I live in Maryland and we reciently had a large local drinking water main pipe break.

The water main pipe is 66 inches in diameter. The water main pipe is PCCP (Pre-stressed Concrete Cylinder Pipe) The water main pipe follows the Potomac River which is at a very low elevation. (I do not know if elevation is a factor)

Local news reporting agencies initally reported that the water main pipe break was discharging 135,000,000 GPM. That amount of water seemed like it was way over estimated. Later the reports were that the water loss at the maximum point of discharge was 150,000 GPM. This seems like it would be on the low side for a 66 inch pipe.

Does anyone know how to calculate what the maximum amount of water a 66 inch pipe could discharge at its peak point of discharge.

The water pressure at my house is 83 PSI and I am at the minimum 2000 feet in elevation above the the water main pipe that broke. (I do not know if this is relevant)

I do not know what the actual water pressure in the water main pipe was prior to the pipe rupture. For purpose of calculating the maximum water discharge for a 66 inch water pipe lets assume 100 PSI (Unless anyone may know if the water pressure would be higher)

For calculation purpose I would like to assume that the pipe was completely sheared off, allowing a full discharge from the pipe across the entire 66 inch diameter of the pipe.

Thanks if anyone has any answers to my questions. This will help end a lot of job site discussions and settle a few wagers.

## Replies

You figure it out I cant do fancy math.

http://www.inter-mountain.com/Pipe_Related_Formulas.htm

Cool wab site

Thanks

This task requires serious scientific precision. You need three instruments:

a five gallon bucket

a straight edge

a stopwatch.

As every farmer knows, the technique is to hold the five gallon buchet in front of the 66" pipe. When it starts to fill, you start the stopwatch. When the bucket [bouquet?] is full, you stop the stopwatch. You use the straight-edge to level off the top of the water to make sure you have an exact five gallons.

You divide the reading on the stopwatch by five to seconds per gallon. You divide this into 60 seconds to get gallons per minute or into 3600 to get gallons per hour.

I hope this helps....

~Peter

Use this formula and let us know if your results match the news reports:

Poiselle's law = Pi(radius to 4th power)(ΔP) / 8 (viscosity)(length of tube)

Viscosity of water is 1.003 × 10−3 Pa·s at about 20 °C.

ΔP is 100 using your assumption.

You have to get the units correct, and then it is an easy calculation.

Good piping practice means that you limit your water velocity to 10 ft / sec or less.

The chart I have to hand only goes up to 60" pipe, but for a 60" pipe, at 10 ft/sec, you're flowing about 90,000 gpm.

Since area is related to the square of the diameter, a 66" pipe will typically be designed for (66/60)^2 x 90,000 = 110,000 gpm or so.

So 135,000 is at least in the ballpark.

110,000 to 135,000 sounds reasonable.I got 122,972 gal/minFor pressure difference:

100 lb/in2 = 7034.85 cm water applied to a tube of radius =33inches (corresponding to area =22072cm2 and length = 30.48cm =12 inches, (100 psi essentially constant in the system)for a fluid with viscosity =.01 poise the volume flowrate will be =6439ft3/min=122,972.259 U.S. gal/min.Agreed, lots of assumptions. A back of the envelope WAG.

Edited 1/8/2009 10:39 pm ET by

CJMThanks for the info

Do you know if there is any way I can determine the velocity of the water flow?

Every 1 foot increase in velocity per second of the water flow on a pipe this size, increases the GPM substantially

"Do you know if there is any way I can determine the velocity of the water flow?Every 1 foot increase in velocity per second of the water flow on a pipe this size, increases the GPM substantially"You are asking, if the GPM is known, what is the 'velocity', or how much does a 1' increase in velocity increase the GPM?Using the numbers from post #6, 74,633 gal/min= a velocity of 7'/sec.

Dividing = 10661.85 GPM for every 1 foot increase in velocity.So if the flow were measured at 106,618 GPM and you wanted to determine the velocity, divide 106618 by 10661 to get velocity of 10'/sec.

I am not what to input for the length of the pipe

Nowhere near enough information...flow rates in a given pipe or system are functions of system pressure drop and pipe length, and in the case of a water main, ultimately the pump capacity will determine what the max flow would be from the open pipe. But as for your theoretical problem of "calculating the maximum water discharge for a 66 inch water pipe", the short answer is: 'There is no equation, formula or relationship that will calculate the "maximum flow allowed" in a pipe.'

If you want to argue the point with your job-site wagerers, read this discussion/debate here: http://www.eng-tips.com/viewthread.cfm?qid=136432&page=1

If you really want to get closer to the truth, you might get this tech manual: http://www.flowoffluids.com/tp410.htm

But as for the reported numbers of flow rates, they're probably in the ballpark. In theory, the typical design flow velocity in a pipe is around 7 ft/sec.. That would be in the 'ideal pipe/system'. Thus, for a 66" pipe, finding volume of flow at 7'/sec is a simple calculation: pi(r^2)(7ft) = 53cu.ft./sec. Substituting 0.1337cu.ft./gal and multiplying by 60 sec., we get a flow volume of 74,633 gal/min. In other words, that water main and it's pumping system was probably designed to handle 75,000 gal/min at that system head (pressure). So then, if the pipe was broken, we'd have the pump side flowing out at that rate, plus the 'downstream' side also draining out (by gravity or 'elevation head')... say a max flow of also 75,000 gal/min gives a total of 150,000 gal/min. On the other hand, w/ a break in the pipe and the loss of resistance (friction head + elevation head), the system flow rate would no doubt increase beyond the design and the pumps would effectively be operating at their MAX capacity now.. which sort of screws up the problem a bit.

But no worries, the water utility no doubt had a flow meter monitoring all of this on the pump/supply side of the break and they had an accurate flow measurement. The speculation would come from the discharge side of the pipe at the break and what was lost there (from backflow).

Overall, quite the complicated fluid dynamics problem... and impossible to know exactly how much water was lost.