example 11-2 - Example 11-2 Oil (SG = 0.67) flows upwards...

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Example 11-2 Oil ( SG = 0.67) flows upwards through a transition piece which has the shape of a truncated cone. The oil enters at 16 ft/s with an absolute pressure of 20 psia. Assume the flow is incompressible and inviscid. The volume of the truncated cone can be calculated as 165 in 3 . Determine a) exit velocity 2 V b) exit pressure P 2 c) anchoring force (include the weight of the oil, but not the weight of the pipe itself.)
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Solution: a) From conservation of mass 12 mm = ±± Assuming the oil is incompressible 11 2 2 A A ρ = V 2 2 A A = () ( ) 2 2 2 1 1 3 ft 0.0491ft 22 1 2 D A ππ ⎛⎞ == = ⎜⎟ ⎝⎠ 2 2 2 2 2 7 ft 0.267ft 1 2 D A = 2 2 2 ft 16 0.0491ft ft s 2.94 s 0.267ft b) To find pressure, apply the Bernoulli equation PP gz gz ρρ ++=++ VV 21 2 P Pg =+ + z z ( ) water SG = EES can be used to convert units: 3 lbm 1000*convert(kg/m^3,lbm/ft^3) 62.4 ft water
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() 33 lbm lbm 0.67 62.4 41.8 ft ft ρ ⎛⎞ == ⎜⎟ ⎝⎠ 22 2 2 2 23 2 2 2 32 2 2 16 2.94 lbf lbm ft 1lbf 1ft 20 41.8 lbm ft in ft 2 s 144in 32.2 s lbm ft 8 1lbf 1ft 41.8 32.2 ft lbm ft ft s 12 32.2 s P ⎛⎞⎛ =+ +
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example 11-2 - Example 11-2 Oil (SG = 0.67) flows upwards...

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