The Trouble with Estimating Main Drain Flow

One of the curiosities I have every time I run a main drain or see one run is how much flow the system is actually discharging.

From the amount of discussion and inquiries one of our tools has generated, I know many of you are curious about it, too.
 
HOW MUCH DOES THE MAIN DRAIN ACTUALLY FLOW?
For one – if we knew with some certainty how much flow came through the main drain, then we could actually complete a backflow forward-flow test entirely just by opening up the main drain all the way.

That’s the theory, at least, that I’ve heard some people point to as to why they don’t provide another fixed means of forward flow.

For a lower hazard system; say a system whose greatest challenge is still Light Hazard – it’s not unfathomable that a fully-open 2-inch main drain could flow at least the system demand (which might be as low as 120 gpm for a minimum quick response (QR) reduction area and 30% overage, no hose allowance included).

Even for an Ordinary Hazard Group 2 system using a QR area reduction and 30% overage, the system flow may still be in the 220-250 gpm range. Would a fully open 2-inch main drain be enough to handle it?
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Or what if that main drain was upsized to 2-1/2 inches?
 
This piques the curiosity, right?
 
IS FORWARD-FLOW ACHIEVABLE THROUGH A MAIN DRAIN? IF SO, WHEN?
It would be very nice to have an idea if forward flow was achievable for some of these lighter-weight systems just through the main drain.
 
The Drain Flow Estimator

We introduced a tool we called the Drain Flow Estimator tool a while back (https://www.meyerfire.com/blog/a-new-fire-sprinkler-test-drain-flow-calculator), which was built to estimate the maximum possible flow from an inspector’s test or a main drain.

That tool only uses one calculation: discharging water through an open orifice:

The Drain Flow Estimator calculates the maximum possible flow rate through an opening, but isn't a good way to estimate the actual flow through an opening

Let’s say we have a very large water storage tank and poke a hole in the side of it near the bottom. How fast does water drain from the tank?

We have a formula for that. It’s Q = 29.84 C d^2 √p.

That is, we have a flow (gpm) that is constrained by the type of opening (C, the discharge coefficient), the diameter of the opening (d, in inches), and the total system pressure at the opening (p).

​We use this regularly when we conduct fire hydrant flow tests. The equation translates pitot pressure to how much flow comes out of the opening. We took measurement inaccuracy into account and built this out into its complete tool for converting pitot pressures to flows (https://www.meyerfire.com/blog/new-pitot-to-flow-rate-converter-with-precision).

The Flow Rate Conversion tool takes a pitot pressure and converts it to flow, while doing an error analysis to give a realistic range of accuracy of the combined measurements

THE PROBLEM
​Here’s the problem with using only that equation to estimate flow from a main drain – it’s the maximum possible flow.
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Now, it meets the need that we had for building the tool—to estimate the maximum possible flow so that we could size drains appropriately (hint: don’t run an inspector’s test or main drain to a janitor’s sink).

It serves its purpose of estimating the maximum possible flow.

However, the Drain Flow Estimator tool doesn’t provide a realistic amount of flow through the main drain or inspector’s test and drain, only the maximum.

That’s problematic if we want to know the actual flow through a Test and Drain or a Main Drain, as discussed earlier.

Why is it the maximum and not actual?

#1 PIPE CONSTRICTION
That is, we’re not accounting for the pipe's constriction between the opening and the riser, the friction loss within the riser itself, the loss through the elbows along that path, or the constriction at the valve opening.

#2 TYPE OF PRESSURE
Another thing we’re not really considering is the type of pressure that’s measured. When we take a pitot pressure measurement, we insert a tube into the centerline of the water flow.

The pressure measurement taken from a pitot gauge accounts for the static pressure of the water (the normal pressure that is exerted in all directions) and the velocity pressure caused by the forward motion of the water.

​That’s what a pitot gauge is measuring—the total pressure.

Measurement taken from a pitot gauge measures total pressure, which is the sum of normal (static) pressure that is exerted in every direction, and velocity pressure that is created from the movement of the water in the stream

​A gauge on a riser does not measure total pressure; it measures normal pressure. That is, it doesn’t matter if the water is standing still or moving at 20 feet per second. The gauge is only measuring the pressure that runs perpendicular to the pipe in the normal direction.

#3 LOCATION OF PRESSURE
The last source of error is where the pressure is measured.

For a hydrant flow test, we measure the pitot pressure immediately after the hydrant opening. We use the formula and convert it to a flow, knowing the pressure right at that opening.

If we instead use this same formula for an open orifice but add a pressure upstream at the riser, then we’re using a higher pressure than what will be available downstream at the opening of the main drain.

If we want to know the maximum possible flow, that’s probably fine. That’s the extreme case.

But if we want to know the actual flow through the drain, then that’s problematic; it’s another source of error.
 
BUILD A TOOL THAT CAPTURES ACTUAL?
So, how would we construct a tool that estimates the actual flow through a main drain?

Well, in theory, we could work an iterative loop like this:

1. Assume a pitot pressure right at the opening of the main drain (the 45-degree elbow discharging to the outside, for instance).
2. Translate the pitot pressure to a flow based on the characteristics of the opening.
3. Knowing the flow through the opening, we could calculate the friction loss as we move upstream through the main drain.
   1. We will gain pressure as we move upstream, just as in a hydraulic calculation.
   2. This would require an estimated C-factor for the pipe, knowledge of how the main drain is routed, and information about the pressure loss at a main drain valve.
4. At the point where the drain connects to the riser, we could determine the pressure at that intersection, and we still know the flow.
5. We calculate the friction loss going upstream through the riser until we reach the riser pressure gauge.
   1. We would need to have an estimated C-Factor for the pipe and know the routing of the riser.
6. Now, we would have a total pressure where the gauge is located.
7. We also know the velocity of the water movement in the riser, which we can use to translate our total pressure into the normal pressure, which is what the gauge is reading.
8. We would compare the estimated normal pressure calculated to the actual normal pressure in our real-world test.
   1. If our estimated pressure at the riser is too high, we restart our loop and assume a lower initial pitot pressure.
   2. If our estimated pressure at the riser is too low, we restart our loop and assume a higher initial pitot pressure.
9. We iterate this loop until we’re close enough for our needed accuracy.

 
As a result of this process, we would have an iterated, balanced supply-side hydraulic calculation that estimates the flow coming through the main drain.
 
If you love the math or the theoretical exercise – weigh in on your take. Open to ideas on this.

DOWNSIDE & POTENTIAL MISUSE
Now that’s great Joe, so go ahead and build it (typed in sarcastic voice font).

We can build it (and probably will because I’m curious). If we do, I’d want to go out to a parking lot and validate this in the real world 30 different ways (looking at you Fire Sprinkler Podcast).

But beyond that, there’s a fundamental issue with a calculator like this – it’s still an estimated amount of flow based on a pressure measurement at the riser but with the flow coming out downstream some distance later.

AN ESTIMATE BUT NOT REALITY
It’s not a measure of the actual flow through the opening; it’s only a calculated estimate.

The downside of not being a measurement is that if there’s some wrong assumption—say a C-factor or number of elbows or whatnot—then we introduce inaccuracy.

But it's probably hard to detect. What if we have some type of pipe constriction that we can’t see from the outside? Say there’s a large rock or dirt buildup, or the coupon that was cut for the main drain tap is actually smaller than it should be.

That constriction would throttle the actual flow down but maintain the same or higher pressure upstream at the gauge.

That is – it would look like it’s flowing more water than it actually is.

The advantage of measuring the actual flow out of a main drain is that we know with some certainty what the flow is achieving and not an estimate.

Fundamentally, I know of two quick(er) ways to measure the flow, even for a main drain.

There’s the bucket test, in which you flow into a large 55-gallon drum and time how long it takes to fill it up. Divide your bucket size by the time it takes to fill up, and you then have your average flow.
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Two of the most-obvious ways to measure flow are to measure a pitot pressure and convert to a flow, or run a hose to a "bucket test" and time how long it takes to fill up the volume.

​Then there’s the pitot measurement. Connect a test hose with an adapter to the main drain, measure the pitot pressure, and convert it to a flow.

​Either way, you could measure the flow coming from the opening. That’s far more accurate, of course, than a tool that estimates and incorporates a handful of assumptions.
 
THE UTILITY?
Is this kind of tool, that provides a theoretical balanced supply-side flow with the supporting math and documentation, something that would be of interest?

Do you see the harm in having an estimate doing more harm than good here?

Do you ever use a main drain for forward flow on less hazardous systems, and if so, do you verify what that flow is?

Curious on your thoughts about this as a challenge in the lens of trying to create helpful resources and not circumvent or obstruct good practices.

As always, appreciate you being here and being part of the community.

​- Joe