How Do You Calculate Air Pressure with Varying Flow Rates and Orifice Sizes?

[Norgie]

I have a basic airflow question and my mind is in the fog. I'm trying to find the air pressure at a known flow rate and orifice size but I'm having issues with the unit conversions. I'm using Bernoulli's equation Pressure = 1/2 x Air Density x Flow Rate/Area. My Flow Rate is in L/M and the area is CM2. The air density is in KG/M3. The area of the orifice is not round but square. Could anyone help me with the correct formula and unit conversions.

Thanks

 

[russ_watters]

Welcome to PF!

We need more information to be able to adequately help: what kind of pressure are you trying to calculate (static/dynamic/differential?) And where are you trying to calculate it? And how do you know the incompressible flow equation is valid here; is this a low pressure/velocity situation?

 

[SteamKing]

I have a basic airflow question and my mind is in the fog. I'm trying to find the air pressure at a known flow rate and orifice size but I'm having issues with the unit conversions. I'm using Bernoulli's equation Pressure = 1/2 x Air Density x Flow Rate/Area. My Flow Rate is in L/M and the area is CM2. The air density is in KG/M3. The area of the orifice is not round but square. Could anyone help me with the correct formula and unit conversions.

Thanks

Flow rate units should be written L/min to avoid confusion with using M to represent meters and minutes. In any event, change the flow rate to L/s by dividing L/min by 60.

1000 L = 1 m³

100 cm = 1 m, therefore 10,000 cm² = 1 m²

You're on your own with a square orifice. Are you sure the orifice isn't 'square edged'?

 

[Norgie]

I'm trying to find the dynamic pressure of an airflow at 60 LPM. I'm trying to calculate the air pressure on the inlet side of a variable orifice. The variable orifice is a diaphragm loaded by a coiled spring. As the diaphragm opens, the air vents out to atmosphere through a square slot at a known size. The larger the airflow the more the diaphragm opens.

 

[russ_watters]

I'm trying to find the dynamic pressure of an airflow at 60 LPM...

The larger the airflow, the more the diaphragm opens

These two sentences either constrain or contradict each other: it sounds like you have a flow regulaing device that uses a spring to maintain a near-constant pressure somewhere. But what pressure/where?

Are you looking for the dynamic pressure (or velocity pressure VP) inside the orifice? Is it regulated inside the orifice? If that were the case, there'd be nothing to answer: it would be constant at whatever pressure was specified by whomever designed the device.

Are you looking for the dynamic pressure somewhere else - upstream or downstream of the orifice? Then it would be set by the pipe size. A diagram showing exactly where you want to measure the VP and how the orifice spring behaves would help.

In either case, if we assume that the incompressible flow equation works, it is basically plug-and-chug from the information you already have. I'd say give it a try with what you have and we'll go from there.

 

[Norgie]

Thank you for your reply and now I know I need to explain what I'm doing a little more. I'm trying to measure air flow through a variable orifice that is made of a spring material. Attached is a rough drawing of the device. Air flow enters the device at point A and pushes against the metal spring. The air is exhausted out the vent on the top. The faster the airflow the more deflection I get on the metal spring. I measure the deflection of the spring and correlate it to a calibrated airflow rate versus deflection. I'm trying to model the device through flow equations so I can compensate the effects of barometric pressure changes and temperature. I was starting with the formula as first described to determine the pressure required to move the metal flat spring at a given flow rate. The flow rates this device measures is 0 L/min to 900 L/min. I used the equation as first described but my numbers were not coming out correctly. Again, the formula is Pressure = 1/2 x Air Density x Flow Rate / Area of the open vent. My air density is in Kg/m³, Flow Rate is in L/min and Area is cm². I'm not sure what units the Pressure will come out to be.

 

[boneh3ad]

Well first of all, the unites of $\dfrac{\rho Q}{2A}$ are not pressure if $Q$ is volumetric flow rate. Consider that the units of your equation are $\frac{[kg/m^3]\cdot[m^3/s]}{[m^2]} = \frac{kg}{m^2\cdot s}$, which is not the same as $[Pa] = \frac{[N]}{[m^2]} = \frac{[kg\cdot m]/[s^2]}{[m^2]} = \frac{kg}{m\cdot s^2}$.

The actual definition of dynamic pressure is $q = \frac{1}{2}\rho v^2 = \frac{\rho Q^2}{2A^2}$. You forgot to square the velocity.

Also, depending on your pressures, Bernoulli's equation is not necessarily going to be valid. In fact, I would bet that it is not valid here (and that is even assuming that you are ignoring viscosity in the first place. I can almost guarantee that the flow here is compressible unless you are dealing with very small pressures in whatever line you are venting.

Also, you are going to run into the issue here that you have an object blocking your flow, so that is going to tend to change the flow field and nothing you can calculate by hand will be anything other than a rough estimate.