Pressure required to move a liquid

[KenR]

I have a container that measures 1 cubic foot and is full of water. I have another empty container that is 4.5 feet higher than the empty container. The full container has a fluid outlet on the bottom, and an air inlet on the top. A hose (1 inch diameter, 4.5 feet long) connects the fluid outlet to the empty container. I want to know how much air I need to add to the full container to move all of the water out of the full container. I tried figuring this out, but my answer is clearly incorrect.

I reasoned that since 1 pound of pressure is required to raise the water 2.31 feet, 2 pounds of pressure should be sufficient to accomplish the job. Next (based on this thread: https://www.physicsforums.com/threads/volume-and-pressure.87911/) I calculated that (assuming no temperature change) it would take 2/14.7*1=0.136 cubic ft. This does not make sense, as it would not even fill the container, let alone pressurize it.

 

[Nidum]

You first have to decide how fast you want the water to flow from the lower tank to the upper tank . Once you have that information you can determine the necessary air pressure .

 

[KenR]

Speed is not important to the practical application, but if it is required to calculate an answer let's assume 2 minutes.

 

[Nidum]

Bernoulli's principle can be used to find the pressure needed . Are you happy working with simple formulas ?

 

[KenR]

I think so. Certainly willing to try.

 

[KenR]

Note to Nidium. I am not so much interested in pressure as I am in volume of air required. I don't want to pressurize the container and then open a valve. I want to add air to the system and as the air is added, the liquid moves. I do recognize that it is necessary to first calculate the pressure required, and then from that the volume.

 

[jbriggs444]

I calculated that (assuming no temperature change) it would take 2/14.7*1=0.136 cubic ft.

0.136 atmospheres of pressure is required, yes. 0.136 atmospheres more than ambient, to be precise. One assumes that the empty container has a vent, so it is under 1 atmosphere of pressure already.

So you need to displace one cubic foot of water with air that will end up at 1.136 atmospheres of absolute pressure. How many cubic feet of room pressure air would you expect that to take.?

 

[russ_watters]

Your equation is just upside down, that's all that is wrong with the second part.

For the first part, remember that it is the top surface of the water that matters, not the bottom surface.

 

[KenR]

Jbriggs, Would it be as simple as 1 X 1.36 = 1.36 cubic feet?

 

[jbriggs444]

Jbriggs, Would it be as simple as 1 X 1.36 = 1.36 cubic feet?

Yes. But @russ_watters makes a good point about the water levels.

One could quibble about adiabatic versus isothermal compression as well.

 

[KenR]

Thanks everyone. This is a great resource. It looks like my idea for a refueling system is feasible.