# How do I calculate the max flow rate for a pump with no power restrictions?

Let's assume we have a pump and it can draw as much power as it needs. As the pump speeds up, it creates vacuum in the intake. At some point it draws the gas/liquid so fast, the intake pressure is so close to 0. At that point, no matter how much power we put into the pump, the flow rate doesn't increase.

I figured out it strongly depends on the intake size and shape, the type and design on of the pump etc.

On what other factors does it depend? Is there a way to calculate or at least estimate the maximum? Is it even a valid question?

This phenomenon is known as cavitation for pumping liquids - i.e. for anything that can change phase. If you are pumping gas, then the scenario really does come from choked flow.

Let's say you've got a compressor and you're running it as a vacuum pump to evacuate a tank - at some point the tank's pressure on the inside is so low, you can't pump any more air out. This shows your question is a valid question. It's a slightly different scenario, but it's easier to analyze using a real compressor at it's maximum suction pressure then your mythical high power compressor.

Using a piston-style compressor analogy, the maximum that the pump could remove would be based upon the max lift of the valve. If you can't compress the gas to the point that the outlet valve will open to prevent air from coming back into the tank, then that's it - that's your maximum suction. No matter how much power you put on it, you can't have more suction.

Other compressor designs work on the different principles, but the analogy holds - rotary turbines ultimately start with a gas at a pressure, then compress it with stators, rotate it again, compress it, etc. in cycles. However, at the back end of the compressor is air (or in the case of a jet engine, combusted fuel) pushing back. So long as the compression from that last stage of the turbine can push back on the air coming in (and all the way down the line), the compressor will work. Beyond that point it will not.

• The phenomenon known as choked flow occurs for supersonic flows. When the gas reaches the speed of sound in the pipeline from the tank to the compressor, then it will reach "choked flow". No matter how much the compressor pulls on the gas the flow rate can't exceed it's own speed of sound - effectively the compressor can't communicate the pressure differential back to the tank to make it speed up. While similar to the phenomenon I described above, the compressor will still compress the gas - just not any faster. The phenomenon described above is the way to calculate the maximum compression.
– Mark
Jul 8, 2015 at 13:01

### What you are describing is known as "choked flow".

I am only familiar with choked flow in a gas, however a brief wikipedia snoop shows that liquids are limited by a different phenomenon, which makes physical sense if you understand the mechanism of choked flow in a gas.

In its simplest form, it depends only on minimum cross sectional area and fluid properties.

If you are pumping using suction, the flow is driven by the pressure difference between atmospheric pressure and the vacuum. So if atmospheric pressure is 1 bar then 1 bar is the maximum pressure difference you can create, regardless of the pump design or power as you can't have negative pressure (in the sense of less pressure than a vacuum). So in this case the flowrate is quickly limited by the size of the orifice you are pumping through.

To get higher pumping pressures you need to be directly pressuring the fluid you are trying to pump