Question

Water flows through a cylindrical pipe of internal radius 3.5 cm at 36 km/hr. Calculate the time it would take to fill a cylindrical tank whose radius and height are 35 cm and 1 m.

Answer 1

Given:

Internal radius of pipe,

r1 = 3.5cm

Speed of water = 36 km/hr

= 36 × `(1000 xx 100)/(60 xx 60)` = 1000 cm`

Radius of cylindrical tank

r2 = 35 cm

Height of tank,

h = 1 m = 100 cm

Step 1: Volume of water flowing per second through the pipe

Area of cross-section of pipe:

A = πr1^2​ = π(3.5)²

Volume per second:

= π(3.5)² × 1000

Step 2: Volume of the cylindrical tank

V = πr2²​h = π(35)² × 100

Step 3: Time required to fill the tank

Time = `("Volume of tank")/("Volume per second")`

= `(π × 35^2 × 100)/(π × 3.5^2 × 1000)`

= `(35^2 × 100)/(3.5^2 × 1000)`

= `(1225 xx 100)/(12.25 × 1000)`

= 10 Seconds