4 replies to this topic

[calgary]

Hi,

I am recently studying isothermal flow and adiabatic flow in horizontal pipe. In most fluid mechanics books, the sonic velocity is expressed as sqrt(krt), where k is specific heat ratio. Following link is one of the examples.

http://onlinelibrary...275276.app5/pdf

My question is: k should be only used in isentropic process (adiabatic reversible). But adiabatic flow in a pipe with friction is apparently irreversible process. why is k in the sonic velocity formula?

Another questions is: the adiabatic flow equation is derived in the context of ideal gas, which has z=1. but in some papers, z (not equal to 1) is in the pressure drop equation. why?

Appreciate any thoughts. thanks.

[Bobby Strain]

Your question is how to calculate sonic velocity. And the formula you present is correct. Pressure loss in a piping system is different for adiabatic flow and isothermal flow. In adiabatic flow, the temperature is reduced as the pressure decreases, which is not the case with isothermal flow. If you are looking at flow through a nozzle or orifice, you need to take special care to apply the right flow model, of which there are many.

Bobby

[calgary]

Hi Bobby,

thanks for you comments. I understand your point that isothermal and adiabatic flow are different. For isothermal flow, we can drop the k out of the sonic velocity expression since k=1 (PV=constant). For adiabatic flow with friction, my understanding is that k should not appear in any equation since k is only for adiabatic reversible process.

Best regards,
Tim

[paulhorth]

Tim,
You seem to be confusing two different problems - (1) sonic velocity, which is a property of a fluid,at a given T and P,, and (2) pressure drop in a pipe for various types of compressible flow (such as isentropic, adiabtic and isothermal). This is the point Bobby Strain is making.

The sonic velocity is a particular value regardless of the process which occurs upstream, so you don't have different formulae and different results for the sonic velocity in isothermal flow and adiabatic flow.
The sonic velocity for a given T and P is given by c = sqrt (dp/d.rho) at constant entropy for the given T and P. For a "perfect gas", that is, a gas which obeys PV = RT, this equates to c = sqrt ( k.RT) where k = Cp/Cv. Don't drop the k for isothermal flow.
For a real gas, you have to solve the equation given above, using an eqatioin of state or a process simulator.
The limiting velocity reached with compressible flow in a pipe, which will be the sonic velocity at the local conditions, will be different for adiabatic flow and for isothermal flow, because the values of T and P will be different between these processes.

Paul

[calgary]

Hi Paul,

Thanks for your reply. I think now i finnaly catch what you and Bobby are saying. Sound travelling in gas is another process different from the process the gas itself is expericencing. Therefore, the sonic velocity is the property of the gas, nothing to do with firctionless or frictional flow.
I want to quote a paragraph in the book"compressible fluid flow" by Michel SAAD to further clarify this item in case somebody like me has the similar question.
" The amplitude of pressure pulse(sound) is small, resulting in infinitesimal changes in fluid properties across the wave. Hence, the departure of the fluid from thermodynamic equlibrium is negligible, and the process is practically reversible......Consequently, heat interaction is negligible, and the process is seffectively adiabatic. therefore, the process is both reversible and adiabatic-that is isentropic."

Best regards,
Tim