## Pipe Flow

Consider a gas flowing in a uniform (constant cross section) pipe. The mass flow rate and mass flux (G = m/A) are the same at all locations along the pipe:

Now the pressure drops along the pipe because of energy dissipation (e.g., friction), just as for an incompressible fluid. However, because the density decreases with decreasing pressure and the product of the density and velocity must be constant, the velocity must increase as the gas moves through the pipe. This increase in velocity corresponds to an increase in kinetic energy per unit mass of gas, which also results in a drop in temperature. There is a limit as to how high the velocity can get in a straight pipe, however, which we will discuss shortly.

Because the fluid velocity and properties change from point to point along the pipe, in order to analyze the flow we apply the differential form of the Bernoulli equation to a differential length of pipe (dL):

If there is no shaft work done on the fluid in this system and the elevation (potential energy) change can be neglected, Eq. (9-14) can be rewritten using Eq. (9-13) as follows:

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