To whom it may concern,
I have completely understood the king of project you need.
In term of equations, it is necessary to use the Bernoulli's equation to evaluate the parameter such as power, pump head, flow rate, pressure drop.
All of those parameters represent the variable of our system. I can provide a good evaluation and also I can find out in there are any commercial pumps already available for your purpose.
Sincerely,
Fabio Bosio