- #1
Michu
- 2
- 0
Hello All,
I am trying to figure out the solution to a problem I am trying to do for fun. I've been trying this for a while and has annoyed me so any help is greatly appreciated! I attached a picture of the problem/ control area to help.
[PLAIN]http://postimg.org/image/5pytdzie3/[URL]http://postimg.org/image/5pytdzie3/[/URL]
The situation is that there is a tank filled at a certain known pressure P1 and has known area A1. This is connected to a regulator that let's out a certain pressure in a smaller pipe. Inside the pipe P2 is known since it can be set by the regulator and A2 is also known. Typically I would try to use the Bernoulli equation but my aim is to work with compressible air so I can't do that. Working backwards I was thinking using the continuity equation:
(d/dt)( ∫_cv of ρ d∀ ) + (∫_cs of ρVdA) = 0 which then goes to just ρ_2*V_2*A_2=0 so that doesn't work either.
I was also thinking maybe using the Isentropic Equations such as (P_o/P) = [1+ ((γ -1)/2)*M^2] ^(λ/(λ-1)) but that is giving me that I need 5 atm in the tank and 1 atm in the pipe and gives 1.7 Mach which is way to high just by reasoning.
Any advice or help is greatly appreciated, this problems is just annoying me and I can't stop thinking about it.
Also I am new to the forums so if I did something wrong sorry!
Thank you,
~Michu
I am trying to figure out the solution to a problem I am trying to do for fun. I've been trying this for a while and has annoyed me so any help is greatly appreciated! I attached a picture of the problem/ control area to help.
[PLAIN]http://postimg.org/image/5pytdzie3/[URL]http://postimg.org/image/5pytdzie3/[/URL]
The situation is that there is a tank filled at a certain known pressure P1 and has known area A1. This is connected to a regulator that let's out a certain pressure in a smaller pipe. Inside the pipe P2 is known since it can be set by the regulator and A2 is also known. Typically I would try to use the Bernoulli equation but my aim is to work with compressible air so I can't do that. Working backwards I was thinking using the continuity equation:
(d/dt)( ∫_cv of ρ d∀ ) + (∫_cs of ρVdA) = 0 which then goes to just ρ_2*V_2*A_2=0 so that doesn't work either.
I was also thinking maybe using the Isentropic Equations such as (P_o/P) = [1+ ((γ -1)/2)*M^2] ^(λ/(λ-1)) but that is giving me that I need 5 atm in the tank and 1 atm in the pipe and gives 1.7 Mach which is way to high just by reasoning.
Any advice or help is greatly appreciated, this problems is just annoying me and I can't stop thinking about it.
Also I am new to the forums so if I did something wrong sorry!
Thank you,
~Michu
Last edited by a moderator: