# How to calculate effective pump flow-rate across a filter?

• Kaeros
In summary: If they do not, or if you want to check, you can probably calculate it.The filter should have an acutal performance specification you can get from the manufacturer: a specified pressure drop at a specified flow rate or range (curve). The pipe is short so there shouldn't be much static pressure drop along its length, but you can calculate drop through the assembly based on velocity pressure and orifice/fitting losses.Let's start with the clarifications first though because they will affect the methodology...1. What is the inlet flow rate?2. You call this a "pump", not a fan; is it pressurized at
Kaeros
My issue is related to the actual flow-rate I obtain when sampling air across a filtering membrane.
Each pump reports a nominal amount of air that it can draw in a certain amount of time (i.e.: flow-rate, like 10 liters per minute), but this is generally reported assuming normal temperature and pressure and with no "load" applied to the pump.

Let's assume now that I attach to the inlet of the pump 50 cm of a straight pipe with a known diameter (let's say 1 cm) and on top of that an open faced filter holder with a filter with given diameter (50 mm) and porosity (let's say 1 micron pore size).

Let's assume that we turn on the system at ground level in normal conditions (so that the air that the pump is sucking in through the filter is at 1 atm and 20 °C): what would be the actual flow-rate that I would measure with a flow-meter at the outlet of my pump? How can I compute that?

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Welcome to PF! And thanks for including the sketch - too often we don't get them. A few questions:

1. What is the inlet flow rate?
2. You call this a "pump", not a fan; is it pressurized at the outlet? To what pressure?
3. What is the outlet connected to? Are there restrictions there?
4. Is this a factory provided inlet filtration system?

Typically the inlet filter and pipe on an air compressor are sized by the factory to be large enough not to provide a "significant" flow restriction. But if they do not, or if you want to check, you can probably calculate it.

The filter should have an acutal performance specification you can get from the manufacturer: a specified pressure drop at a specified flow rate or range (curve). The pipe is short so there shouldn't be much static pressure drop along its length, but you can calculate drop through the assembly based on velocity pressure and orifice/fitting losses. Let's start with the clarifications first though because they will affect the methodology...

Dear Russ,

Thank you so much for your reply! I'll try to give the clarification you asked me, but please bear with me: I'm a biologist and these kind of physics/engineering problems and terms are not my bread.

1. Sorry, but I don't really understand this. At the pump inlet (i.e.: if you remove pipe and filter) you would have the nominal flow-rate of the pump since you are running it at standard conditions (20°C, 1 atm). At the system inlet (i.e.: before the filter)...that's part of the question: I do not know, it will depend on the combination between the pump "sucking" strength and the resistance given by the filter and the pipe. Does this at least partially reply to what you were asking?

2. I am actually trying to size the system in the sketch to build something that makes sense. To draw air through a filter I would generally use a vacuum pump (like a oilless diaphragm pump) that can reach some Pa/mbar of vacuum (still don't know how many, as I said, I'm still trying to size the system up, but for reference let's say something like this: https://www.makita.co.nz/products/model/DVP180).

3. No restrictions to the outlet. The outlet, in the actual application, might be connected to a flow meter (or some kind of mass-flow controller), but I can size this component on the basis of the pump, so let's assume no restrictions for the sake of simplicity (i.e.: the outlet just blows in standard atmosphere at 20°C, 1 atm).

4. Not exactly. Filters and filter holders are commercial (here's an example of the filters: https://www.merckmillipore.com/IT/it/product/MF-Millipore-Membrane-Filters,MM_NF-C152#specifications; and there are some filter holders: https://shop.pall.com/us/en/laborat...re-parts/open-face-filter-holders-zidgri78l6k), but the system itself, including the connection between the filter holders and the pump inlet, would be custom built. I am, in fact, trying to understand what are the constraints and the calculations I should make to understand exactly what to buy for this application.

From the filters manifacturer I can only get this information about the filters I am interested into: that if I apply a differential pressure of 0.7 bar (10 psi) to the filter, I will obtain a flow rate of 2 liters per minute per cm2 of filter.

Thank you again for your reply and I hope that the clarifications make any sense!

Regards!
russ_watters said:
Welcome to PF! And thanks for including the sketch - too often we don't get them. A few questions:

1. What is the inlet flow rate?
2. You call this a "pump", not a fan; is it pressurized at the outlet? To what pressure?
3. What is the outlet connected to? Are there restrictions there?
4. Is this a factory provided inlet filtration system?

Typically the inlet filter and pipe on an air compressor are sized by the factory to be large enough not to provide a "significant" flow restriction. But if they do not, or if you want to check, you can probably calculate it.

The filter should have an acutal performance specification you can get from the manufacturer: a specified pressure drop at a specified flow rate or range (curve). The pipe is short so there shouldn't be much static pressure drop along its length, but you can calculate drop through the assembly based on velocity pressure and orifice/fitting losses. Let's start with the clarifications first though because they will affect the methodology...

## 1. What is the formula for calculating effective pump flow-rate across a filter?

The formula for calculating effective pump flow-rate across a filter is: Flow-rate = (Area of Filter x Velocity of Fluid) / Time

## 2. How do I determine the area of the filter?

The area of the filter can be determined by measuring the length and width of the filter and multiplying them together. Make sure to use consistent units of measurement.

## 3. What is the velocity of fluid?

The velocity of fluid refers to the speed at which the fluid is moving through the filter. This can be calculated by dividing the volume of fluid passing through the filter by the time it takes to pass through.

## 4. How do I measure the time it takes for the fluid to pass through the filter?

The time can be measured using a stopwatch or timer. Start the timer when the fluid begins to flow through the filter and stop it when the fluid has completely passed through.

## 5. Can I use this formula for any type of filter?

Yes, this formula can be used for any type of filter as long as the flow-rate and velocity of fluid are measured accurately and consistently.

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