Friction

The equations governing the infinitesimal changes in a constant area flow due to the addition of a small adverse friction force are:

In this case, total enthalpy remains constant, but the small increase in frictional force shows up in the momentum equation (2).

From continuity, (1), the velocity change is small compared to the density change, so from (3), the enthalpy remains constant, which means that the speed of sound remains constant.

We conclude that for low Mach numbers for the flow with friction:

• The flow is aproximately isenthalpic, which implies that the speed of sound is also approximately constant.
• The frictional force causes a decreasing pressure.
• The density decreases correspondingly, causing the fluid to expand, which in turn causes the fluid to accelerate.

The third item above is the difference from the incompressible flow with friction, such as Poiseuille flow, in which the density does not vary, so the flow velocity remains constant.