Lecture 21 Notes - EGN 3353C Fluid Mechanics Lecture 21...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 21 Example 3 A reducing elbow is used to deflect water flow at a rate of 14 kg/s in a horizontal pipe upward θ = 30° while accelerating it. The elbow discharges water into the atmosphere. The cross-sectional area of the elbow is A 1 =113 cm 2 at the inlet and A 2 =7 cm 2 at the outlet. The elevation difference between the centers of the outlet and the inlet is 30 cm. The weight of the elbow and the water in it is considered to be negligible. Determine (a) the gage pressure at the center of the inlet of the elbow and (b) the anchoring force needed to hold the elbow in place. Sol Assume : (1) steady, (2) incompressible, (3) uniform flow at inlet and exit, (4) neglect body forces CV Draw fixed CV as shown. Note it is outside (not inside) to avoid shear forces at wall. Denote “1” as inlet and “2” as exit. Continuity 11 2 2 VA V m A ρρ ρ == = G ± x-momentum x CV d Fu d dt =∀ r CS u V ndA +⋅ G G ( ) ( ) 1, 1 1 2 cos x gage R PA FV m V m θ += + ±± (1) Æ 2 unknowns Æ need another equation Bernoulli : If we follow a streamline from the center of inlet to center of the outlet and neglect friction (which is not really true here), then
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This note was uploaded on 08/17/2011 for the course EGN 3353C taught by Professor Lear during the Spring '07 term at University of Florida.

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Lecture 21 Notes - EGN 3353C Fluid Mechanics Lecture 21...

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