Venturi flow calculations

[bjenks]

I am trying to do some energy calculations for an aquaculture project that is trying to calculate different methods of creating flow in a channel and injecting air into water. So I am electrical engineer in background, but have some basic fluid knowledge. They currently want me to evaluate a 2 HP pump with a 2" PVC pipe going in to multiple 2" venturi with a 1"x 60" pipe at the throat of the venturi. My job is to determine how much air is being injected and then the total flow. So assuming the entry is P1*A1 and the throat is P2*A2 and the water going into the venturi is at 30 psi at a velocity of 8.17 f/s in a 2" pipe I solved for P2. I came up with P2=P1 + C*(SW*V1^2(1-1/B^2)/(2*g)) where B=A2/A1 and SW=Specific weight and g=gravity rate and C=discharge coefficient. Is that correct? Step 2) Assuming the 1" throat injector pipe is supplied from sea level atmosphere at 14.7 psi, is it true that I have to get P2 below 14.7 to start sucking air in? by playing with the B I can get the pressure down to minus 45 psi which is impossible so there must be a theoretical limit on P2 (Choke flow)? Suppose P2 is at 7 psi from the water flow and I used Poisevilles Equation to determine R of .667, does that mean the air intake is (14.7-7)/.667 (I have some conversion in so that I come up with 298 CFH. The problem is Mazzei Injectors show a much different number. I have enclosed a spread sheet to show my calcs.

 

[chicopee]

Get Mark or Kent ME Power handbooks and the subject on injectors is well covered. If your static pressure at the throat of the venturi is greater than atmospheric pressure, I don't see how air can be aspirated, so you'll have to size the throat using Bernouilli's equation. The specific weight of the liquid at the throat will need to be modified with the introduction of the air stream and a subject on that aspect is well covered under air lift pumps also detailed in the above references.

 

[bjenks]

Thanks chicopee, I actually have the Marks Standard Handbook for ME and it does have the basic venturi info, but nothing on design of a system that consist of a incompressible fluid going through a venturi that then suck in air and pushes out a combined mixture. air lift pumps are based on blowing air into a tube that changes the density of the water/air and thus causes it to rise. I am not sure if you were envisioning that as part of your response. Venturi Injector aeration is a different process.

 

[chicopee]

With air lift pumps, I am suggesting that there are formulae for densities of water, air and solids(which become entrained) in the mixtures. A mixture of water and air at the throat is what you'll need in the application of the first law, at least that is the way I would approach the problem.
There will be suction of air at the throat or even past the throat where you still have high velocities. A simple experiment would be to expose one end of a plastic tube perpendicular to the water jet from a nozzle supplying recirculated water to a pool and the other end to atmosphere. Air will be aspirated which is what you want,a two phase flow. Another example would be the old snow gun technology used in ski area where water and air are combined in a ventury and released to atmosphere as a fine spray turned to ice.