby during the Fall '08 term at N.C. State.

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308-22-25 - NCSU MAE308 22. Assuming frictionless,...

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