High Velocity Air Flow in a Tube

[denniskb]

I need to determine the flow of dry air to atmosphere through a small tube so we can correctly set up a series of tests. The aim is to achieve near sonic velocity (say M = 0.9) at the discharge by setting an appropriate upstream pressure. Software available to me will not cope so I am using Fanno tables but the calculations (see attached) assume ideal gas, require lots of manual iterations and I am not sure I have done this correctly. Accuracy is important if we are to avoid sonic flow as we will not be able to detect this during the tests.

I would appreciate guidance from those with the right experience?

Inputs:
Dry Air at 20°C, Tube ID 7.66 mm, roughness 0.03 mm, length 6.0 m

Required:
inlet Press,
mass flow,
inlet Mach,
outlet Mach,
Outlet temp
Inlet Press to achieve sonic flow at outlet (My calculation suggests 590 kPag)

My first priority is an answer then I would like to understand how the calculation is done?



Dennis Kirk Engineering

http://www.ozemail.com.au/~denniskb

 

[Latexman]

Dennis,

It depends a little on the inlet connection to the tube, but if I assume what feeds the tube is the same ID (k=0), then I get:

inlet Press, 569 kPa
mass flow, 66.4 kg/hr
inlet Mach, 0.165
outlet Mach, 0.900
Outlet temp -19.5 C

Inlet Press to achieve sonic flow at outlet 671 kPa

The method I am using is a spreadsheet using the equations for ideal gas derived in Shapiro's Dynamics and Thermodynamics of Compressible Fluid Flow.


Good luck,
Latexman

 

[denniskb]

Thanks Latexman,

Two clarifications please:
Are the pressure listed kPa(g) or kPa(a)?
The outlet temp seems too low for what should be isenthalpic flow?




Dennis Kirk Engineering

http://www.ozemail.com.au/~denniskb

 

[Latexman]

kPa(a) and the method does assume 100% adiabatic.

Good luck,
Latexman