Answer:
a) Mechanical efficiency ()=63.15% b) Temperature rise= 0.028ºC
Explanation:
For the item a) you have to define the mechanical power introduced (Wmec) to the system and the power transferred to the water (Pw).
The power input (electric motor) is equal to the motor power multiplied by the efficiency. Thus, .
Then, the power transferred (Pw) to the fluid is equal to the flow rate (Q) multiplied by the pressure jump . So
.
The efficiency is defined as the ratio between the output energy and the input energy. Then, the mechanical efficiency is
For the b) item you have to consider that the inefficiency goes to the fluid as heat. So it is necessary to use the equation of the heat capacity but in a "flux" way. Calling <em>H</em> to the heat transfered to the fluid, the specif heat of the water and the density of the water:
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Finally, the temperature rise is: