How do I get a rough estimate of how many litres per minute a motor can push?
First order approximation: Do it as a work problem.
Power = energy/time
so Energy = power * time.
Energy = Work = force * distance = pressure * volume. (Do the dimensional analysis...)
So power * time = pressure * volume
power/pressure = volume/time
The rest is picking a compatible set of units so you don't end up with something weird like board-feet per fortnight.
So given a 5 horse motor, and a 100 foot head, how much water can I move?
1 hp = 746 watts 5 hp = 3730 watts
100 foot head = 43 psi.
If you leave it in psi you will end up with a bizarre unit. I think it would be kgm/lbft*s which gives me a headache trying to visualize.
Easier to conver 43 psi to about 280 kPa
So 3730 W/280 kPa =.013 cubic meters per second or about 13 liters per second.
Add 5% losses to the pump. 10% pump loss. 10% hydraulic losses and you get about 10 liters per second.