2 replies to this topic

[rxnarang]

Roy,

Excellent question. You are right in locating the tailpipe vent away from any platform, which an operator can access.

Sizing the tailpipe to ensure that the allowable back pressure is not exceeded is required. Sizing for compressible flow at high velocities is not as straightforward as is often believed.

First, it has to be evaluated if the flow will be sonic. I believe it will be. The following arguement then holds for flow through conduits of constant cross section:

Flow through pipes in a typical plant where line lengths are short or the pipe is well insulated can be considered adiabatic. A typical situation is a pipe into which gas enters at a given pressure and temperature and flows at a rate determined by the length and diameter of the pipe and downstream pressure. As the line gets longer friction losses increase and the following occurs:

a) Pressure decreases
Density decreases
c) Velocity increases
d) Enthalpy decreases
e) Entropy increases

The question is “ will the velocity keep on increasing till it crosses the sonic barrier?” The answer is NO. The maximum velocity always occurs at the end of the pipe and keeps on increasing as the pressure drops till it reaches Mach 1. The velocity cannot cross the sonic barrier in adiabatic flow through a conduit of constant cross section. If an effort is made to decrease downstream pressure further the velocity, pressure, temperature and density remains constant at the end of the pipe corresponding to Mach 1 conditions. The excess pressure drop is dissipated by shock waves at the pipe exit due to sudden expansion. If the line length is increased to drop the pressure further the mass flux decreases so that Mach 1 is maintained at the end of the pipe.

The above is important to appreciate. After you have established that sonic exists by calculating the critical pressure,

[ ( k + 1 ) / 2 ] k / ( k - 1 )

then the next step is to calculate the pressure drop through the line. The formula for this is given in McCabe and Smith or Shapiro. I would have copied that formula here, but this website does not allow pasting of Micrsoft equations.
( Admistrators help!). The file containing this formula is attached. Look at the text book for explanation of terms, and the solution is pretty starightforward, with the unknown being the length of the pipe required to flow a given mass of fluid. In case the flow is sub-sonic the same equation holds, but the solution is now iterative.

Word of caution:-This equation is for adibatic flow of ideal gas in constant diameter pipes.

Milton's website www.air-dispersion.com is also an excellent source to understand compressible flow. However I believe the site does not contain flow through a conduit. ( I could be wrong- Milton ?)

I hope the above helps.

Regards

Attached Files

•  Equation_1.doc   14.5KB   161 downloads