Raleigh Flow!

[interface222]

Hi,
I am attempting to complete a pneumatic circuit with a known requirements for flow to approximate pressure loss in the circuit and therefor the operating head for the pump in the circuit. I am neglecting friciton in the tubing simplifying it a little. The circuit contains heated and cooled portions as well as one point where the flow is volumetrically split to be reunited at the same pressure near the end of the loop.

My question is two parted.

1) Regarding splitting the flow, I am using an area ratio to split the flow and will emperically match the pressures when they join together later in the circuit. Due to manufacturability of the holes I am scaling the area of the exiting ducts to double that of the entrance duct. Is this better for head loss in the split or will keeping a 1:1 ratio for the split ducts and the entrance duct minimize head loss. I believe 1:1 would minimize the pressure drop because there would be less heat generated and dissipated in the non-ideal non-isentropic expansion in an area change.

More importantly.

2) I have run into this analysis block at any of the heating or cooling portions of a constant area "no friction" duct. I only have all the starting conditions and the change in temperature. I believe I need to have TWO flow characteristics at the exit to be able to calculate the rest of the flow characteristics (ie. density, velocity, entropy, enthalpy, Mach #, T stag, pressure, temperature).
Is there a way around this?!

Many thanks and godspeed.
Your help is appreciated.

 

[25362]

I'm not familiar with the problem in hand but may be this definition taken from a book may be of help:

Rayleigh flow is an idealized type of gas flow in which heat transfer may occur, satisfying the assumptions that the flow takes place in constant-area cross section and is frictionless and steady, that the gas is perfect and has constant specific heat, that the composition of the gas doesn't change, and there are no devices in the system which deliver or receive mechanical work.

Highlights are mine.

 

[interface222]

Thanks friend, but I'm beyond the defenition in the book.

It's well worded and highlighted!

 

[interface222]

Not beyond the spelling though, in any measure, it seems.

 

[25362]

Do you mean Rayleigh, not Raleigh (wrong!) as in the heading ?

 

[interface222]

Yep! Rayleigh.

So I think I'm going to work with convection and conduction equations to find the dQ for use in flow calculations.

Any comments or questions?

 

[interface222]

Hey 25362,
I was looking over the definition that I am "beyond." What is your interpretation of the reference that the composition of the gas doesn't change. This is due to the Cv staying constant.

 

[25362]

Just a thought. In the case of splitting the flow of a gas mixture, segregation due to factors such as density or viscosity wouldn't take place.

 

[interface222]

Yes, ok, that makes sense. The composition would stay at the same composition regardless of the various gas properties in the mixture.