Question

A pump is pumping water at a flow rate of 1200 litres per minute. In the pump the mechanical energy of the water increases by 250 J/kg. The density of water is 1000 kg/m3.
a) Determine the pressure difference between the pump outlet and the pump inlet. Assumptions: there are no frictional losses in the pump, and differences in velocity and elevation between inlet and outlet of the pump can be neglected.
b) Show that the mechanical power added to the water flow is 5.0 kW. We call this the useful pumping power.

For the next section, assume that the useful pumping power is 5.0 kW. The pump is driven by an internal combustion engine. A gearbox is installed between the engine and the pump to have optimal rotational speeds of engine and pump. Further information: efficiency of the internal combustion engine is 27% ; efficiency of the gearbox is 95%; efficiency of the pump is 70%; the fuel used by the engine is diesel oil with a heating value of 44 MJ/kg. To support your calculations, make a sketch (block diagram) of the total system and show by means of arrows and symbols the flows of heat and work.
c) Determine the frictional losses in the pump in kW.
d) Determine the shaft power of the internal combustion engine
e) Determine the fuel consumption of the engine in kg per hour

Answer 1

Flow rate is l2004trulmin-0.02 m?/sec冫 Enerpy increased is 250 J/ - 20 kg /sec ied) x (tlouo rate) (250) (20) = 5000W, 5 kW e) Ramp is 70% efheent, Sothe frichoal lossen adont Mechanical power added is Enc forthe d) Shaft is 95% efheant , i.e 95 the shalt Puer is skW Sothe shalt Poser is R =100 x5z 5.263 kW. Now the engine is 27% ethcent, ie the Oulput of eng ine is onlJ wer and 1.4a3 ku 27 in pua to,he engine in an hour is E =尼 3600:09.493) x (103)(36,00)丁ん -so-lne ener 7 -So the rate a, which d is ansured is zend 1.595 k hr