Pressure in parallel pipes

<...the flow into the three seperate pipes is just the initial flow out of the hydrant divided by 3...>

Not necessarily. It depends upon the restrictions to flow in each pipe, which is a function, among other things, of the pipe length and the number and type of fittings.

Iterative calculation is the only way to do network modelling, and there are programs available to speed up the process for critical applications.

<<I know the pressure changes due to the pipes being smaller but does the pressure change due to the pipe spliting into three?>>

In a piping system with "no flow" you have "static pressure". 60 psi at the hydrant equals 60 psi in the plumbing. A larger diameter pipe will not yield or generate more pressure. A larger pipe will allow more flow "gpm" gallons per minute.

With water "flowing" in a piping system you have "Dynamic Pressure". The 60 psi at the hydrant will drop as soon as water flow begins "within reason". The more branches in the piping system with water flowing the more the pressure drop. add in length of pipe and turns plus elevation.

I might add that a smaller pipe will give you more velocity "fps" feet per second at a given psi. Sort of like squeezing the end of a garden hose to water the flower bed thats just out of reach.

Just my 2 cents. Maybe someone else will chime in.

(Old school - Little bus)

What I was stating before is that there will be a pressure drop when the 3" dia. pipe reduces to the 2" dia. pipe according to Bernoulli's equation. The statement about the larger pipe allowing more flow is not true according to continuity. By continuity the flow in will equal the flow out. This is what you stated later when stating that the smaller pipe will have greater velocity, however the flow will be the same entering as exiting. I agree with your statement that the more branches in the system with longer pipe will cause the pressure to drop however how do you quantify this?

With the water flowing the pressures and flow rate at each outlet will be different.

Water follow the route of least resistance and more water will exit at the first riser.

The more water will result in higher pressure at the closer emitters. This may however not be critical.

To offset this imbalance you could introduce flow / pressure regulators. The spring-loaded valves Will introduce additional obstruction (equal to the friction in the remaining horizontal pipe). The pump duty can then be calculated as the static, emitter pressure and friction to the furthest outlet at 3 times the outlet flow. Note that a the pressure loss over the valve must be added as well.

Pressure regulators are going to be used in the system for the record, however what I am really trying to calculate is the theory behind the system, neglecting friction and other losses. You state that more water will exit at the first riser, which intuitively makes sense however how do I quantify this and how do you calculate the pressure at each outlet?

Static pressure would be transmitted equally in all directions. However, you can have pressure effects derived from velocity of flow, which are vectored. Also, as you propigate through the system friction losses are huge factors that can effect pressure in a flowing pipe, and elevation differences play a role in effective pressure of flowing water. You can account for pressure losses from flow in the pipes and minor losses in bernoullis equations. There are some standard loss equations for pipe fixtures and pipe itself, e.g. Darcy-Weisbach. Incorporate these into your calculations. If you know the flow you want to delivery you can calculate these. It is not necessarily true that you will deliver the flow equal to 1/3 of the flow from the hydrant when free-flowing. It will be likely much less, after you run the calcs assuming maximum possible flow at the hydrant is equal to free-flowing condition. You can calculate the equations based on the pressure you want to achieve at output from the sprinkler nozzle. Thus you have some boundary conditions and parameters to work with-maximum possible flow, minimum possible pressure at nozzle, design pressure at nozzle.

Example let us consider it at a irrigation lateral.

For a start replace the riser pipe and sprinklers with an equivalent nozzle mounted on the 3" pipe.

The discharge at the desired pressure can be calculated.

say P3 and Q3 @ Diam

Now calculate the friction of that flow in the 175'x 3" section.

The pressure at the centre point would then be P2 = P3 + F3

Q2 can then be calculated.

Now determine the friction loss in the first 175' x 3" section.

Q = Q3 + Q2 == F2

the pressure at the first nozzle can now be calculated P1 = P2 + F2

The total discharge Qt can be calculated. (Q3+Q2+Q1)

It the same procedure is repeated with 10% above and below design pressure the system curve can be plotted.

If the pump curve is plotted on the same graph the discharge can be determined (where the 2 curves cross)

This can also be done using software.

The same principle can be used with riser pipes.

The following opinions are based on a BS/Chem E with 40 yrs experience who has been a firefighter/fire truck driver for about 20 yrs (if you don't like them push the DEL. key) --> Your rational and orders of importance need to be realigned. Friction loss can not be ignored, it is your 3rd most important factor after inlet pressure and pipe sizes. Yes, press. will be even with no flow but will change drastically with the pipe sizes and runs you are stating. Regulators reduce pressure yes, but also create alot of additional loss in doing so, press reduction equals flow loss.

You must figure out what is the available pressure/flow into the system, what are acceptable outlet pressures/flows and then design your system around those figures by changing pipe sizes, configurations, flows, etc. Perhaps over simplified but that is the basics of piping design.

What you are trying to do is done every day by fire pumer operators and officers. You have an available hydrant pressure and flow, frictional loss through the supply hose to the pumper, pump capacity both press and flow, frictional loss through the appliance delivery hose (most often a "hand line" of 1-1/2" to 2-1/2" dia) which is also dependent upon the flow through the hose, frictional loss of the nozzle and finally you get to put the wet stuff on the red stuff. Add in some other devices being supplied by the pumper, mix in some elevation loss and several other factors and you have to have alot of knowledge to operate that red vehicle with the loud siren and the horn.

I would suggest that you get in contact with a engineer with much practical piping design experience, a good fire engine operator (the pumper type) or a sprinkler system designer to quickly get to know the important things in flowing water.

What you are trying to do is more relevant to firefighting than what Bernoulli's equation can help you with.

Bill, ChemE & Asst Fire Chief

sure yes

This is a complex scenario.

In simple terms if the hydrant is opened fully then the flow will cause a head loss in the 3 inch pipe. This head loss can be drawn on your section as a straight line from the upstream point to the hydrant. This is the Total Energy Line for your system

Starting at the original pressure reducing to the pressure at tha hydrant

If any of your sprinklers is situated below this Total Energy Line, Then no flow will come out of the sprinkler

The amount of flow coming out of each sprinkler will depend on how high the Total Energy Line is above that sprinkler. ie The Available Head at the sprinkler

Very simple really to calculate

It may be that if a fire breaks when no one is there the Sprinklers will all work.

If someone is there and opens the Hydrant the Sprinklers will all dry up

In a static condition, no flow, the pressure will be the same at all places.

If all sprinklers are open and flowing the 3" diameter pipe has less area than 3, 2" pipes.

The closest 2" will get the lions share of flow and highest pressure. There will be less flow and pressure from those units farther away from the source during flow.

The Spriklers are higher than the hydrant (20 feet ) so evan if the sprinklers are working the hydrant will still work (at reduced pressure).

When the hydrant is open it will likely take all the water, and the Toatal Energy Line will be below the sprinklers

If you are looking for software to calculate this I would recommend EPANET. It is used for pressure pipe systems and is fairly easy to use and best of all it is free. It is available on EPA's website. http://www.epa.gov/ord/NRMRL/wswrd/dw/epanet.html

AS YOU CAN SEE BY THE NUMBER AND VARIETY OF THE ANSWERS YOU HAVE ALREADY BEEN GIVEN, THIS IS A VERY COMPLEX QUESTION IF YOU CONSIDER ALL THE FACTS AND VARIABLES HERE. HENDRIK SEEMS TO HAVE A REASONABLY GOOD GRIP ON THE QUESTION. HIS ANSWER HAS MERIT. LET ME JUST GIVE A FEW OF MY OWN OBSERVATIONS.

FIRST OF ALL, THE ARRANGEMENT OF PIPES AND VALVES AND ELEVATION DIFFERENCES, ETC. ARE COLLECTIVELY KNOWN AS THE "SYSTEM" OF PIPING. WHERE THE 2" BRANCH LINES GO OFF FROM THE 3" IS THE BEGINNING OF A NEW PIPING SYSTEM. THERE ARE AT LEAST FOUR "SYSTEMS" IN THE SCENARIO AS GIVEN. THE FIRST IS THE 3" PIPE FROM THE HYDRANT TO THE INTERSECTION OF THE FIRST 2" PIPE. THE DESIGNER MUST FIGURE THE TOTAL DYNAMIC HEAD IN THE SYSTEM FROM THE HYDRANT TO THAT POINT FIRST. THE SECOND SYSTEM WOULD BE THE 2" PIPE FROM THAT INTERSECTION TO THE END OF THAT 2" PIPE. AGAIN, ELEVATION, LENGTH OF PIPE, FLOW, ETC MUST BE CONSIDERED TO GET A TOTAL DYNAMIC HEAD FOR THAT SECTION (SYSTEM) OF PIPE. TO GET THE EFFECTS OF THE FLOW FROM THE HYDRANT TO THE END OF THE FIRST 2" PIPE, THE 3" SYSTEM TO THE INTERSECTION OF THE FRIST 2" MUST BE ADDED TO THAT OF THE 2" TO GET THE TOTAL DYNAMIC HEAD FROM THE HYDRANT TO THAT POINT. EACH SUCCESSIVE BRANCH MUST BE SIMILARLY CALCULATED TO DETERMINE THE CHARACTERISTICS OF EACH BRANCH. THEN THE TOTAL EFFECTS FOR EACH BRANCH WOULD BE ITS OWN CHARACTERISTICS ADDED TO THE 3". AS YOU CAN SEE, THIS IS QUITE COMPLICATED. THAT IS WHY THERE ARE MANY MENTIONS OF SOFTWARE. IT CAN BE DONE MANUALLY, BUT IT IS TEDIUOUS AT BEST. A FINAL CONSIDERATION IS THE AMOUNT OF ACCURACY THAT IS REQUIRED BY THE APPLICATION. IF THIS IS A CLASSROOM ASSIGNMENT, THE ACCURACY IS PROBABLY REQUIRED BEYOND WHAT WOULD BE NEEDED IN AN ACTUAL APPLICATION. IF IT IS AN ACTUAL APPLICATION, THEN IT CAN PROBABLY BE CALCULATED OR "GUESSED AT" WITH A REASONABLE AMOUNT OF ACCURACY FOR THE APPLICATION. LOOKS LIKE SOMEONE HAS A LOT OF WORK AHEAD OF HIM. GOOD LUCK!!

IIRC Sprinkler calculations must be based on flow to a specific number of heads, (Outlets).

Isn't it customary to assume that your fire is in one area and thus the hydrodynamic effect of anything but the pipe leading to the flow is irrelevent?

I think that what is appropriate is a worst case, (longest path) calculation based on the flow required by the Code specified number of heads to be served.

You can not ignore the friction losses in a pipe system for the purpose of calculation of pressure in the system. Pressure losses in the system are directly related to the friction losses in the pipe including minor losses from fittings and losses due to nozzles at the end of each pipe where the demands are registered. Friction losses are directly related to the velocity in the pipe. As the total area of the system changes, going from one 3-inch to 3 2-inch pipes the velocity will change at each branch. Due to friction losses, the pressure at the first branch will be higher, given that all branches are at the same elevation, than that at each subsequent branch. Depending on the flow rates this pressure difference can be very large. Pipe system calculations are very complex and required iterations to solve this type of problem. Pipe system modeling software is available that will do this very quickly. Spreadsheets can be developed to do this. Engineers can be retained to run these calculations.

There are then 3, 2" dia pipes that vertically connect to the 3" pipe.

These pipes connect to another three seperate locations which go to the sprinkler system.

Configure a manifold at each location to ensure pressure drop is not an issue.