A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m s^-1. Calculate, in minutes, the time it takes to fill the tank.

Given,

Diameter of cylindrical tank = 2.8 m

So, its radius (R) = $\dfrac{2.8}{2}$ = 1.4 m

Height (H) = 4.2 m

Volume of water filled in it = πr²h

= $\dfrac{22}{7}$ x 1.4 x 1.4 x 4.2

= 25.872 m³

= 25.872 × (100)³ cm³

Given,

Diameter of the pipe = 7 cm

Radius (r) = $\dfrac{7}{2}$ = 3.5 cm

Area of cross section of pipe = πr²

= $\dfrac{22}{7} \times (3.5)^2$

= 22 × 0.5 × 3.5

= 38.5 cm².

Volume of water discharged per second = 38.5 cm² × 4 m s^-1

= 38.5 × 400 cm s^-1

Let the pipe fill the tank in n seconds.

∴ n × Volume of water discharged per second = Volume of tank

$\Rightarrow n \times 38.5 × 400 = 25.872 × (100)^3 \\[1em] \Rightarrow n = \dfrac{25.872 \times 100^3}{38.5 \times 400} \\[1em] \Rightarrow n = \dfrac{25872000}{15400} \\[1em] \Rightarrow n = 1680 \text{ seconds} \\[1em] \Rightarrow n = 1680 \times \dfrac{1}{60} \text{ minutes} \\[1em] \Rightarrow n = 28\text{ minutes}.$

Hence, it takes 28 minutes to fill the tank.