Fixture Simultaneous Demand Probability Calculator

Adding every fixture flow together gives a number nothing in the building will ever draw. Taking a flat percentage off it gives a number with no reasoning behind it. The honest middle is to say how long each thing runs in the busy hour, treat that as the chance it is running at any instant, and work out the whole distribution of total flow — which is arithmetic, not judgement, and it produces a curve rather than a single figure.

Four things per line: what the fixture is, how many of that kind, the flow one of them draws in gallons per minute, and how many minutes one of them runs during the busy hour. The flow comes off the fixture label or from filling a bucket and timing it. The minutes are yours to observe — a shower that runs nine minutes in the peak hour is running fifteen percent of that hour. Blank lines and lines starting with # are ignored.
One dial for the whole schedule. 100 leaves your minutes as entered. 150 asks what a busier hour than the one you described would look like without retyping every line.
The flow the total stays at or below for this share of the time. 99 means one instant in a hundred goes above it. There is no correct value here — it is how much overlap you are willing to be caught by, and it is a design choice somebody has to own.
Anything that runs without stopping while the rest of this is going on, so it gets no diversity at all — an irrigation zone on a timer, a filter backwash, a recirculating pump loop. Added to every point in the distribution.
Simultaneous Demand Calculator — Probable Peak GPMBuildFigure

Why the additive number is useless and the flat discount is worse

Add the default schedule up and it comes to 30.8 gallons a minute. Two showers, three basins, a kitchen sink, three toilets refilling, a washer, a dishwasher and two hose bibs, all open together. That state has probably never occurred in the building and never will.

The usual response is to knock a percentage off. Sixty percent, forty percent, whatever the rule of thumb in circulation says. The trouble is that the correct discount depends entirely on the mix. A house with one shower and eight rarely used basins diversifies enormously. A house with four showers and nothing else barely diversifies at all, because the showers are the load and they run for a long time each. One flat percentage cannot be right for both.

Minutes are the input, probability is the output

The only thing this page asks you to estimate is how long a fixture runs in the busy hour. A nine minute shower in a sixty minute hour is running fifteen percent of that hour, so at any instant chosen at random there is a fifteen percent chance it is open. That is the whole conversion, and it is a much easier thing to estimate honestly than a diversity factor, because you can stand in the bathroom and time it.

From there the arithmetic is fixed. Each kind of fixture gives a binomial distribution over how many of that kind are open. The kinds are combined by convolution, exactly, on a fixed grid of a twentieth of a gallon a minute, which produces the entire distribution of total flow rather than a single figure. The percentile you ask for is read straight off it.

Reading the curve instead of the number

With the defaults the average draw is 2.03 gallons a minute, half the time the total is under 1.8, and 42 percent of the time nothing is running at all. The 99 percent figure is 9.7, which is nearly five times the average and less than a third of the additive total. The gap between those numbers is the entire subject: a service sized on the average would be short almost every morning, and one sized on the additive total would be three times bigger than anything the house does.

The percentile is a choice, not a fact. Ninety-nine percent of instants still leaves roughly half a minute in an hour above the line. Whether that matters depends on what happens when it is exceeded — a shower that goes lukewarm for twenty seconds is a different consequence from a fire pump that does not reach pressure.

The independence assumption, stated plainly

Every fixture here is treated as opening independently of every other. Households do not behave that way. Morning use is clustered, the toilet follows the shower, and two people leaving at the same time overlap far more than chance would put them. Clustering fattens the upper tail, so the real 99 percent flow in a busy family house is higher than this model gives.

There is no correction factor offered for that, because a made up one would be worse than the honest statement. If your building clusters, put the clustering into the use times: a shower that is genuinely running for twenty minutes of the peak hour, across the two people using it, should be entered as twenty.

Questions people ask

How do I estimate the minutes a fixture runs in the peak hour?

Watch one hour of the actual building if you can. Failing that, count the events and multiply by their length: two showers of nine minutes each in the peak hour is eighteen minutes of shower running, which you can enter either as one shower running eighteen minutes or as two showers running nine each. The second is more accurate, because it allows for both being open together, which is exactly the case the calculator exists to price.

What percentile should I use?

There is no right answer and the page will not pretend otherwise. It is a statement about how often you are willing for the system to be pushed past the figure you sized on, and what happens when it is. Ninety-nine percent of instants still leaves about half a minute in a busy hour above the line. Somebody with responsibility for the design has to own that choice, and in most jurisdictions the sizing method itself is prescribed anyway.

Why is the answer so much lower than adding the flows up?

Because the fixtures are open for a small fraction of the hour and the odds of many of them coinciding fall away fast. Two fixtures each open fifteen percent of the time are both open only a little over two percent of the time. Extend that to nine kinds of fixture and the far corner of the distribution — everything at once — has a probability with a lot of zeros after the decimal point.

Does this replace the fixture unit method?

No. If your jurisdiction sizes by fixture units, the fixture unit load is what the inspector will want and the table is what the size comes from. This is for the questions the table cannot take: what a longer shower does, what adding an irrigation zone does, what happens if the household grows. It also makes the diversity assumption visible, which a table quietly hides inside its own numbers.

Is the distribution exact or simulated?

Exact. Each kind of fixture gives a binomial distribution over how many are open, and the kinds are combined by convolution on a fixed grid of flow. Nothing is sampled and nothing is iterated, so running it twice gives the same answer. The probability total shown at the bottom adds to 1, which is the check that the convolution stayed intact.

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