Re: Air pressure displacing water (revised)

The short answer is yes, the flow rate will change (decrease) as the water level in the tank decreases for a fixed pump pressure.

Let’s examine what happens with the system. First, Imagine there is no pressure applied by the pump, and thus the water will not flow. As the pump starts to supply pressure, the water will just begin to flow when the pressure is equal to the difference in height between the tank water level and the highest point in the exit spout. Pressure is often expressed as “head” with units of distance, often in feet or meters, but can be converted to pressure, such as PSI (pounds per square inch). For each 1 foot of head is equal to 0.433 PSI. So if the difference between the water level in the tank and the highest point in the exit spout is 1 foot, then the pressure needed to start the system to flow is 0.433 PSI. Additional pressure will make the system flow faster. The faster the water flows the more pressure is loss by friction (similar to air resistance). But note that as the water level decreases in the tank, more and more of the pressure applied from the pump will be used to overcome the height difference between the water level in the tank and height of the exit spout peak. Once the water in the tank has dropped to the point that it is 2 feet below the peak height of the exit spout, then 2 x 0.433 PSI is required to pump the water up and over the exit spout peak. Even if you have sufficient pressure to start flow, the water in the system could stop flowing if the water level in the tank drops to the point that the difference between the tank level and peak exit spout level is greater than the applied pressure.

The exact flow is dependent on the flow resistance and NET resultant pressure applied by the specific pump being used. The Net or total available pressure to generate flow is the difference in pressure between the pump pressure and the height between the water in the tank and the peak height of the exit spout. The flow resistance is primarily a function of the tubing diameter, tubing surface roughness and tubing length. Also the entrance and exits conditions (shape of inlet and outlet orifices) from the tubing will effect the flow resistance and flow rate. All this can be estimated from empirical data and analytical calculations available from many sources.

I would suggest further reading, a good place to start is at the engineering toolbox, and they have many equation and descriptions of this topic. See

http://www.engineeringtoolbox.com/fluid-mechanics-t_21.html

Engineering toolbox, pressure – head conversion
http://www.engineeringtoolbox.com/pressure-head-converter- d_406.html