Did you know to exclude the exit pipe fitting in your PSV outlet pressure drop calculations if your PSV discharges to atmosphere?
If you have performed an outlet pressure drop calculation for a PSV relieving to atmosphere, you may have noticed that often a significant portion of the pressure drop is contributed by the exit pipe fitting. This is because the equivalent resistance of the fitting is high relative to a typical length of pipe.
Did you know to exclude the exit pipe fitting in your PSV outlet pressure drop calculations if your PSV discharges to atmosphere?
Per Hooper (1981), the friction loss coefficient, Kf, for a pipe exit is 1.0. However, Darby (2001) provides a clarification and states that Kf is actually zero if the fluid exits the pipe into unconfined space [such as atmosphere], because the "velocity of a fluid exiting the pipe (in a free jet) is the same as that of the fluid inside the pipe (and the kinetic energy change is also zero)." In fact, the friction loss can be shown via the Bernoulli equation to be zero or essentially zero, regardless of relief fluid phase, whether the flow is critical or subsonic, or whether the fluid in the unconfined space is vapor or liquid.
Darby then indicates that Kf is 1.0 if the fluid exits into a confined space, because "the kinetic energy is dissipated as friction in the mixing process as the velocity goes to zero… In this case the change in the kinetic energy and the friction loss at the exit cancel out."
The typical exit pipe fitting coefficient, Kf, is 1.0. In these cases, exclude the exit pipe fitting for pressure drop and dispersion calculations if the PSV discharges to atmosphere. In cases where the relief system discharge piping is routed to process, a different assumption may need to be made.
References:
- Hooper, W. (1981, August 24). The 2-K Method Predicts Head Loss in Pipe Fittings Chemical Engineering, 97.
- Darby, R. (2001). Chemical engineering fluid mechanics (2nd ed., pp. 213-214). New York: Marcel Dekker.