Question

Water emerges from a horizontal pipe of varying cross section at the rate of 30litre/min find the velocity of water at a point in the pipe where the radius of the pipe is 2cm.

Answer 1

Given info : water emerges from a horizontal pipe of varying cross section at the rate of 30 litre/min.

To find : the velocity of water at a point in the pipe where the radius of the pipe is 2 cm ..

solution : we know, the rate of flowing of a liquid is given by, R = Av

where A is cross sectional area of pipe and v is velocity of water.

here, radius of pipe, r = 2 cm

so, the cross sectional area of pipe, A = πr² = 3.14 × 2² = 12.56 cm²

the rate of flowing of water, R = 30 litre/min = 30 × 10³ cm³/60 sec [∵ 1 litre = 10³ cm³ ]

= 500 cm³/sec

now, 500 cm³/sec = 12.56 cm² × v

⇒ v = 500/12.56 = 39.8 cm/s = 0.398 m/s ≈ 0.4 m/s

therefore the velocity of water is 0.4 m/s at a point in the pipe where the radius of the pipe is 2cm.