# B How much power required to generate a particular pressure

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1. Oct 29, 2016

### escape_velocity

Are there any general guidelines or rule of thumb regarding how much power in watts would be required to pressurize a cylinder to a particular pressure and can I use this as a general rule,

For eg. I want to pressurize a vessel of volume 1 cu. m how much power would be required and can we generalize this so the this formula can be applied to a vessel of any volume?

2. Oct 29, 2016

### Staff: Mentor

There is no meaningful general relation between power and pressure. Not even between energy and pressure.

3. Oct 29, 2016

### sophiecentaur

Testing divers' compressed air cylinders is done by pressurising them with (nearly incompressible) water). If they 'fail' catastrophically, they just form a split and there is very little disturbance. There is very little energy stored.
OTOH, if a cylinder fails when being over-pressured with air, you have a BOMB on your hands. So much more energy involved. You can pressure test a cylinder with a few strokes of a manual water pump but an air compressor (a few h. p.) runs for minutes and everything gets too hot to touch.
No simple rule to connect the two.

4. Oct 30, 2016

### escape_velocity

What if I say that the fluid is "air" now would there be an equation for power to pressurize a cylinder with air to a particular pressure?

5. Oct 30, 2016

### sophiecentaur

OK But that is still not specific enough. Are we doing this quickly or very slowly? (Isothermal or Adiabatic) Diving cylinders are kept cool (in a water bath) during compression or their 'final' pressure will go down as their temperature drops.
Actually, if you Google Divers' Air compression, you may find some actual examples. That could answer your question if it is practical rather than theoretical.

6. Oct 31, 2016

### CWatters

The pressure (and other info such as temperature) give you the energy stored in the tank.

Power = ΔEnergy/ΔTime so to calculate the power you need (at least) some info on how fast you are putting the air in.

Even then it's not that simple because (as Sophiecentaur says) the temperature may also depend on how fast you put the air in and factors such as the thermal mass of the container, how well insulated it is etc.

How accurate an answer do you need?

7. Oct 31, 2016

### Staff: Mentor

Let me provide some examples in hopes they may help:

Say, you are pressurizing a car tire to 200 kpa. You can:
1. Use a base mounted compressor with a tank, which can provide compressed air at thousands or tens of thousands of Watts.

2. You can stomp on a foot-pedal pump for a peak power of perhaps a thousand Watts.

3. You can use a hand-held bike pump with a peak power of perhaps 50 Wattts.

As you can see, all of these give the same result (an inflated tire) but require/use vastly different power to do it. The main difference is how long it takes. So you see, there is more to finding the power required than just the final pressure.