I have a tank that is filled with a viscous liquid (~3000 CPs). At the bottom of the tank there is a pipe that leads to a gear pump. There is 22" of pipe straight down from the tank followed by a slight bend (~ 20 degrees) and then 7" to the pump. The liquid level in the tank is variable (H). It is very important that the pump is not starved on the inlet side. The flow-rate out of the pump is 3000 grams per minute. The liquid has a specific gravity of 0.93.
I want to know at what viscosity will I starve the pump. Conceptually, I can imagine that as the viscosity of the liquid increases there will be more and more resistance to it flowing from the tank through the pipe to the pump. To compensate for this the pump will have to work harder to pull the liquid through the pipe to achieve the same mass flow rate. At some point the pump will not be able to pull hard enough to overcome the resistance and it will starve. I found the following equations which seem to be the right way to go:
Q = (dP * Pi * r^4)/(8*viscosity*L)
The problem I have with the equation above is I do not know how to calculate the delta in the pressure. If I just use gravity (dP = rho * g * dH) the flow rates I get are too small. I assume this is because it is not taking into consideration the negative pressure produced by the pump.
Is there a way for me to calculate the hydraulic vacuum force of the pump? Can I put it in terms of pressure? Can I assume there is a pure vacuum inside the pump and say the pressure difference is -1 atm + the contribution from gravity? Is this something I should be able to look up in the manual for the pump?
Any help or suggestions are appreciated. Thanks!