Question

A rectangular tank of internal dimensions 14 m × 11 m × 8 m is filled with water by a cylindrical pipe in 2 hrs. 15 minutes. If water runs through the pipe at the rate of 5 m/s, find the internal diameter of the pipe.

Answer 1

Given:

Rectangular tank 14m × 11m × 8m filled in 2h 15 min by a cylindrical pipe; water speed = 5 m/s.

Volume of tank, V = length × breadth × height

= 14 × 11 × 8 = 1232 m³

Required volumetric flow rate, `Q = V/t = 1232/8100`

 = 0.1520987654 m³/s

Cross-sectional area of pipe,

A = `Q/"velocity" = 0.1520987654/5`

= 0.03041975309 m²

Let d = internal diameter. Area A = `(π d^2)/4 → d^2`

= `((4A)/(π))`

= `(4 × 0.03041975309)/π

= 0.038742213  ... d = sqrt(0.038742213)

= 0.196826 m ≈ 0.1968 m.

Convert to centimetres:

d = 0.1968 × 100

= 19.68 cm

= 19.7 cm (20 cm)