The amount of horsepower that is needed to pump the water for 3 floors of a building is 1 HP to 2 HP.
A 1 HP to 2 HP pump should be able to lift water up 3 floors, although the exact HP that is needed will also depend on height of the lift and flow rate.
Flow rate is how much water needs to be moved per minute in gallons per minute or GPM.
The Height of the lift is the vertical distance that the water needs to be pumped, including any friction losses in the pipes.
The length, diameter and the number of fittings that are in the plumbing system also affect the HP needed as well as the efficiency of the pump.
To determine the exact horsepower needed for the pump you calculate the total dynamic head and determine flow rate.
Total Dynamic Head is the total vertical distance the water has to travel plus any friction losses in the pipes.
And the flow rate is the amount of GPM or gallons per minute that are needed at the upper floors.
Higher pump head is better, especially for when you need to move fluids against a high resistance like when lifting the fluids to a higher elevation or when pumping the liquids over a long distance.
Having a higher pump head indicates that the pump can also generate more pressure and enable the pump to overcome the resistances and move the fluid more effectively.
The higher the pump head the more powerful the pump is and the more pressure the pump is able to generate.
To increase the height of your pump head you need to increase the diameter of the pumps impeller and increase the pumps power or modify the pumps system to reduce friction and other losses.
Increasing your pump's power can be done using a more powerful pump or by increasing the RPM of your current pump, "if the pump is designed for variable speed".
You can also reduce the friction losses in the pumps system by using fewer fittings and or larger pipes which can also result in an increased pump head.
Larger pipes also reduce friction and allow the pump to generate more head for a given flow rate.
And fittings in the pipe system cause friction losses, so minimizing the number of fittings can also increase the pump head.
And using a longer vertical pipe can also increase the head of the pump by allowing the pump to push water higher before it encounters resistance from the system.
And in some cases you can add a second pump above the first pump to increase the vertical lift.
Also the suction lift or how high a pump can suck water from below can also affect the head as it also adds to the total head requirement.
And understanding of the pump curve can also help you to determine the maximum head and flow rate for a given pump.
The TDH or Total dynamic head is also the total amount of resistance that the pump has to overcome, which includes vertical lift, friction losses and other factors.