Please provide a formula for working out pressure and volume of water. known as Hydraulics?

Question

I have a 4 inch pipe supplying water at 6.7 bar pressure to hotel rooms in a 4 story block.
Connected into the 4 inch main feed pipe are a number of Risers to the floors which are 1 inch pipe.
Each riser supplies water to 2 rooms each on the 4 floors making a total of 8 rooms.
Each room has a shower, a vanity sink and a toilet.
The piping to each of the above utilities is further reduced from the 1 inch riser to 1/2 inch.
Problem: If a number of rooms is using the shower at the same time, the water pressure to the 4th floor is almost zero.
Question 1: What is the formula for working out the pressure drop to the 2nd 3rd and 4th floors.
At the present time the 4th floor rooms are the main problem areas.
Question 2: how do I increase the volume of water without increasing either the pressure, or the size of the main riser pipe.
Note: The main 4 inch supply pipe has 32 1 inch risers tapped into it thus supplying 128 rooms.

Answer 1

What you need to do is estimate the water usage in GPM of each unit, and then calculate water flow rates and pressure drops based upon that info.

The recommended maximum flow rate thru a 1/2" copper line is about 2.2 gpm. You have (8) of these lines connected to each riser, however the maximum flow rate recommended for a 1" line is only about 10 GPM, so my guess is that your 1" risers are sized too small if everybody in all the apartments are up and getting ready to go to work.

Increase the riser size, or double the number of risers, but check the numbers first.

The 4" main header may be OK.