example 15-1 - Example 15-1 Water is pumped through a 3 cm...

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Example 15-1 Water is pumped through a 3 cm diameter pipe to an elevated reservoir, as shown. The reservoir is very large; therefore, the velocity of the top surface is approximately zero. At a certain time, the height of water in the reservoir is 290 cm above the level of the pump. Neglecting viscous effects, calculate the power input to the pump. Solution: Begin by finding the pressure at point 2. From Bernoulli’s equation 2 2 33 22 23 P P gz gz ρρ ++= ++ V V The velocity at point 2 can be determined using the velocity at point 1 and conservation of mass.
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12 mm = ±± 111 2 22 A A ρ = V The fluid (water) is incompressible. The area does not change between 1 and 2, so = 3 kg density(water, 20, 105) 998 m TP == = = () 22 32 23 2 P Pg ρρ ⎛⎞ =+ + ⎜⎟ ⎝⎠ V z z 2 2 2 4.7 kg m 1kPa 101kPa 998 m2 s 1 0 0 0 P P =+ ⎜⎟ a kg m 1kPa 998 9.81 2.9m m s 1000Pa + 2 118.4kPa P = Now that pressure at point 2 is known, the power required for the pump may be calculated from
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This note was uploaded on 04/06/2009 for the course ENGR 2250 taught by Professor Borca-tasciuc during the Spring '08 term at Rensselaer Polytechnic Institute.

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example 15-1 - Example 15-1 Water is pumped through a 3 cm...

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