Pressure in a tank with continuous flow

[SBNY444]

I feel like this is easy to answer but I'm coming up with answers I don't trust. Basically, I have a tank of air where I want to keep the pressure at a certain value. Let's say 1 psig for the sake of argument. I have a 1/2" ID hose connecting to inlet flow to the tank and an outlet hose of 3/4" ID flow. What flow of air at the inlet do I need to stabilize the pressure in the tank to 1psig? How I'm going about this is treating the outlet hose as an orifice in the tank - which there are equations for and I calculate the flow through the orifice assuming 1psig in the tank and thereby getting the flow at the inlet. Logically, i think it's correct but I also feel like I'm missing something. Any thoughts?

 

[PumpkinCougar95]

Well for a certain pressure and volume of the tank you have a definite amount of gas which you can calculate from $PV = nRT$ Hence the volume of air in per sec should be equal to the volume of air out per sec.

So you would have $$ \sqrt{ \frac 2 {\rho} P } \times A_{out} = V \times A_{in}$$ where i have used the Bernoulli equation. $A_{in}$ and $A_{out}$ are area's. P is the excess pressure in the container and $\rho$ is the density. Finally, V is the velocity of air you are putting in. Did you have something like this in mind?

 

[anorlunda]

Show your math if you want us to say if you did it right.

The volume of the tank should not matter. For the outlet orifice, what is the mass flow rate with 1 psig pressure difference? Assume the initial pressure was 1 psig, and set the inlet flow to that same mass flow rate and you have a steady state. In other words, rate of change of pressure is proportional to flow in minus flow out. You want rate of change of pressure to be zero.

That calculation does not tell you how to transiently regulate the inlet to change from a different pressure to 1psig, and then hold it steady thereafter.

 

[SBNY444]

Show your math if you want us to say if you did it right.

The volume of the tank should not matter. For the outlet orifice, what is the mass flow rate with 1 psig pressure difference? Assume the initial pressure was 1 psig, and set the inlet flow to that same mass flow rate and you have a steady state. In other words, rate of change of pressure is proportional to flow in minus flow out. You want rate of change of pressure to be zero.

That calculation does not tell you how to transiently regulate the inlet to change from a different pressure to 1psig, and then hold it steady thereafter.

So, I'm using an online tool:

http://www.tlv.com/global/TI/calculator/air-flow-rate-through-orifice.html?advanced=on

setting temp to 20C, Primary pressure to 1psig, out pressure to atmospheric (0 psig), diameter 0.75", discharge defaults to 0.7. I get 44.5 scfm. Trying to reproduce this in excel is not even close. The units to the equations provided are not even in vol/time. It works out to like in/sqrt(temperature). Which is not a quantity. I'm almost certain all of the coefficients used are unitless so I'm not to sure what the hang up is.

 

[SBNY444]

anyone?

 

[Asymptotic]

Trying to reproduce this in excel is not even close.

OK. The online tool you've referenced shows the equations they are using.
Let's see what it is you are doing in Excel.

 

[SBNY444]

its attached. Aside from whether or not the calculation is correct, is it the right approach I think is an equally important question.

 

[anorlunda]

You're asking for a lot of free labor to understand your Excel sheet, not to mention the security risk of opening a stranger's spreadsheet. Below are the equations used by the online calculator.

Can you show us your equations in a similar form?(see https://www.physicsforums.com/help/latexhelp/)
Or can you summarize for us the difference between your equations and those?

 

[SBNY444]

I didn't ask for you to open the excel. Frankly, I don't think it is relevant at this stage. Someone asked to see my calculations, I presented them. I'm using the first very long equation from the tool i already provided in the excel sheet. I get a much different answer, that's all. Here's a better question(s) - is it the right approach to treat the outlet as an orifice and just solve for flow to determine the flow at the inlet? And if so, why are the units for the equation bogus (length/sqrt(Temperature))? or am I doing something incorrect to see that the equation is in fact in correct units (vol/time).

 

[Asymptotic]

I didn't ask for you to open the excel. Frankly, I don't think it is relevant at this stage. Someone asked to see my calculations, I presented them. I'm using the first very long equation from the tool i already provided in the excel sheet. I get a much different answer, that's all. Here's a better question(s) - is it the right approach to treat the outlet as an orifice and just solve for flow to determine the flow at the inlet? And if so, why are the units for the equation bogus (length/sqrt(Temperature))? or am I doing something incorrect to see that the equation is in fact in correct units (vol/time).

1. Fy = Specific Heat Ratio Factor = (Specific Heat Ratio/1.4).
Is 1.4 the value you want to use?
2. You show values of inches and PSI, but the Excel formula in cell B15 is modeled closely to the original which uses units of kPa (absolute) and millimeters.
You'll need to do the appropriate conversions.
3. I don't know where "in/sqrt(T)" comes from, but it can't be correct. The original formula is in cubic meters/minute; simply convert to cubic feet per minute (or cubic inches per minute, depending on what you want to end up with).

 

[SBNY444]

Am i going crazy?

I was wrong before. It's actually lbs*sqrt(1/T)

Anyway, clearly there is something wrong with my excel. And maybe there is something wrong with this equation above. But the million dollar question is, if this is the right approach - assuming my answer agrees with the online tool and there are no unit discrepancies. Does modeling flow through an orifice properly characterize the system I describe in the OP?

Thanks for all of your patience.

 

[anorlunda]

See #3

 

[SBNY444]

See #3

The third term group? Are you saying my assumption about that being unit less is incorrect? If so great, we can move on.

Can you comment on whether the analytical approach is in fact sound?

Thanks again.

 

[anorlunda]

Sorry, I meant post #3 in this thread. That was my answer about the approach.

 

[JBA]

Based upon the above I can only state that using US units my long verified flow program confirms the value of the online calculator to be essentially accurate at 44.5656 SCFM (Actually my program solution is 44.40 SCFM).
One thing I did see in reviewing your spread sheet display in post #10 is that you used all US units except for the temperature in °C, which should be in °F which then converts to 527.67°R as the correct temperature value for the equation in US units.