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Pipeline Velocity Increases in Compressible Fluid Systems

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For compressible fluids (in which density is not a constant), the fluid velocity increases as the flow progresses through a pipeline.  At first, this fact may seem counterintuative to some users.

Under normal subsonic conditions, the velocity of a compressible fluid tends to increase as the fluid flows through a pipe with friction.  This statement seems counterintuitive, since we normally think of frictional forces as only serving to slow systems with moving parts.  However, note the following:

For a constant mass flow rate:

   W(in) = r(in) * v(in) * A(in) = r(out) * v(out) * A(out) = W(out)     (Equation 1)

      Where,
            W = mass flow rate
            r = fluid density
            v = velocity
            A = pipeline area

Also, from the Ideal gas law:
  
   r = P/RT     (Equation 2)
      Where,
            P = fluid pressure
            R = gas constant
            T = fluid temperature

As the fluid passes through the pipe:
  • the pressure decreases
  • the density also decreases, since it is proportional to pressure (see Equation 2)
Since the mass flow rate into the pipe must equal the mass flow rate out of the pipe (see Equation 1), the fluid velocity must increase to compensate for the decreased fluid density at the pipe outlet.

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Article Details

Last Updated
12th of May, 2009

Program
PIPE-FLO Compressible

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