Question

✬ Hey There!

A water pump takes 20 minutes to pump water to fill a tank of volume 40 m³. If the efficiency of pump is 40 % and the tank is at a height 50 m, how much electric power is needed for the pump?

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Answer 1

Answer:

$Hello!!$

Given:-

• Volume of tank = 40 m
• Density of Water = 10 kg/m

To Find:-

• Electric Power needed

Solution:-

⬤Mass = Volume x Density

⬤Work Done = Potential Energy = mgh

⬤Power Work/Time

⬤Ep 30% of power needed

★Mass of the water pumped:-

→Mass= Volume x Density

→Mass = 40 x 10³

→Mass = 4 x 10^4 kg

★Work Done:-

→Work = mgh

→Work 4 x 10^4x 9.8 x 40

→Work = 1568 x 10^4J

→Work= 1.568 x 10^7J

★Power Required:-

→Power = Work/Time

→Work = 1.568 x 107J

→Time = 20 min = 20 x 60 1200 sec

→Power (1.568 x 10^71200)

→Power = 13.006 kW

★Electric Power Consumed:-

→Electric Power = 30% of power needed to pump

→Electric Power = 13.066 x 30/100

→Electric Power 3.9 kW

Explanation:

$Hope \: it \: helps...!!$

Answer 2

$\mathfrak\bold{Question :}$

A water pump takes 20 minutes to pump water to fill a tank of volume 40 m³. If the efficiency of pump is 40 % and the tank is at a height 50 m, how much electric power is needed for the pump?

$\frak\bold{Answer : }$

$\sf \bold{Given :} \\ \sf{volume \: of \: water \: = 30{m}^{3}} \\ \sf{t \: = 15min \: = 15 \times 60 = 900s} \\ \sf{h \: = 40m} \\ \\ \sf \bold{Solution : } \\ \sf{efficiency,η \: = {10}^{3} kg \: {m}^{ - 3} } \\ \sf \footnotesize{\therefore \: mass \: of \: water \: pump \: = volume \: \times density } \\ \sf{ = (30 {m}^{3})( {10}^{3}kg \: {m}^{ - 3}) = 3 \times {10}^{4} kg} </p><p></p><p></p><p></p><p>$

$\sf{{P}_{output}} \: = \frac{work}{time} \: = \frac{mgh}{t} \\ \\ = \sf \frac{ (3 \times {10}^{4})(10m {s}^{ - 2}) (40m)}{900s} \\ \\ = \sf\frac{4}{3} \times {10}^{4} \: W$

$\sf{efficiency, η \: = \frac{ Power_{output}}{Power_{input}}} \\ \\ \sf Power_{input} \: = \frac{Power_{output}}{η} \\ = \frac{4 \times {10}^{4} }{3 \times \frac{30}{100} } \\ = \frac{4}{9} \times {10}^{5} \\ \sf{ = 44.4 \times {10}^{3} W} \\ \sf\blue{ = 44.4kW}$