Liquid water enters a horizontal iron pipe at 20 degree C an

Liquid water enters a horizontal iron pipe at 20 degree C and 101.3 kPa. The pipe is in surroundings of 20 degree C, and there is a suction pump at the other end. The pipe flow rate is 88 gpm, pipe diameter is 4\", and velocity is 2.25 ft/s (these English unit data are not necessary to solve the problem; just to show the type of real-world problem). In this scenario the friction (viscosity) will typically cause the pressure to drop by about 3 kPa for each 100\' of pipe that the water has flowed through. At what distance from the entrance will the water in the pipe begin to boil?

Solution

Boiling point of water depends on the vapour pressure. At 20 degrees the vapor pressure of water is 2.334 kpa. Liquid boils when its vapor equals the pressure exerted on the liquid by the surrounding. So the pressure on the surface of water inside the pipe should be 2.334 kpa. Since the pressure reduces by 3 kpa for every 100\' length, pressure becomes 2.334 kpa from 101.3kpa at a length of 3298.86\'. Hence the answer

100/3=33.33.

Pressue must be reduced by an amount 101.3- 2.334=98.966 kpa

This happens at a length of 3298.86\'.