Question

A cylindrical water tank of diameter 1.4m and height 2.1m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/s. Calculate the time it takes to fill the tank.

Answer 1

Hint: It is known that the volume of cylinder is \[\pi {r^2}h\] where r is radius equal to $\dfrac{{1.4}}{2} = 0.7m$ and h is height equal to 2.1m. It is given that the rate of flow of water in the tank is 2 m/s which means in 1 sec 2m of height of pipe is covered by water. Time required to fill the tank is the volume of the tank divided by the volume of pipe.

Complete step-by-step answer:
Given dimension if tank
Diameter (d) = 1.4m
Radius (r) = $\dfrac{{1.4}}{2} = 0.7m$
Height (h) =2.1m
Volume of tank = \[\pi {r^2}h\]
$ \Rightarrow \pi \times {\left( {0.7} \right)^2} \times 2.1{m^3}$
Dimension of pipe
Diameter (d) = 3.5
Radius (r) =$\dfrac{{3.5}}{2}cm = 1.75cm = \dfrac{{1.75}}{{100}}m = 0.0175m$
Rate of flow of water = 2m/s
So, the height pipe in the 1 sec =2m
The volume of pipe in 1 sec= \[\pi {r^2}h\]
$ \Rightarrow \pi \times {\left( {0.0175} \right)^2} \times 2{m^3}$
$\Rightarrow time = \dfrac{{{\text{volume of tank}}}}{{{\text{volume of pipe}}}}$
$\Rightarrow t = \dfrac{{\pi \times {{\left( {0.7} \right)}^2} \times 2.1{m^3}}}{{\pi \times {{\left( {0.0175} \right)}^2} \times 2{m^3}}}$
\[t = 1680\sec = \dfrac{{1680}}{{60}}\min = 28\min \]
Hence time required to fill the tank is 28min.

Note: Points to be taken cares. Units of all the quantities must be the same. Conversion units used in questions are 1m=100cm and 1min=60sec. Time required to fill the tank is the volume of the tank divided by the volume of pipe.