Question

A horizontal pipe radius 1.5 cm and length 25 cm is connected to the output that can sustain an output gauge of 10 kPa. What is the speed of 20 degrees Celsius water flowing through the pipe? If the temperature of the water is 60 degrees Celsius, what is the speed of water in the pipe?

Answer 1

Given: Radius of the pipe, r = 1.5 cm, diameter, d = 3 cm, length of the pipe, l = 25 cm, a maximum pressure that can be recorded, P_o = 10 kPa

1. The temperature of water, T₁= 20^oC

The viscosity of water depends on the temperature of the water.

First, we have to calculate the flow rate of water in the pipe.

By Hagen-Poiseuille Law

But the length of the pipe is very small, which gives unphysically high flow rates.

Please check the length of the pipe if it is m or cm

For l = 25 m, and using same above formulae

1. F = 7.9 x 10^-3 m³/s

which gives, Velocity, V= F/A = 11 m/s at 20^oC

2. F = 0.017 m³/s ....at T= 60^oC and length l= 25 m

which gives velocity, V = 24 m/s at 60^oC.