Question

Calculate the horse power of an engine, which lifts 4000 m³ of water from a depth of 50 m in 40 minutes.

[g = 10 ms⁻², \[ \mathrm{D}_{\mathrm{H_{2}O}} \] = 10³ kg m⁻³, 1 HP = 750 W]

Answer 1

Mass of water = V × D

= 4000 m³ × 10³ kg m⁻³

= 4 × 10⁶ kg

∴ Work done in lifting water = PE = mgh

= 4 × 10⁶ kg × 10 ms⁻² × 50 m

= 2.0 × 10⁹ J

\[ \therefore\ \text{Power of engine} = \frac{W}{t} \]

\[= \frac{2.0 \times 10^{9}\ \mathrm{J}}{2400\ \mathrm{s}} \]

\[= \frac{1 \times 10^{9}}{1200}\ \mathrm{W} \]

\[ \therefore\ \text{Power in Horse Power} = \frac{1}{1200 \times 750} \times 10^{9} \]

= 1111.1 HP