Question

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.

Answer 1

Diameter of cylindrical tank = 2.8 m

Therefore, radius = 1.4 m

Height = 4.2 m

Volume of water filled in it = πr²h 

= ${\displaystyle \frac{22}{7}\times 1.4\times 1.4\times 4.2 m^3}$ 

= ${\displaystyle \frac{181.104}{7}{m}^3}$ 

= 25.872 m³      ...(i) 

Diameter of pipe = 7 cm 

Therefore, radius (r) = ${\displaystyle \frac{7}{2}}$ 

Let length of water in the pipe = h₁ 

∴ Volume = πr²h₁ 

= ${\displaystyle \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times h_1}$ 

= ${\displaystyle \frac{77}{2}{h}_{1}c{m}^3}$    ...(ii) 

From (i) and (ii)   

${\displaystyle \frac{77}{2}{h}_{1}c{m}^3=25.872\times {100}^{3}c{m}^3}$ 

${\displaystyle \Rightarrow h_1=\frac{25.872\times {100}^3\times 2}{77}}$  

${\displaystyle \Rightarrow h_1=\frac{25.872\times {100}^3\times 2}{77\times 100}}$  

${\displaystyle \Rightarrow }$ h₁ = 0.672 × 100²m

${\displaystyle \Rightarrow }$ h₁ = 6720 m  

Therefore, time taken at the speed of 4 m per second 

= ${\displaystyle \frac{6720}{4\times 60}}$ minutes

= 28 minutes