A fire engines raises water at the rate of 6000 litres per minute through a height of 2 m and discharges it at 10 m/s. The H.P of fire engine is nearly equal to (Take acceleration due to gravity as 9⋅81 m/s²)

Concept:

Total work done = (Potential work) + (Kinetic work) = (m × g × h) + \(\frac{1}{2}~\times~m~\times~v^2\)

Power = \(\frac{Total~work~done}{time}\)

Calculation:

Given:

Amount of water raised = 6000 litres / minute, Height, h = 2 m, Velocity, v = 10 m/s, g = 9.81 m/s²

Volume = 6000 litres, Density, ρ = \(\frac{m}{V}\)

⇒ 1000 = \(\frac{m}{6000~\times~10^{-3}}\) (∵ 1 Litre = 10^-3 m³)

⇒ m = 6000 Kg

∴ Total work done in 1 minute = (m × g × h) + \(\frac{1}{2}~\times~m~\times~v^2\) = \(6000~\times~9.81~\times~2~+~\frac{1}{2}~\times~6000~\times~10^2\)

⇒ Total work done in 1 minute = 417720 J

Power = \(\frac{417720}{60}\) = 6962 watt = \(\frac{6962}{746}\) = 9.33 hp