# Process Control Problem

1. Jun 4, 2004

### Whiskey Sour

Neglecting friction:

I have a four inch diameter pipe that has a constant 8 psi input of natural gas(It is regulated and any psi drop throughout the pipe are negligable in this situation).

I found a site to tell me that the avg natural gas density is 0.4445 kg/m^3 at .06 MPa which I converted to .000016 lb/in^3 at 8 psi. It's close enough for me to assume there is a linear decrease in density v.s. pressure from this point on I suppose - unless that is where I'm going wrong.

This pipe has 'ignitors' which are 1 and 1/4 inch tubes leading into an unpressurized furnace.

I am wanting to also assume, initially at least, that the fire at the end of the tube has no effect (Basically 1 and 1/4 inch holes in the pipe). On other units I can manually set the pressure... and after it ignites, pressure does not noticably change.

I have researched and tried and failed and I cannot come up with mass flow rate through either of the tubes. I've focussed on the Bernoilli equation - but velocity on either side of my equation is unknown.

Any suggestions? A calculation would be a lot cheaper than trying to measure the flow like I have on other units.

Also, Natural Gas is close to 1000 btu per cubic foot so my end result I feel should be around 6 - 30 million btu/hr (mmbtu/hr) output. A Main Burner with huge pipes from a 1 psi 20" source supplys 150 million btu/hr - so it will not be close to that, and a class 2 ignitor by NFPA must be 4 % of that total - so it's not lower than 3 million btu/hr.

Help??? James

2. Jun 5, 2004

### Clausius2

Hi Whiskey Sour.

Perhaps my solution does not like you, but is the simplest one. You say pressure in the pipe does not change although ignitors are switched on, and you state the pipe discharges to an unpressurized furnice (discharge pressure Pa=0).
With this, I can assume that Mach number Ma=1 inside of the pipe, whose behaviour would be similar to a converging nozzle. Thus, mass flow is not a function of pressures. The real discharge pressure Ps of the flow is determined by means of the boundary condition Ma=1:

(Po/Ps)^(g-1/g)=1+(g-1)/2Ma^2 we obtain Ps (over expanded jet)

mass flow: G=rho*a*((g+1)/2)^((-g-1)/2(g-1)) where

rho=density in the inlet tank of gas,
a=sound speed in the inlet take of gas.

You can check that rho*a only depends of Po=8psi and To=?.

As you can see, I have seen the problem like a pipe whose entrance is connected to a large tank of gas with pressure 8psi, and discharges to vacumm.

3. Jun 5, 2004

### Clausius2

Sorry, I have forgotten that g=adiabatic constant=1.4.