jazzcutie0h
2021-11-20
Answered

A water pump that consumes 2 kW of electric power when operating is claimed to take in water from a lake and pump it to a pool whose free surface is 30 m above the free surface of the lake at a rate of 50 L/s. Determine if this claim is reasonable.

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mylouscrapza

Answered 2021-11-21
Author has **22** answers

Givens:

Power=2kW=2000 W

$\mathrm{\u25b3}z=30\text{}m$

$V}_{ol}=50\text{}\frac{L}{s}=\frac{0}{05}\text{}\frac{{m}^{3}}{s$

$g=9.8\text{}\frac{m}{{s}^{2}}$

Solution:

The total cahnge in the system mechanical energy can be calculated as follows,

$\mathrm{\u25b3}e=g\mathrm{\u25b3}z=9.8\times 30=294\text{}J$

The power required can be calculated as follows,

$Power=m\mathrm{\u25b3}e=\rho {V}_{ol}\mathrm{\u25b3}e=14700\text{}W=14.7\text{}kW$

The claim is false as the claimed power consumption is 2 kW which is much less than the required power consumption (14.7 kW)

Result: The claim is false as the claimed power consumption is 2 kW which is much less than the required power consumption (14.7 kW).

Power=2kW=2000 W

Solution:

The total cahnge in the system mechanical energy can be calculated as follows,

The power required can be calculated as follows,

The claim is false as the claimed power consumption is 2 kW which is much less than the required power consumption (14.7 kW)

Result: The claim is false as the claimed power consumption is 2 kW which is much less than the required power consumption (14.7 kW).

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