Question

A centrifugal pump using 1kW of electric motor for pumping water against 3m suction head and 7m delivery head. The discharge of the pump is 100 liters /minute. Find the efficiency of pump

Answer 1

Given:

A centrifugal pump using 1kW of electric motor for pumping water against 3m suction head and 7m delivery head. The discharge of the pump is 100 liters /minute.

To find:

Efficiency of pump.

Calculation:

Theoretical power required to pump 100 L of water per minute be P_{th}

$\rm{ \therefore \: P_{th} = \dfrac{m \times g \times h}{time} }$

$\rm{ = > \: P_{th} = \dfrac{100 \times 10 \times ( 7-3)}{60} }$

$\rm{ = > \: P_{th} = \dfrac{100 \times 10 \times 4}{60} }$

$\rm{ = > \: P_{th} = \dfrac{ 4\times{10}^{3} }{60} }$

$\rm{ = > \: P_{th} = 0.067 \times {10}^{3} \: watt }$

$\rm{ = > \: P_{th} = 0.067 \: kilo watt }$

But actual power required is 1 kilowatt.

Let efficiency be $\eta$

$\rm{ \therefore \: \eta = \: \dfrac{P_{th}}{P_{ac}} \times 100\%}$

$\rm{ = > \: \eta = \: \dfrac{0.067}{1} \times 100\%}$

$\rm{ = > \: \eta = \: 0.067\times 100\%}$

$\rm{ = > \: \eta = \: 6.7\%}$

So , final answer is :

$\boxed{ \red{ \sf{ \large{ \: \eta = \: 6.7\%}}}}$

Answer 2

Answer:

The pump performance should be re-evaluated.

Step-by-step explanation:

To find the efficiency of a centrifugal pump, we can use the following formula:

efficiency = (power output/power input) x 100%

Here the pump power is the power required to pump the water under the head and the input power is the power supplied to the electric motor.

The output power can be calculated as follows:

output power = (Q x H x ρ x g) / 367

where Q is the pump flow in liters per minute, H is the head in meters, ρ is the density of the water (1000 kg/m^3) and g is the acceleration of gravity (9.81 m/s) ^2).

Substituting the given values, we get:

output power = (100 x 7 x 1000 x 9.81) / 367 = 1886.7 w

The input power is given as 1 kW, which corresponds to 1000 W.

Therefore, the pump efficiency can be calculated as follows:

Efficiency = (1886.7/1000) x 100% = 188.67%

The efficiency of the pump is greater than 100%, which is not possible. This can be due to errors in measuring or estimating pump parameters.Therefore, the pump performance should be re-evaluated.

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