# A little bit about hydraulics.



## sprinklertech (Oct 24, 2010)

Most of you who are going to be installing these systems won't be all that much involved with the design, especially hydraulic calculations or evaluating water supply requirements, but I feel it would help to know some of the basics.

You are going to run into something similar to where you have an 18'-6" x 21'-0" room where the designer showed four sprinklers but you have enough experience to know the Viking VK568 Residential Pendent Sprinkler is listed to cover an area 20'x20'. Obviously the room could be covered with two sprinklers so why did the designer show four?

Most likely there is a very good reason. 

NFPA 13D Standard for the Installation of Sprinkler Systems in One- and Two-Family Dwellings and Manufactured Homes *Section 8.1.2*



> Number of Design Sprinklers. The number of design sprinklers under flat, smooth, horizontal ceilings shall include all sprinklers within a compartment, *up to a maximum of two sprinklers*, that requires the greatest hydraulic demand


If we have a room (compartment is the correct terminology) where heads are spaced in such a way they each require 13.0 gpm the total demand required will be to two sprinklers for a total of 26.0 gpm. This could be a vary large room having four, six or even eight sprinklers but still all the pipe and water supply need only to adequately supply two of those heads. Even with eight sprinklers in the compartment all we need is 26.0 gpm.

Given our 18'-6" x 21'-0" room (compartment) consider the *Viking VK468 *pendent sprinkler.










Obviously two sprinklers can cover the room as long as they are supplied with enough water at sufficient pressure. An 18'-6" x 21'-0" compartment will require a minimum of two sprinklers two will be spaced along the 21' length... most likely they will be 10'-6" apart and 5'-3" from each wall. Along the 18'-6" length they will be spaced 9'-3" off the wall.

Because the width is more than 18' you need to use the demand for 20'x20' which is 20 gpm. It doesn't matter if it was a 3' wide hallway if the maximum spacing length ways is 18' to 20' the required demand will still be 20 gpm.

With two sprinklers the total water available will be 40 gpm and that is a lot of water. You are certainly not going to get that from a 3/4" line and probably not from a 1" line either. Probably could get it from a 1 1/4" line but what if the city has outrageous tapping fees for anything over 1"?

But what if we installed four sprinklers?

Along the 21' length we'll keep 10'-6" apart and 5'-3" from each wall but well move them over 4'-6" off the each wall the 18' length and 9'-0" apart.

Now how much water do we need?

Even though we have four heads in the compartment we only need water for two.... they are now spaced 10'-6"x9'-0" so we can use the 12'x12' spacing or 13 gpm @ 7.0 psi from each sprinkler. With two sprinklers operating out total demand is now 26.0 gpm which is a lot less than the 40.0 gpm we had with just two sprinklers in the room.

But there are hundred of different heads to select from. Viking, GEM, Globe, Reliable... they and others all make a couple dozen different residential sprinklers each you are probably approaching 100 different residential heads, all with different specific listings, from just these four manufacturers and there are many I didn't mention.

I should say I use Viking just because that is what I use and I am most familiar with their data sheets.

Take a look at the *Viking VK435* Residential Pendent Sprinkler.

Notice this head is only listed to a maximum spacing of 14'x14'.










In our compartment having four sprinklers spaced a maximum of 10'-6" apart we can use the 12'x12' spacing which requires only 9.0 gpm per sprinkler or 18.0 gpm for the maximum of two sprinklers.

I've done a few residential jobs over the years and under the right conditions, with the right spacing, the right head and a relatively short distance from the city water main to the house, it is very possible to make a 3/4" domestic line work.

You need to recognize not all sprinklers are created equal. When changing sprinklers out, perhaps some got painted, you need to be very careful to use the exact same manufacturer and SIN # sprinkler originally installed. 

SIN # stands for Sprinkler Identification Number. VK435 is an example of a SIN #. It is unique, no other sprinkler is like it.

So now if you get a job where the designer used four sprinklers instead of the minimum two you know the very probable reason. 

More to it that you thought, huh?

I plan to add a little more to this thread over the coming days. Next up we'll talk about friction loss (or head loss) in pipes. 

Have a good night.


----------



## Tommy plumber (Feb 19, 2010)

Sprinkler Tech, so you're saying that in the hypothetical room with (4) heads, in the event of a fire only (2) heads would be activated in the event of a fire? That is what accounts for the lower GPM? Whereas with only (2) heads in that room, when both activate, the total GPM will be higher. That makes sense. Thanks for the information.


----------



## sprinklertech (Oct 24, 2010)

Tommy plumber said:


> Sprinkler Tech, so you're saying that in the hypothetical room with (4) heads, in the event of a fire only (2) heads would be activated in the event of a fire? That is what accounts for the lower GPM? Whereas with only (2) heads in that room, when both activate, the total GPM will be higher. That makes sense. Thanks for the information.


Exactly correct.

It doesn't matter if the room has 4, 6 or 100 sprinklers if the design is per NFPA 13D it is assumed *only two heads* will operate. I am being ridiculous on the 100 sprinklers in a compartment but it is a correct statement.

With two sprinklers in the room the area covered is larger and as you can see the larger the area a sprinkler covers the more water required.

By installing four sprinklers the area of each becomes much less and in residential the area of application is limited to two sprinklers. So with two sprinklers in the compartment it's 20 gpm from each for a total of 40 gpm or with four sprinklers the spacing is less, all you need is 13 gpm from each head if you are using the VK468 sprinkler or 10 gpm if you opt to go with the VK435 sprinkler. In any case all you need open for calculations is two sprinklers whether two are in the compartment of four. 

It's like a puzzle you get to put together.

Let's talk regular sprinklers for a moment. Full 13 systems.

I am often asked if a size pipe coming into a building is "large enough" to cover an addition.

*It is always large enough because size of the building or number of total sprinkler heads have nothing to do with the size of the main coming into the building.

*Years ago much was done using "pipe schedule" systems where the size of pipe was determined by the number of sprinkler heads being fed from it.

For ordinary hazard systems, grocery stores and shopping malls for example, 1" pipe could supply up to 2 sprinklers. 1 1/4" could supply 3 sprinklers, 1 1/2" could supply 5 while 2" could supply 10... 2 1/2" could supply 20 heads and so on.

You can find lots of these systems around. Find the end of a line and the last 2 sprinklers will be supplied with 1" pipe. The 3rd sprinkler from the end will be supplied with 1 1/4" pipe with the 4th and 5th head fed using 1 1/2" pipe.

This was the pipe schedule system... I am sure everyone here has worked with schedules.

Problem is, with few exceptions, pipe schedule systems have been "outlawed" for over 20 years now. Nearly everything today must be hydraulically calculated to a specific density over a given area.

There are two exceptions to pipe schedule. You can still use it if you are adding onto an existing pipe schedule system or if the building does not exceed 5,000 sq. ft.. So while I can't say they are "illegal" because of the limits placed upon them I can say I haven't designed a pipe schedule system in over 20 years.

The most standard design density for an Ordinary Hazard building (stores, machine shops and factories) is .20 gpm over the most remote 1,500 sq. ft..

What this means is I take a rectangular area (about 50'x30') located in the hydraulically most remote area and demonstrate if all the sprinklers went off in this 50'x30' area each sprinkler would discharge a minimum of 20 gpm (assuming sprinklers are spaced 10'x10' for 100' sq. ft. intervals).

With 15 open heads each discharging 20 gpm the sprinkler system will need a theoretical minimum of how much? 15*20.0=*300 gpm* for sprinkler.

If the building is very small, let's say it's jut 1,500 sq. ft.,the sprinkler system will need a theoretical minimum 300 gpm. If all you got is 15 heads in that tiny building I have to calculate every one of them.

Now lets say we have a 1 million sq. ft. manufacturing facility. This thing is big, it has 10,000 sprinkler heads and 25 miles of piping. How much water would this monster require? It's the same, 300 gpm.

The idea of sprinklers is to extinguish or control the fire at the beginning stages. If the fire grows so big ten thousand heads open the building is lost anyway... there isn't anything left to save. Also, with 10,000 sprinkler heads all operating at once discharging 20 gpm each you'd need Niagara Falls to feed it. With all operating you would empty a 1 million gallon water tower in five minutes.

The same holds true for residential systems. The idea is to control the fire at its beginning stages to prevent flash over. If all the sprinklers in the house have gone off the house is gone and everyone in it is dead anyway.


----------



## sprinklertech (Oct 24, 2010)

Consider my house.... there's an encased beam forming a lintel between my living room and dining room.










If my living room measured 15'-11" x 15'-6" and dining room measured 18'-0"x16'-0" it would be possible to design the system with one sprinkler in the center of each room using the the VK568 pendent sprinkler.










The living room could be designed to discharge 13.0 gpm while the dining room would be designed to discharge 17 gpm.

When I speak of "designed" I am speaking to the size of pipe.

Because the living and dining room have the lintel they are considered two separate compartments. I need to show only a single sprinkler opening up and in this case the most hydraulically demanding sprinkler would probably be the head in the dining room because it requires more water. 

But what if that lintel was 0'-7" in depth instead of the 1'-4"? If this was the case then the living room and dining room would be considered one compartment... I would have to flow or open both sprinklers in my design.

If this were one compartment I would require 34 gpm. We will get into it more but you don't add different gpm... with two heads you double the most demanding. This is not entirely correct but it is very close... without the minimum 8" lentil it is all one huge compartment.

Friction loss through pipes is calculated using the Hazen-Williams formula. Friction loss is the amount of pressure lost while fluid is moving through a pipe.

Consider the following chart.










The CPVC I used in preparing this chart is the diameters for BlazeMaster CPVC. For the copper tubing I used Type L.

With 17 gpm flowing through 3/4" CPVC I am losing 0.155 psi per linear foot. Over a linear distance of say 120' to the street I would be losing 18.6 psi. (120*0.155=18.6)

For the head to discharge 17 gpm it needs 12.0 psi at the head.

The head is 10' above the point int he street the pressure was measured. For elevation I need to always add 0.433 psi per foot of elevation difference. For 10' I need to ad 4.3 psi.

Add these all together

12.0 psi for sprinkler to operate
4.3 psi for elevation
18.6 psi for friction loss through all the 3/4" cpvc to the street.
*34.9 psi is the total pressure* we would need at the street for this system to work. Most likely we have that... true, we would be losing a little through the meter and equivalent fitting length losses but even with that the figure would end up maybe 45.0 psi. Nearly all public water supplies provide 45.0 gpm so with 3/4" this system would work just about anywhere.

Yeah, it isn't rocket science it really is that easy!

But what would happen if that lintel wasn't there OR it was less than 0'-8"?

We would be in trouble is what would happen.

We would need enough water to supply two sprinkler heads for a total of 34 gpm.

When you double the amount of water flowing through a pipe the pressure loss does not double. It nearly quadruples or, in reality, the pressure loss increases by ^1.85. As you can see from the chart the pressure loss from the head to the street is 0.558 psi/linear foot. Over the 120'-0" total distance our pressure loss would be 67.0 psi which you can see is almost four times as much as the 18.6 psi we lost flowing one sprinkler at 17.0 gpm or just half the water.

Now our system would have 
12.0 psi for sprinklers to operate
4.3 psi for elevation
67.0 psi for friction loss through all the 3/4" cpvc to the street.
*83.3 psi is the total pressure. * Most likely we wouldn't have that because you could figure 10 psi easy loss through meters (the more water flowing the higher the loss) and I could see us easily ending up with a need of 90 to 100 psi. Many public water systems don't have that much pressure. Some do but most probably don't.

Some of you already knew this but to some it might be a surprise that doubling the amount of flowing water through a pipe does a lot more than doubling the pressure loss due to friction.

You can really see it when it's graphed out on a piece of N^1.85 paper.










The losses are in psi per 100 foot length so to arrive at a per foot loss simply divide by 100.

Here I have losses for 3/4", 1" and 1 1/4". 

If anyone has any questions please feel free to post them or you can PM me.

Gee, that was fun!


----------



## sprinklertech (Oct 24, 2010)

A little insight into fire sprinkler hydraulic calculations.

It might help to know the goal isn't to show a systems performance but more that a system is capable of doing at least the minimum acceptable. If it does more (most do) that's all fine and good but our goal is to show it will do at least the minimum requirement.

Friction loss calculated through pipe is calculated using C-values (or roughness values) based on older pipe. For example new steel pipe has a C-Value of around 140 but we are required to use C-Values of 120 for wet pipe systems which approximate the pipe to 40 and 50 years old. Newly installed systems will always perform better than calculations indicate.

In doing calculations per NFPA #13 everything is done backward to the way it is installed. In working calculations we don't start at the street connection and move in we start at the hydraulically most remote sprinkler and work from there out to the street. 

Exact type pipe and exact internal diameter makes a big difference. It really means something and you can't just say "It's 1" diameter and I don't know if I will install it in plastic or copper...." to do a proper job we need to know exactly what it is for the design. This is especially important if using 3/4" and yes, it is possible to design a residential system using 3/4" feed.

To see what a difference it makes consider for a moment a system that requires 20 gpm with 100' from the city water main to the house. From the chart above if we used 3/4" L copper having an ID of 0.785" our friction loss flowing 20.0 gpm would be 0.352 psi per linear foot for a total of 100*0.352=35.2 psi just from the street to the house. If we used 3/4" CPVC having an ID of 0.874" our friction loss flowing 20.0 gpm would be 0.229 psi per linear foot for a total of 100*0.229=22.9 psi. Both pipe is 3/4" but just that small of a difference in internal diameter makes a 35.2-22.9=*12.3 psi difference.* 

12.3 psi is significant.

This is why if I were designing a system for you I'd drive you nuts wanting to know exactly what you were installing and if I weren't familiar with it I would want to know what the manufacturer published as the actual internal diameter. Not to drive you nuts but it's really important.

With anything having to do with these kinds of calculations if it's garbage in you'll get garbage out. If you told me you were going to use CPVC having a inside diameter of 0.874" but ended up using 3/4" copper because you had some left over from another job we could very likely end up with a system that "wouldn't work".

Also need to know the linear footage of pipe from the city connection to the house. Having someone say "it's between 100 and 150 feet" is pretty worthless to me and dangerous for your job. I know it is sometimes tough to get exact but I would like to see a dimension within a couple feet. There's a difference between 90 and 100'.

Another important thing is to obtain an elevation height between wherever the water pressure was measured and the first floor of the house. For many living in Nebraska this might not be a problem but in the hills it can be very significant.

If you are getting into this work another term you will hear is "most remote" sprinkler. While the term is often used it really isn't correct. The correct term should be "hydraulically most remote" or "hydraulically most demanding" because more often than not the most remote sprinkler, the one farthest away from the feed, will turn out not to be the "hydraulically most remote".

I've designed systems for 40,000 sq. ft. building ending up where the hydraulically most remote area was right next to the riser. There's things you can do with pipe sizes that enable a designer to move the hydraulically most demanding area to pretty much anywhere desired.

In my next post I will show you how a system is designed and I will attempt to present it in such a way that with a few hours study you could actually design your own system. It really isn't that hard but what messes most people up is having preconceived ideas on how it is done which goofs up anyone.

Note: I am not teaching you so you can design your own... most regulatory agencies will require they be done by an engineer or someone certified but I believe it can only help if you can follow along.

Now take a deep breath before we start... honest, it ain't that hard to do.


----------



## Tommy plumber (Feb 19, 2010)

*A Question For SprinklerTech*

I would like to know if a fire contractor's license is needed for one to apply the fire collars and fire-proof caulking around pipes that penetrate a slab in multi-story building? You stated that among other state you possess a fire contractor's license in FLA. Sorry for off-topic question, but I'd like to know. Or would I be "working outside the scope of my license?"


----------



## sprinklertech (Oct 24, 2010)

Tommy plumber said:


> I would like to know if a fire contractor's license is needed for one to apply the fire collars and fire-proof caulking around pipes that penetrate a slab in multi-story building? You stated that among other state you possess a fire contractor's license in FLA. Sorry for off-topic question, but I'd like to know. Or would I be "working outside the scope of my license?"


I don't think you would even in Florida which can be as bad as California as far as licenses are concerned.

I've done jobs in Florida where someone else has done the caulking.


----------



## sprinklertech (Oct 24, 2010)

Even if you never touch a sprinkler system being professional plumbers I think you will find this knowledge useful in many areas.

In determining friction loss through pipe you can either refer to a chart similar to the one I created here:










Or you can use the Online Hazen-Williams online calculator found in the Engineering Toolbox found *here*.

where

f = friction head loss in feet of water per 100 feet of pipe (fth20/100 ft pipe)
c = Hazen-Williams roughness constant
q = volume flow (gal/min)
dh = inside hydraulic diameter (inches)

For nearly all your work the c=150 because most likely you will be using copper, brass, pvc or cpvc. If using unlined steel pipe (I don't see anyone doing this in a residence but it certainly is permitted but not on a circulating system) the c-value would be 120. 

First let's find what the friction loss through 3/4" copper having an ID of 0.785" when flowing 20.0 gpm. From the chart we find it is 0.352 psi per foot or 35.2 psi over a 100' length. 100*0.352=35.2.

Everyone reading this has seen the results of friction loss we see it every time we add two sections of hose together in an attempt to water the far end of the back yard.

Consider the following:










We're going to string three pieces of 3/4" copper together but at every joint we're going to have a tee with an outlet for a highly accurate water test gauge. On the left hand side we're going to connect to a water supply which could be nearly anything. Perhaps a hose bibb on your house with a short 3/4" hose.

At the far right side we're going to fix an adjustable nozzle.

When we shut the nozzle completely off if we turn the water on all 5 pressure gauges are going to read the same thing. Let's assume it's 80 psi. Without any water flowing all four gauges will read the same... 80 psi.

But what if we open the nozzle and it takes 1 minute to fill a 15 gallon container. We are now flowing 15 gpm and looking at the gauge #4 adjacent to the outlet (far right side) we might find it reads *24.0 psi*.

What will the rest of the gauges read? Yep, we can calculate this and hit it pretty darn close.

At 15 gpm 3/4 copper will produce a friction loss of 0.207 psi/linear foot. With 20' between gauges we can expect to see it read (20.0*0.207)+24.0=*28.14 psi* at gauge #3. As water flows through the pipe it is going to experience a 4.14 psi loss between gauge #3 and #4. 

At gauge #2 we can expect to see (20.0*0.207)+28.14=32.28 psi on the gauge. In other words we need *32.28 psi* @ gauge #2 to be able to deliver 24.0 psi at the nozzle or gauge #1.

Following so far?

Now what about gauge #1 up by the house?

Easy, it's (20.0*0.207)+32.28=*36.42 psi* at gauge #1. You need to have 36.42 psi at gauge #1 to be able to maintain a pressure of 24.0 psi at gauge #4 or garden hose nozzle. Why? Because you will lose 12.42 psi over the entire 60' of 3/4" between gauge #1 and gauge #4.

But there are more tricks we can do with this. Knowing the nozzle discharges 15.0 gpm when supplied with 24.0 psi pressure it is easy to calculate a discharge coefficient for that nozzle.

*Stay with me now!*

We will call the discharge coefficient the k=factor using the formula:










I know most of you learned ohm's law in high school... this isn't any harder than that.

In this formula k is the discharge coefficient. q is water in gpm and p is pressure in psi.

k=q/p^.5 

Another way to say this is k is equal to gpm divided by the square root of pressure or k is equal to 15.0 divided by the square root of 24.0. The square root of 24.0=4.89 so k=15.0 divided by 4.89.

The discharge coefficient (k-factor) for our nozzle will be *3.07*

Now you are probably confused by what the k-factor is... don't overbuild it in your mind it's just a number but with this number we can do practically anything.

For example what if we opened the hose bibb so the gauge at #4 increased from 24.0 psi to 32.0 psi? Naturally we would expect, and we would get, more water from the nozzle but how much more would we get?

Do we have to measure it or is there some other way to determine the discharge?

We don't have to measure because q=k*p^.5 

In case you don't know p^.5 gives the exact same result as the square root of p. We all know the square root of 25 is 5 (5*5=25) but 25^.5 is 5. Go head, find a small scientific calculator and try it.

The symbol ^ is carrot.

Back to the problem if we supply the nozzle with 32.0 psi we can expect the nozzle to discharge q=k*p^.5 or q=3.07*32.0^.5 

The answer is 17.36 gpm.

If you up the pressure from 24.0 psi to 32.0 psi you will only increase the discharge by 2.36 gpm.

Lots might jump to the conclusion if you double the pressure you double the discharge but nothing could be farther from the truth.

If we got 15.0 gpm @ 24.0 psi pressure how much could we expect if we opened the hose bibb wide enough give us a reading of 48.0 psi at gauge #3?

q=k*p^.5 or q=3.07*48.0^.5 or q=3.07*6.93

The correct answer is we could expect the nozzle to discharge 21.28 gpm.

*Doubling the pressure comes nowhere close to doubling the discharge.*

So the question is how much pressure would we need at gauge #4 to be able to discharge 30.0 gpm from the nozzle?

We can calculate this.:thumbup:

p=(q/k)^2

(30.0/3.07)^2=95.47 psi

Notice what happened? It takes four times the pressure to discharge twice the water.

As I said even if you never touch a sprinkler a basic understanding of fluid hydraulics can can go a long way.

Oh, and as far as hydraulics go that's about all there is in basics. It really isn't any harder to understand than Ohm's law you had in high school shop class. 

I'll be back with more later... if you have any questions please feel free to ask and if you want to ask in private feel free to pm me.


----------



## ILPlumber (Jun 17, 2008)

Do you write for a trade mag? 

If you don't, you should....


----------



## sprinklertech (Oct 24, 2010)

Matt said:


> Do you write for a trade mag?
> 
> If you don't, you should....


No, I don't.

I know a lot about a very small niche area, especially when it comes to fluid dynamics, and I like to share. 

And it just isn't about sprinklers. A good plumber can use this just about anywhere.

*Let's have some real fun for a change.
*
Take this problem that has nothing to do with fire sprinklers. 

You're a plumber and I am one of your customers. I got this problem I want you to solve for me.

I have a farm and at the back of my yard I have one of those frost proof water... what do you call them.... you put a garden hose on it, life a handle and water comes out.

I am very happy with the quantity of water and water pressure I get. This yard bib (I don't even know what the proper name for it is) is fed from my well through a 180' length of 3/4" plastic pipe having an ID of 0.778".

Here's what I want to do.... I want to move this yard hydrant to the back 40 pasture 2,500 feet away but we all know from experience if I pipe it with 2,500' of 3/4" I would be lucky to get a drop a minute that far away.

But when I move it (assume level terrain) I want you to run a pipe big enough so I get the exact same performance half a mile away as I get in my own back yard.

Is 1" big enough? 1 1/4", 1 1/2" or 2" big enough? Will I have to run 4" to make it work? You know I am a penny pinching cheapskate so I will balk at paying the $1.20 a foot difference between 1" and 1 1/4" but you know I will be even more upset if after paying you $4,000 for the work I don't get the same performance you promised.

From 180' to 2,500' I'm 13.8 times farther away; does the pipe have to be 13.8 times as big?

Thing is we don't have to guess.

We can solve this problem in 30 minutes using nothing more than a 55 gallon drum and the *Hazen-Williams online calculator* at Engineering Toolbox. We'll dazzle em and you'll get paid for your knowledge and skill!

Ok, I know some of you can already do this but I am sure there are some around here that can't so pipe down!

Placing the 55 gallon drum under the spigot we fully open the yard hydrant (still bugs me I don't know the proper term for this) and time how long it takes to fill the barrel.

It takes 4 minutes and 25 seconds to fill the barrel.

That's 55 gallons in 265 seconds or 0.207 gallons per second or 12.45 gallons per minute.

You're going to move this line 2,500 away running a new pipe (size unknown for now) from the well to the new location but after it's all done I still want to be able to fill that barrel in 4 minutes and 25 seconds just like I did before. If I can't I'll probably be very unhappy and refuse to pay you causing you to have a very crappy Christmas.

Ok, we know the line is 180' long, has an inside diameter of 0.778" (we were very careful and measured because we know a tenth of an inch means a lot) so how much friction loss did we have flowing 12.45 gpm?

Go to the toobox and plug your numbers in. Should look like this

Putting your numbers in correctly your should get this










We know we lost 27.7 psi in 180 feet and what we want to do is pick the smallest pipe that doesn't create a head loss more than 27.7 psi over 2,500' when flowing 12.45 gpm.

We call the supply house and get ID's for the following pipe sizes.

1" has an ID of 1.065"
1 1/4" has an ID of 1.287"
1 1/2" has an ID of 1.612"
2" has an ID of 2.060"

Now it's easy, starting with 1" we just plug the values in working our way up until the total head loss over 2,500' is less than 27.7 psi.

Whoa, 1" won't work!










Head loss over the entire 2,500' is a whopping 83.6 psi. You run this in 1" and you will have a very unhappy customer!

Let's try 1 1/4" (easy enough to do all we have to do is change one number)










1 1/4" won't work either. We lose 33.3 psi through 1 1/4" and we've already established we can't lose more than 27.7 psi.

1 1/2" will work but we'll run the numbers just to make sure.

Seriously, why guess what you can be sure?

As we thought 1 1/2" works very well!










With a total head loss of just 11.1 psi by running 1 1/2" we can fully expect even better performance than when 180' away. Fact is we can move this thing more than a mile away and still get the same or better performance.

Play around with this, I think you'll find it sort of fun once you get the hang of it.

But some cautionary notes.

If I were doing it for real I would probably want to use a roughness coefficient of 140 instead of 150. It doesn't make that much of a difference (just 1.5 psi through the 1 1/2") but you do not want to make these sort of calculations and be wrong.

Be very careful on obtaining the ID's of pipe used. Be exact, do not guess.

Don't look for exactness. Nothing is perfect. We know we couldn't have a loss more than 27.7 psi and if the 1 1/2" turned up a loss close to 27.7, say it was 26.5) I would err on the side of caution and up the size by one. Nothing sucks worse than not being paid right before Christmas.

That was fun.

Now what if the back 160 acre pasture was 40' higher in elevation? What do we do then?

A column of water weighs 0.433 psi per foot. If the elevation you are going to is 40' higher you have to add 0.433*40=*17.3 psi* to to the 11.1 psi loss developed through the 1 1/2" for a total of 28.4 psi. If the spigot was 40' higher you would have to up the size to 2" which would give you a 3.8 psi loss. 3.8 +17.3=21.2 psi which is less than 27.7 so it would work just fine.

So, anyone ever run into something where knowing how to do this (it really is easy) would have helped?

It just dawned on me this is practically all there is to hydraulics and residential sprinklers. We already covered how to do it now all we need is some basic rules to follow. It really isn't all that hard.


----------



## Tommy plumber (Feb 19, 2010)

That was very interesting. So essentially the pipe size needs to be increased when a long run is installed to increase the volume in order to overcome the friction loss due to the inside of the pipe.

But what about the sheer weight of the water? Does the formula factor that in? If it did I didn't catch it.

That is some very useful information. Thanks for the post- it must have taken you awhile to type it. By the way, an outside hose faucet is called a hose spigot or a hose bibb, depending on where one is located.


----------



## sprinklertech (Oct 24, 2010)

Tommy plumber said:


> That was very interesting. So essentially the pipe size needs to be increased when a long run is installed to increase the volume in order to overcome the friction loss due to the inside of the pipe.


Exactly correct and in using the Hazen Williams formula takes all the guess work out of it. Before the work is started we can determine in a scientifically correct manner what will work and what won't. As we saw if someone would have guessed 1" would do it he would have been mistaken wrong. Knowing how to do this you don't have to guess guess.

As water moves through pipe it encounters friction which results in a loss of energy which can be measured as pressure. This is why gauges will read differently when placed at intervals along a pipe as I showed in the diagram. The higher the flow the more friction loss which will result in a wider variation between the gauge readings.

With no water flowing the pressure at all gauges will read exactly the same as long as long as all gauges are at the same elevation.

Think about this. When watering the back of the back yard you use two sections of garden hose.... you have 100' of nice 5/8" hose and then you have 100' of cheap 1/2" garden hose you got at Diamond Jim's trading post.

Does it matter what hose you have first in the line from the hose bibb? Is there anything to be gained by having the 5/8" hose first then the 1/2" hose which connects to the occilating lawn sprinkler?

Against intution the answer is no. It doesn't matter because the friction loss is going to be the same whatever comes first. 5+3=8 just like 3+5=8. It doesn't matter what comes first.

Everything that discharges has a discharge coefficient whether it be a garden hose, a piece of machinery, a sprinkler head or fire hydrant.

Take a fire hydrant. Most 6" barrell fire hydrants have a discharge coefficient of around 145.0 when discharging water from a single 2 1/2" open hydrant butt.

Using the Ohm's law for water (I just made that term up but electricians don't have anything on us because we got our own now)










If a fully opened hydrant is discharing 940 gpm how much water pressure is available where the the hydrant shoe connects to the city water main?

p=(q/k)^2 or p=(940/145.0)^2 or p=*42.0 psi*.

By the same token knowing the discharge coefficient of a 2 1/2" hydrant (6" barrell) is 145.0 how much water can we expect if we have 120 psi available in the city water main when the hydrant is fully open and flowing?

Easy... q=k*p^.5 or q=145.0*120^.5 or q=*1,588 gpm*.

How accurate is this sort of thing? It's pretty accurate... not dead on but close. In measuring different 2 1/2" hydrants Factory Mutual Engineering (I got this from their handbook) has found discharge coefficients vary from 135 to 150 depending on the make/age of the hydrant. Even so if you use 140 to 145 you're going to be closer to the correct answer than anyone just "guessing".

It is the same thing with roughness or C-Values in different kinds of pipes. Engineering Toolbox gives guesses on *different C-Values here*.

Notice they have the C-Value of CPVC or PVC at 130 but I used 150 because NFPA standards tell us to use 150. New unlined steel pipe is 140 to 150 but NFPA standards tell us to use 120 so go figure. While not rocket science accurate these will get us close and for most of our work close is good enough and it is still better than guessing.

Also remember Hazen-Williams is an empirical formula and error becomes more pronounced at very low or very hgh flows. The error with low flows don't really effect us because the friction loss is so low anyway and by high flows I would start to be concerned with anything having a velocity higher than 35 feet per second which is pretty fast. Remember when using the Hazen Williams online calculator found at the toolbox it does tell you the velocity.

In fire sprinklers most highly protected risk insurers have us limit our velocity to 32 feet per second. 

Not saying this to confuse anyone but it is something you should be aware of.



> But what about the sheer weight of the water? Does the formula factor that in? If it did I didn't catch it.


Weight of water would only come into play if the pipe is at different elevations. If it is all horizontal, same elevations, then it is no factor.

I did raise the issue in the last part of our problem by having the pasture at a higher elevation. The weight of water in a column is 0.433 pounds per foot.

If you took a 100' section of pipe, capped one end, attached gauges every at the top, bottom and at 10' intervals, stood the pipe on end then filled it with water the gauge at the very bottom would read 43.3 psi. Even with the pipe 100' in the air with an open top the gauge would still read 43.3 psi.

At the very top gauge the pressure would read zero.

If you looked at the gauge 40' above the bottom it would read 25.98 psi because you would have a water column 60' high above it and 60*0.433=25.98.

The size of pipe doesn't matter... it could be 1/2" pipe or 48" pipe and gauges would still read the same. Remember, we are weighing the column of water and not the total weight of the water in the pipe.



> That is some very useful information. Thanks for the post- it must have taken you awhile to type it. By the way, an outside hose faucet is called a hose spigot or a hose bibb, depending on where one is located.


Thank you. I enjoy sharing and doing this sort of thing it's like solving puzzles. Now you can solve puzzles too.

I wanted to call it a hose bibb but hose bibbs are on houses and I thought these were called something else.


----------



## plumbpro (Mar 10, 2010)

Bibbs in the yard are called yard hydrants here


----------

