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Fluid Flow Questions involving Bernoulli Equation?
Water at 15°C is pumped from a large reservoir to an elevated water storage tank through a 8 cm diameter pipe.
The water surface in the tank is located at an elevation of 26 m above the water surface in the reservoir.
Energy losses due to friction and pipe fittings are equivalent to a total of 18 m of water.
Determine how much energy must be added to the system (in J/kg) so that a constant pumping rate of 0.040 m3/s is maintained.
I know the density of water is 999.1 kg/m3 at 15 degrees C.
I know the diameter needs to be converted to meters = 0.08m, the radius = 0.0016m
Q = 0.040 m^3/s
I just don't really know how to solve for energy... help me please, thanks.
Ignore the radius part of the question, thanks for your help guys!
2 Answers
- ?Lv 51 decade agoFavorite Answer
a pipe with a diameter of 8cm and has a flow rate of 0.040 m^3/s has a velocity of 7.9577 m/s.
and you know the energy conservation equation is (v^2)/2 + g*h + P/rho
since you have everything there, you should be able to solve it very easily. By the way, I'm not sure where that radius of 0.0016 came from??
(7.9577^2)/2 + (18+26)*9.81 = 463.302 J/kg .... Theres no pressure difference
- RoadkillLv 61 decade ago
I dont' have a complete answer but maybe this will get you going in the right direction.
The amount of work being done on each kg of water would be equal to lifting that chunk of water 44 meters height plus friction loss.
The force applied by 1 kg in earths gravitational field would be 9.8 m/s^2 * 1 kg = 9.8 N
the height is 44 m . 9.8 N * 44 m = N*m = joules. Since basis is 1 kg that would be joules per kg of water.