# Force due to a submersible water pump to move an underwater vehicle

## Homework Statement

I'm trying to find the force exerted by a 500 GPH (gallons per hour) submersible bilge pump.

My team is designing a submersible vehicle for our university course. The vehicle is only supposed to move up and down in the vertical direction; basically it should just be able to change its depth. We're using submersible bilge pumps to move the vehicle. I'm designing the control system using an embedded microprocessor and I'm trying to understand the force exerted by the pump to correctly design the control logic.

The spec for the pump is just gallons per hour, and I think there should be a way, using pressure, water density etc, to convert this to a force in newtons, but I can't quite get there.

## Homework Equations

Pressure = Density * Gravity * Height
Pressure = Force / Area
Density = Mass / Volume

## The Attempt at a Solution

I first tried a dimensional analysis to get Gallons per hour into newtons, but it isn't quite that simple:

1 N = 1 kg * m / s^2
1 Gallon / hour = 1.05 * 10^-6 [m^3 / s]
Density of water = 1000 kg/m3

I don't think there is a way to manipulate the units to obtain newtons. I don't think that Gallons per hour is in fact a force, but a flow rate, so we need more information.

Then I tried using the equation for pressure:
Assuming the water pump is facing up, and the vehicle is 10 m under the surface of the water tank, then I think that the pressure on the pump is:

Pressure acting on the pump = pgh = (1000 kg / m^3) * (9.8 m/s^2) * 10 m

Then, to move the vehicle, the pump must exert a force:

F = Pressure acting on the pump / Area of pump nozzle

But this doesn't take into account the 500 GPH rating of the pump, so we still need more information.

I don't particularly want to include hydrodynamics in this simple model because it would definitely complicate things.

I think the pieces are there, I just can't make them fit.

Any help would be greatly appreciated.