Question

Calculate the power of an electric pump in horsepower with can lift 2000m^3 of water from a depth of 20 metre in 25 minutes.(g=10m/s^2)
Answer..355.55 HP​

Answer 1

Answer:

Given:

Volume of water = 2000 m³

Depth = 20 m

Time = 25 min

To find:

Power of electric pump

Conversion:

First convert volume of water into mass of water.

As per question , 1 m³ = 10³ kg

=> 2000 m³ = 2000 × 10³ kg

=> 2000 m³ = 2 × 10^6 kg.

Also convert time from minute to seconds.

25 mins = 25 × 60 = 1500 secs.

Calculation:

$power = \dfrac{work}{time}$

$= > power = \dfrac{m \times g \times h}{time}$

$= > power = \dfrac{(2 \times {10}^{6} ) \times 10 \times 20}{1500}$

$= > power = \dfrac{4}{15} \times {10}^{6}$

$= > power = 0.266 \times {10}^{6} watt$

Final conversion:

To convert from watt to HP , we need to divide the power value by 746 .

$= > power = \dfrac{0.266}{746} \times {10}^{6}$

$= > power = 0.000356 \times {10}^{6}$

$= > power = 356 \: hp$

So final answer :

$\boxed{ \red{ \sf{ \bold{ \huge{ power = 356 \: hp}}}}}$

Answer 2

Answer:

1m³ of water = 10³kg

∴ 2000m³ of water has mass = m = 2000×10³ kg

wt. = force = mg = 2000 x 103 x 10N

Displacement = Depth = 20m

Work done = F×S×t = 25min = (25×60)seconds

Power = Work done / Time

= (2000×10×10³)×20/(25×60)

∴Power in H.P. = (2000×10³×200)/(25×60×750)

= 3200/9

= 355.55 H.P.

Therefore, the power of an electric pump in horsepower(H.P.) is 355.55 H.P.