Introduction to part 2

It is common engineering practice to convey gases, often at high pressure, through pipes of circular cross section. I think that the pneumatic systems that most of us see are those in garages specialising in tyre and exhaust replacement. There a compressor runs somewhere in the background in order to reduce the noise level at the workplace where power tools are used for nut running, tyre removal, vehicle lifts and so on. Similar systems are used in factories for nailing, stapling, spraying paint, abrasion and many other purposes. In every case a pipe or a pipe system must be installed to convey compressed air to suitable connectors to the flexible pipes to the air tools. The system would have to be very extensive to justify much design input to the pipe system. However there are other much longer pipes that convey gas, e.g. methane, from country to country and then there must be a serious design input. A working knowledge of the physics of the pipe carrying a gas under pressure has value to the engineer as a necessary part of having a grasp of the wider physics of engineering.

 

In the garage the conveying pipe is a small part of the total cost but for conveying gas over a long distance the goal must be to design pipes that give the best compromise between first cost and running cost. The running cost in any system is really that of pumping to overcome the friction loss that occurs as the gas flows through the pipe. We might expect the friction loss to increase in a non-linear way with velocity and low running costs are associated with low velocities. Inevitably some compromise has to be made between the cost of large and therefore expensive pipes for conveying at low velocities and running cost. Too often the cost of the installation dominates the decision and running costs are too high.

 

So let us have a look at the physics of such pipes.

 

All the gases are compressible fluids. To date we have considered the flow of incompressible fluids typified by water. We found that when any real fluid flows in, say, a pipe of uniform bore, the pressure drops and we attributed this drop to fluid friction. We must expect a similar pressure drop in pipes carrying gas. If the fluid is incompressible no change in volume per unit mass occurs even though the pressure falls but, if the fluid is compressible, the gas expands as the pressure falls. This means that the steady mass flow of a gas in a pipe of uniform bore will be associated with a steadily increasing velocity of flow along the pipe. This is a major difference to the uniform velocity of steady incompressible flow and it has ramifications where the velocity becomes high. This means that we have to have a new way of designing pipe systems when they are to carry gases. I shall follow the traditional approach and that starts by exploring the implications of the continuity equation.