Question

Fire is caught at a height of 125 m from the fire brigade. To extinguish the fire, water is coming out from the pipe of a cross section 6.4 cm with rate 950 litre/ min. Find out the minimum velocity of water exiting from the fire brigade tank. (Assume $g = 10m/{s^2}$)

A. 5 m/s

B. 10 m/s

C. 25 m/s

D. 50 m/s

Answer 1

The rate of flow of a liquid is different from its velocity. It depends on the amount of liquid flowing out of a cross section at a specific speed.

Formula used:

$R = \pi {r^2}V$

where R is the rate of flow of liquid from an orifice of cross-sectional radius r, and velocity V. The SI unit of the rate of low is ${m^3}/s$.

Complete step by step answer

In this question, we are provided with the following information about the flow of water:

Rate of flow $R = 950\dfrac{{{\text{litre}}}}{{{\text{min}}}} = 950\dfrac{{{{10}^{ - 3}}{m^3}}}{{60s}} = 15.8 \times {10^{ - 3}}{m^3}/s$.....(Convert the units to standard form)

Diameter of the pipe $d = 6.4cm = 0.064m$

Hence, radius of the pipe $r = \dfrac{d}{2} = \dfrac{{0.064}}{2} = 0.032m$

Although the height of the point at which fire exists is given to us, it is not of importance in our calculations. We know that the rate of flow is given as:

$R = \pi {r^2}V$

We are required to find the velocity V of the flow of water. Thus, we substitute the known values to get:

$15.8 \times {10^{ - 3}} = \pi {(0.032)^2}V$

$V = \dfrac{{15.8 \times {{10}^{ - 3}}}}{{\pi \times 1.024 \times {{10}^3}}} = \dfrac{{15.8}}{{3.14 \times 1.024}}$

Solving for V, we get:

$V = \dfrac{{15.8}}{{3.21}}$

$\therefore V= 4.9 \simeq 5m/s$

Hence, the correct answer is option A.

Note
As we saw, rate of flow is used to measure the output of a fluid in terms of volume per unit time. For example, the heart of an adult at rest pumps blood at a rate of around 5 litres per minute (L/min).