# Does the pressure in a pressure tank depend on the amount of air?

I have a pressure tank which is filled with water and air. What want to know is: if I change the ammount of air in the tank would the ammount of water that leaves the tank, when pressurized, change?

If the tank was initially pressurized and the water keep refilling as to keep the volume of water constant would the ammount of water expelled from ythe tank depend on the initial volume of pressurized air

• Can you clarify what you're asking? Obviously if you increase the air pressure in the tank it will push the water out faster. Were you after an equation to predict the relationship between the water flow rate and tank pressure? – John Rennie Sep 2 '14 at 5:56
• No i mean to increase the voleme of air in the tank but it will remain at the same pressure also if there is an equation that relates the pressure on the tank to the speed at which the water is spelled – user165129 Sep 2 '14 at 6:09

You can answer this question yourself with a simple thought experiment. If you removed all the air, what would happen? The answer is, that regardless of how much you pressurize the tank, only a tiny bit of water could escape before the pressure has dropped (because water is essentially incompressible).

At the other extreme, if there was so much air in the tank that only a tiny bit of water remained, then the air could expel all the water, but that would not be very much water.

Right there, you can see that the answer to your question is "yes". Somewhere between these two extremes lies the amount of air that optimizes how much water can come out. What that optimum is depends on the maximum pressure your tank can withstand, and the minimum pressure needed to expel water. If we call these $p_{max}$ and $p_{min}$ respectively, and the pressurized volume is $V_p$ while the tank volume is $V_t$, then you can write down the following equations:

If $$\frac{p_{max}}{p_{min}} < \frac{V_t}{V_p}$$

then there is enough water in the tank, and the volume of air that ends up being expelled is

$$V_{out}=V_p \frac{p_{max}}{p_{min}}$$

From these two equations you should be able to determine the optimum amount of air in your pressure tank.

• That's actually pretty intereating so what if the water volume was constant but the air was only compressed once? Then the ammount of water released would be proportional to the initial pressure but as the volume of the water doesn't change then.... the water expelled would depppend on the volume of the tank that is filled with air? – user165129 Sep 2 '14 at 7:23