Calculating Water Flow from Burst Pipe in Chicago

[berniebs]

A pipe broke on the roof of a public building here in Chicago. Although I am an electrical engineer and very rusty on hydraulics and water flow, I have been asked to estimate the amount of water dumped on the roof of this building, as follows:

Diameter of the burst pipe: 3/4 in.
Water temperature: 130 degr F
Pressure: 15 lbs

Water flowed for 45 minutes before being shut off. I assume the break allowed water to flow freely from a 3/4 in diameter opening.

I would appreciate it if someone can send me the formula for this calculation. I have searched a number of PF postings, without luck.

Thanks,

berniebs
berniebs@comcast.net

 

[tiny-tim]

Welcome to PF!

… I have been asked to estimate the amount of water dumped on the roof of this building, as follows:

Diameter of the burst pipe: 3/4 in.
Water temperature: 130 degr F
Pressure: 15 lbs

Water flowed for 45 minutes before being shut off. I assume the break allowed water to flow freely from a 3/4 in diameter opening.

Hi berniebs! Welcome to PF!

Bernoulli's equation along a streamline (essentially, KE = work done ), assuming zero speed at zero pressure:
pressure + (density)(speed)²/2 = 0

and of course flow rate = speed x area.

(For details to impress your colleagues with, see the PF Library )

 

[oswaler]

I can provide you with the formula and steps to calculate the water flow from the burst pipe in Chicago. The formula for water flow is Q = A * v, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water.

First, we need to calculate the cross-sectional area of the pipe. The diameter of the pipe is given as 3/4 inches, which is equivalent to 0.75 inches. We can use the formula for the area of a circle, A = πr^2, where r is the radius of the pipe. The radius can be calculated by dividing the diameter by 2, so the radius in this case would be 0.375 inches. Plugging these values into the formula, we get A = π * (0.375)^2 = 0.4418 square inches.

Next, we need to calculate the velocity of the water. We can use the Bernoulli's equation, which states that the pressure energy of a fluid is equal to its kinetic energy. In this case, the pressure is given as 15 lbs and the temperature of the water is 130 degrees Fahrenheit. We can use a conversion factor to convert the pressure from lbs to psi (pounds per square inch), which would be 2.03602 psi. Similarly, we can also convert the temperature from degrees Fahrenheit to degrees Rankine, which would be 690 degrees Rankine. Plugging these values into the Bernoulli's equation, we get v = √(2 * 2.03602 * 144 * (1 - (690/518.67)^1.4)) = 97.301 inches per second.

Finally, we can plug the values of A and v into the formula for water flow, Q = 0.4418 * 97.301 = 42.95 cubic inches per second. This is the flow rate of water from the burst pipe. To calculate the total amount of water dumped on the roof, we need to convert the flow rate from cubic inches per second to gallons per minute, since the water flowed for 45 minutes. This can be done by multiplying the flow rate by 0.004329, which gives us 0.186 gallons per minute. Multiplying this by 45 minutes, we get a total of 8.37 gallons of water.

I hope this helps