You may stir some discussion about your assumptions as to the displacement of a person in the tub. Your 20-40 gallon estimate would mean that about 160 to 320 pounds of their mass would be below the waterline.

Be that as it may:
Existing risers should be adequate, providing there is adequate pressure for your fill-valve to provide 24 gpm.
To measure your water pressure, get a water pressure guage (hardware stores sell one made by Watts for around $10) that attaches to a hose fitting and measure it directly. Do this as close as possible to the faucet in question to get the most accurate reading, and subtract 1/2 psi for every foot of vertical distance from the guage to the faucet (if the guage is at a lower level). The flow rate of your tub-fill valve at that pressure would then give you an idea as to how fast it will fill. As an alternative, you could time how long it takes to draw a 5 gallon bucket of water and do the math.

As for your second question: The valves, not the pipes, will have problems if the water pressure is too high, especially the toilet refill mechanism. Even then, it would normally be the valves on the lowest floors that would first experience problems.

Randy,,i hate to differ with you but that method of computing the pressure is totally wrong.

in order to measure dynamic pressure at any point of discharge you must insert a TEE at the discharge with a pressure gage on the side opening of the tee.

Measuring in the manner you describe simply gives the "Static Head" pressure less the "Vertical Head" loss but it does not take into account friction head loss, which would be proportionate to the velocity of flow.

The proposed velocity of flow in the original post far exceeds the recommended velocity for a 3/4" line.

Thanks very much for your replies.

Randy,

On displacement, I need to reread my Archimedes. Or maybe I should excuse my error by noting that this is a 2 person tub!

Lazypup,

I think I am beginning to understand things better now. (The installation instructions are 15 pages long, after all, and this is all completely new to me.)

The HW and CW are both coming into the bath in 3/4" lines. They then enter Dornbracht's Xtool mixing valve. This obviously must be like any other mixing valve with 3/4" inputs.

I can get the mixing valve in 2 different configurations. This one has "volume control" (I think that means the three shower valve bodies.)

As your can see, the output of the mixing valve is a manifold from which 4 different 1/2" lines branch off. I should have mentioned that the shower head is really 3 different heads combined and that each head is fed by a 1/2" supply.

The Alternative is

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Question:
Does this change the water flow equation?

I also see that Dornbracht recommends a *minimum* HW tank of 500 l. or 132 gal. Mine is only 79 gal. Should I add a secondary storage tank?

PS. This riser only serves this bathroom on the 3rd floor and no fixtures on lower floors.

If ever there was a useless piece of equipment offered for sale in the hardware store it has to be the WATTS pressure gage with the attached female hose connecter. For a mere $10 you can purchase the gage, attach it to any faucet in the house with a hose thread, turn the faucet on and voila, you instantly know the static head pressure in your water distribution system. Big Deal, with that fact and about $5 you could get a cup of coffee at starbucks but in the real world of plumbing you donÂt know any more than you did before you got the gage. Ask yourself this question. What psi do you need to get a good shower? What psi does it take to fill your bathtub from the spout? In truth, at this point we havenÂt even established a proper standard of measurement. Is this psi? psia? or Psig?
PSI simply defines pounds per square in, however vacuum can be expressed in psi, and in that case the water would be getting sucked back into to pipe rather that providing a solid force in your shower.

PSIA (Pounds per square inch-absolute) is commonly used in scientific notation because it measure the total pressure above zero pressure (Perfect Vacuum) and a psia gage sitting alone on a workbench not connected to anything would read 14.7psi at sea level. Why? Because the atmospheric pressure is 14.7psi at sea level and a PSIA gage reads all available pressure above zero, but then the atmospheric pressure drops one pound for each 1000ft of vertical elevation so if the gage is on a bench in Denver, Colorado it will only read 9.7psia. In fact, this is exactly how the altimeter on an airplane works. On the other hand, if you lived at sea level and hooked a PSIA gage on your water line and you got a reading of 10psi it would be indicating 4.7pounds of negative pressure (vacuum) on your water line and your not getting any water.

For the record, the WATTS gage in question is calibrated as a PSIG (pounds per square inch gage- meaning pounds per square inch above standard atmospheric pressure). Technically speaking where I live the elevation is 1154ft above sea level so a PSIG gage has a 1psi error here. Some gages such as those used by HVAC technicians have a removable cover glass and a small set screw so the technician can zero the gage for the current atmospheric pressure but for the purposes of measuring water pressure one psi more or less is not going to make much difference.

Now let us consider the question at hand.
The shower is on the third floor in a row house in NYC, For the sake of illustration let us assume the water main is under the sidewalk immediately outside the house about 25ft from the water meter and the post says they have a 1" water line coming in.

The International Residential Plumbing Code says we must have a minimum of 45psig static head pressure (static meaning at rest-no flow) at the junction of the house main shutoff valve. (Under the Uniform Plumbing Code we are only required to have 15psig per UPC 608.1). Assuming for the moment that we have the required 45psig at the main in the basement, what do you suppose the static head pressure is at the tub on the third floor? Water weighs .434pounds per foot of vertical column and the physical weight of the water standing in that riser opposes the flow so while the static head pressure at the main is 45psig at the tub 30ft above the static head pressure would be 45psig  (,434x30)= 45psi- 13.02psi = 31.98psi but keep in mind that this is still the static head pressure. Once flow begins all this will change instantly.

Once flow begins we not only have the vertical static head loss but we also have pipe wall friction loss and pipe wall friction loss changes proportional to the velocity of flow.

The post stated that the showerhead has a flow rate ranging from 9.8 to 15gpm. For simplicity let us use 10gpm as the flow rate.

Consulting the Copper Tube Handbook, page 30, table 6-Pressure loss of water due to friction in types K, L & M copper and let us use the figures for type L.

We now have 10gpm coming in the 1" water line from the municipal main and the distance is 25ft.
At 10gpm the friction loss in a 1" Type L copper pipe is 0.027psi/ft
0.027 x 25ft= 0.675psi so the pressure at the main shutoff is now 45psig  0.675psi = 44.325psig

From the main we have two ¾" risers (hot & cold) and the ratio is 2H to 1C or 6.66gal. of hot water and 3.33gal. of cold water.

At 6.66gpm the friction loss in ¾" copper is approx. 0.030psi/ft and we have a 30ft rise so the friction loss is 0.030 x 30= .9psi and the vertical static head loss on the 30 ft riser is 13.02psi so the combined loss is 13.02 + 0.9= 13.92psi.

The hot water pressure at the shower mixer is then 44.325psig  13.92psi = 30.405psi.

Also keep in mind that if any other demand for water is turned on during your shower the velocity of flow in the main and distribution lines would increase, thereby increasing the friction loss and again lowering your shower pressure.

The reason we donÂt install a pressure gage on the water system is because under normal use the gage needle would be jumping like a windshield wiper and the average homeowner would be in a panic thinking something is wrong with their system.

In fact, these changes are so dramatic that while the International Residential Code requires 45psig static head pressure at the main, TableT-2903,1 only requires a flow rate of 3gpm @ 8psig at the shower.