# Calculation of pressure rise

1. Oct 8, 2015

### Max de Jong

Hello,
I am new to this forum but I have a question for you all. It is about the pressure in a system that changes when leakage changes. The test setup has to following components:

- Air supply with 8-10 bar
- Pressure valve that can be manually adjusted
- A flow meter that measures the pressure and the air flow
- A test object with a valve that leaks air

When testing the the manually adjustable pressure regulator is set in such a way that the test object is subjected to 2000 mbar absolute (1000 mbar overpressure). At this pressure the valve always has some leak rate, lets say 10 L/min. If I try to close the valve further with my hands by applying pressure to it so I decrease the leak rate, the pressure before the valve should increase. This is also registered by the flowmeter.

However I would like to know if there is a theoretical way to calculate this pressure rise.

Can anybody give me some advice as to how to tackle this issue?

I know I probably did not give you all the info but I like to learn the approach and than start talking numbers

Hope to hear from one of you.

Regards,

Max de Jong

2. Oct 8, 2015

### BvU

Hello Max, welcome to PF !

I must be missing something. You have a supply of 2000 mBara to a 'leaky' vessel . If you suppress the leak somewhat, the regulator on the air supply should keep the pressure in the vessel at 2000 mBara, shouldn't it ? And the flowmeter should show a reduced flow to replenish the (now smaller) leak.

3. Oct 8, 2015

### Max de Jong

Hello BvU,

Well I am currently graduating as a automotive engineer and I am performing leak tests. As you might know many cars operate with significant boost pressures and any leak will result in a lower pressure inside the intake system of the car.

Hence my question what the theoretical pressure rise would be if I managed to decrease the leak since less energy dissipates through the leak.

The test setup wont correct for the leak since I manually open the air supply to a specific steady state where I reach 2000 mbar absolute and a certain leakage in the test object.

If you have any idea to calculate the pressure rise and want to give an example calculation you can of course assume some values.

If you need more input from me dont hesitate to ask.

4. Oct 8, 2015

### Baluncore

You have pressure dependent leaks. Those leaks have flow rates. You are balancing the leak flows.
The capacity of your system integrates the difference between the leak flow rates.

The pressure regulator is a dynamic system that requires some flow to adjust. When leakage through the regulator exceeds the leakage from the test chamber, the regulator is unable to function. If the test chamber had a bleed that could be adjusted to be greater than the regulator then pressure regulation could be improved.

Maybe you should be using a fixed height water column to regulate your test pressure. A U-tube half full of water will set the test pressure and allow any regulator leakage to escape as bubbles.

We need a diagram of your system before we can be sure what is happening.

5. Oct 9, 2015

### Max de Jong

I cant seem to upload a picture so I will try to describe:

air supply ---> Pressure valve (manually operated) ----> Flow and pressure gauge ---> Test object

The test object will be subjected to a certain pressure and will have a certain leak rate when the pressure valve is set to a certain position. I will call this situation 1 and has as pressure of 2000 mbar absolute and a leak rate of 10 L/min

Now for situation 2. There are no smart systems present that compensate for anything. So the air supply stays the same, the pressure valve will remain in the same position as situation 1. The only thing I do is decrease the leak rate. This will increase the pressure before the test object (it shows on the flow and pressure gauge). Lets say this situation will result in a leak rate of 6 L/min and a pressure rise to 2300 mbar absolute.

So I know this is what happens due to my experience with the actual tests but I would like to know how to calculate this pressure rise.

I hope I gave you some answers

6. Oct 9, 2015

### Baluncore

The air supply is assumed to remain a fixed pressure. The manually operated pressure valve is an orifice that presents a resistance to the air flow.

The (air supply pressure) - (the pressure gauge reading) will show the pressure drop across the fixed pressure valve orifice. That pressure drop is a function of flow rate which you adjust by changing the leak rate.You need to investigate the pressure to flow relationship of an orifice.
Take a look at; https://en.wikipedia.org/wiki/Blower_door#Power_law_model_of_airflow

7. Oct 9, 2015

### Max de Jong

Hello Baluncore,

If I try and use the theory and formula's on my problem it will also give a pressure drop in the system like all other formula's I've found.
I think it's because they are based on the fact that you can have a certain pressure to create a certain air flow. If you need a lower air flow the pressure has to decrease. This is perfectly logical but it is not what I am looking for.

In reality the pressure rises since you trap more energy (pressure) before the valve which the pressure gauge displays.