## System Curves…

There are one hit wonders, and then there are *one hit wonders*. The group Reunion had one hit in 1974 that really made you, well, wonder. And I dare you…no, I double dare you…no, wait…I *TRIPLE DOG DARE*you to sing along with this one without landing in the emergency room (find the lyrics here):

One take, right? Any song that mentions Bonnie Bramlett, Screamin’ Jay Hawkins, Poco (I can’t say I remember the TV show in the video, but check it out!), Brenda and the Tabulations, Alan Freed and Murray the K – and make it all freakin’ rhyme while singing at warp-speed – has to go down as one of the classics!

Okay, back to work…

Last time we talked about where pump curves come from. This time we’ll sink our teeth into system curves.

When you calculate the flow rate and head loss of a piping circuit, you’re starting to map out the relationship between flow rate and head loss for that piping circuit. It’s kind of like a hydronic “finger print.” All piping loops have a unique system curve, which is plotted on the same graph as the pump performance curve. And the system curve is important because the system itself will operate where the system curve intersects the pump curve.

That’s kind of an important point. We do an awful lot of math to find out the required flow rate as well as the head loss for a piping circuit, even though it’s highly unlikely the system will ever work at those points! And after doing all that work, we often just slap on the “pump we always use.” A friend of mine used to say that this was like measuring with a micrometer, marking with a piece of chalk and cutting with an axe.

Let’s start from the ground up. Let’s say we want to size the system circulator for a zone valve job.

Calculating flow is simple…it’s GPM = BTUH ÷ (Delta T x 500). Let’s presume the calculated heat loss is 89,751 BTUH. And let’s presume we’re sizing the system to a 20 degree Delta T.

GPM = BTUH ÷ (Delta T x 500)

GPM = 89,751 ÷ (20 x 500)

GPM = 89,751 ÷ 10,000

GPM = 8.97

We’ll call it 9 GPM

So our circulator will need to provide that 9 GPM while overcoming the head loss of the boiler and the piping.

Let’s make some more presumptions. Let’s say it’s a normal cast iron boiler (very little pressure drop), and we’re using Type M copper tubing. And let’s say we have four zones, the longest of which is 115′, with 35,000 BTU’s worth of baseboard element. That length includes the element. Here’s a picture:

You see that the boiler supply pipe, all the way through the supply to the third zone, and all the return piping from the third zone return on, is all sized at 1″. That’s due to these basic pipe sizing guidelines:

2-4 GPM = 3/4″ pipe

4-9 GPM = 1″ pipe

9-14 GPM = 1-1/4″ pipe

14-22 GPM = 1-1/2″ pipe

These guidelines are based on a minimum flow velocity of 2 feet per second and a maximum flow velocity of 4 feet per second.

Now the zone we’re sizing is the last zone, Zone 4, which has the biggest single load at 35,000 BTUH. Using the Universal Hydronics Formula we can determine the flow rate through that zone is 3.5 GPM, and using the pipe sizing guidelines we can determine that the zone should be piped with 3/4″ Type M copper (we’ll cover PEX next time).

Since that zone is the longest zone at 128 feet, we’ll use that number to calculate the head loss. We learned in previous blog entries how to calculate head loss (review them by clicking here and here). For simplicity’s sake, we’ll use the easy formula for estimating head loss:

115′ x 1.5 (for fittings, etc) = 172.5′

172.5′ x .04 (4′ head/100′ pipe) = 6.9′ of head. We’ll call it 7′ of head.

Let’s look at the 00 Series Pump Curve Chart, and see what circulator would work best:

From the looks of it, the circulator represented by the #5 green line – the Taco 007 – would be a fine choice.

But now we need to plot the System Curve to find out where it intersects the 007 pump curve.

We already know two points on that plot. We know that at 9 GPM we get 7′ of head. And we also know that at 0 GPM we get 0 feet of head. But how to we fill in the blanks?

You guessed it – more math!

There’s a slick formula to calculate the head loss at different flow rates so you can plot the system curve:

Head 1 ÷ Head 2 = (Flow 1 ÷ Flow 2)^{2}

Head 1 is the original head, head 2 is what you’re trying to find out.

Flow 1 is the orginal flow, Flow 2 is what you’re plugging in.

Let’s figure out the head is the flow was, say, 5 GPM in this system:

(Head 1 ÷ Head 2) = (Flow 1 ÷ Flow 2)^{2}

(7 ÷ x) = (9 ÷ 5)^{2}

(7 ÷ x) = (1.8)^{2}

(7 ÷ x) = 3.24

Now for some of that 7th grade Algebra we all remember:

First, multiply both sides by x (we need to isolate the x!)

7 = 3.24 x

Now, divide both sides by 3.24 to isolate the x:

7 ÷ 3.24 = x

Now finish it off and find that:

x = 2.2

What we’ve just found is that when the flow rate is only 5 GPM (instead of the 9 GPM when all zones are calling on the coldest day of the year), the head loss through the piping system will only be 2.2′.

Using the same formula, we find that when the flow is 7 GPM, the head loss is 4′, and at 8 GPM the head loss is 5.5′.

You should also extend beyond the required flow, in order to see the shape of the curve. At 10 GPM the head loss is 8.6 feet. At 12 GPM the head loss is 12.5′, and at 15 GPM the head loss is 19′. Let’s plot these on the pump curve chart and see what happens:

The point where the system will actually operate with all zones calling is the intersection of the pump curve and the system curve. If you look closely, you’ll see that point is at approximately 9.5 GPM at roughly 7.5 feet of head. Not bad…

As you can see, the head increases dramatically with only the smallest increases in flow. This is why it’s important to select a circulator with a curve that’s fairly close to to the system flow and head requirements.

Pretty slick huh?

Oh, and by the way, if you don’t want to hammer out all that system curve math by hand, there’s a slick-o short-cut on the Taco FloPro Designer software that can do it for you “fast and easy.” We’ll do that next time.

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