Water is flowing at the rate of 1.68 km/h through a cylindrical pipe into a cylindrical tank, whose diameter of the base is 60 cm. If the water level in the tank rises by 2.1 m in 30 minutes, the internal radius of the pipe is (assuming no overflow): 

Given:

Water flow rate = 1.68 km/h = 1680 m/h

Tank diameter = 60 cm = 0.6 m

Tank radius = 0.6 / 2 = 0.3 m

Water level rise = 2.1 m

Time = 30 minutes = 0.5 hours

Formula used:

Volume of cylinder = πr²h, where r is the radius and h is the height.

Volume flow rate = Area of pipe × Velocity of water

Calculation:

Volume of water in the tank:

⇒ π × (0.3)² × 2.1

⇒ π × 0.09 × 2.1 = 0.189π m³

Volume flow rate into the tank:

Volume flow rate = Volume / Time

⇒ (0.189π) / 0.5 = 0.378π m³/h

Let 'r' be the internal radius of the pipe.

Area of the pipe = πr²

Volume flow rate = Area of pipe × Velocity of water

⇒ 0.378π = πr² × 1680

⇒ r² = 0.378 / 1680

⇒ r² = 0.000225

⇒r = √0.000225 = 0.015 m = 1.5 cm

∴ The internal radius of the pipe is 1.5 cm.