Question

A fire hose has a diameter of 2.5cm and is required to direct a jet of water to a height of at least 40 m. The minimum power of the pump needed for this hose is:

• A. 21.5 k W
• B. 40 Kw
• C. 36.5 kW
• D. 48 kW

Answer 1

Answer: (A)

21.5 k W

Answer 2

The speed of the water leaving the horse must be $\sqrt{2gh}$ if it is to reach a height h when directed vertically. If the diameter is d, the volume of water ejected at this speed is $\frac{1}{4}\pi d^{2} \times \sqrt{2gh}\frac{m^{2}}{s}$.

Mass ejected is $\frac{1}{4}\pi d^{2} \times \sqrt{2gh} \times \rho\frac{kg}{s}$The kinetic energy of this water leaving the hose = $\frac{1}{2}$ mv²

= $\frac{1}{8}\pi d^{2} \times (2gh)^{3/2} \times \rho = 21.5kW$