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Unformatted text preview: ME 309 Fall 2008 Section 2 (Merkle) Homework # 25 Due Wed 29 Oct 2008 Problem 251 . a) A plumber connects two sections of 20 mm diameter pipe with a short section of 10 mm pipe. Estimate the extra pressure drop associated with this connector as opposed to a single length of pipe if the average water velocity is 5 m/s . b) Upon realizing his mistake, the plumber replaces the 10 mm section with a short section of 30 mm pipe. What is the effect of this larger section on the pressure drop as compared to a single length of pipe at an average flow velocity of 5 m/s . c) Is it possible that a 25 mm connector would provide less pressure drop than the 30 mm one? (i.e. are there times when larger diameters create more pressure drop than smaller ones?) Explain. Assume that the connector section is short enough that you can neglect the major loss in the connector section. For this problem, you may either use Fig. 8.15 or a ‘digitized’ approximation: 3 2 975 . * 45 . 1 * 025 . 5 . AR AR AR K cont + = ( ) 2 exp . 1 AR K = to compute the loss coefficients for an expansion or contraction. Solution: a b D=10 mm D=20 mm D=20 mm D=20 mm D=20 mm D=30 mm Given: m D h 020 . = m D h 010 . = s m u avg / 5 = Find n contractio p Δ Assumptions: steady, fully developed flow Constant properties Incompressible fluid Analysis: Analysis: diameter ratio: = 50 . 020 . 010 . = Area ratio: 0.25 Find K values from above equations: Sudden contraction: K ext = 0.563 Sudden expansion: K cont = 0.418 Mechanical energy equation: ( ) m L out out out avg out in in avg in h h m W gz u p gz u p + + + + + = + + ρ ρ ρ αρ ρ αρ & & 2 , 2 , 2 1 2 1 No change in elevation No change in average velocity from inlet to outlet No work done Only calculate the additional loss from the contraction—drop the h_L term...
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 Spring '08
 MERKLE
 Orders of magnitude, pressure drop

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