1. Generating and Understanding Theoretical and Experimental Leaks
Sam Gordji San Diego, CA
October 5, 2016

2. Where the Info. on This Presentation Comes From?
My research and programming on this subject
Internet, different webpages
My experimental work

3. Generating Theoretical and Experimental Leaks
SI is the International System of Measurements. Examples are meter, kg, and Pascal to represent distance , weight and pressure
English System of measurements uses foot, pound and psi to represent distance, weight and pressure
Here in this presentation English System of measurements are used
Complete Tables of SI and English System, a copy of this presentation and other and other today’s references may be downloaded from our webpage:

4. Why Leaks Occur in the First Place?
Leaks occur because of different potential between two poles
Liquids tend to move from higher level to the lower ones same as electricity or heat flux, they all obey natural laws

5. Parameters Effecting the volume of Leaks per given time
Size of the orifice
Height or the pressure of the product above the leak
Viscosity and Density of the product
Shape of the orifice, coefficient of discharge

6. Pressure on the USTs and the Lines
The height of USTs are usually about are 9’. If the tank is full and the orifice is at the lowest point possible, then the elevation above the orifice is 9’
Assuming the average product level in the tank to be 4.5’ and that the hole is located about a foot above the lowest part of the tank, then the average height above the hole is 3.5’.
This is a fair assumption

7. Conversion Formula for Converting Height to Pressure in psi and Vice Versa
Conversion formula for converting the height to psi and back is: pressure in psi=height (in feet)*.433
To obtain the height from the pressure in feet the equation is: height=psi/.433 , *** for water
for example in a tank if the level (height) is 3.5 feet, then the pressure at the bottom of the tank is: psi=3.5*.433=1.51 psi.

8. Comparing Tank Pressure and Line Pressure
The average tank pressure is about1.51 psi while the line pressure is about 25psi. So, for the same orifice the leak on lines are way higher than the leaks from tanks.
This formula is an important one in our industry as it let us convert height to psi (pound per square inch) and psi to height.

9. Having a Feel for Pressure
To have a feel for 10 psi, assume a person whose weight is 160 pounds is standing on a 4 inch by 4 inch surface. This person is exerting a force of 10 pounds per square inch on every square inch of this surface of 4” by 4”.

10. Some Example of pressure in different systems
1 Pa
Pascal = 1 N/m2 (The SI unit)
1 psi
= 1 lb/in2 (English unit) = 6,891 Pa
1 Bar
= 105 N/m2 = 100 kPa ≈ 1 atm
1 Tor
= 1 mm Hg = Pa ≈ 1 kPa
1 atm
= kPa = 760 mm Hg = in Hg = psi

11. Pressure-Leakage Relationship for a 1 mm dim (About 1/32 Inch) Hole in a Pipe. Please Note This Is Non-Linear Relationship Between Pressure in Meter and Leak Rate in Liter/h. 25/.433=57.73/3.2=18.04 meters, Where Leakage Is About 32 Liters Per Hour ◊
My Mathematica answers are close to this

12. Example of Pressure Drop
Original water pressure is 115 psi
At low leakage of about 2.3 gallons per hour or less the pressure remains constant at the original pressure of 115 psi.
Completely opening one valve the pressure drops to 70 psi and at two valves completely open the pressure drops to 55 psi. 
Outside diameter of these hoses are 1 1/16’

13. Water Leaking From the Gage

14. Drill Set and Sizes Used 1/32 to 1/8

15. A Picture of 1/32, 3/64 & 1/16 Leaks Tried to Use Gasoline Container

16. Water Leaks from 1/32, 3/64, and 1/16 Orifice

17. 1/16 Hole finished Draining, 1/32, 3/64 still draining

18. 1/32 orifice is now dripping

19. Second try of draining of 1/32, and 3/63

20. Drain Time for One Gallon of Water 82 Min. for One Gallon of Gas 41 Min. Under Gravitational Force with 1/16 orifice

21. Drain Time for One Gallon of Water 82 Min
Drain Time for One Gallon of Water 82 Min. for One Gallon of Gas 41 Min, Second Slid. Under Gravitational Force

22. Experimental and Theoretical Results, Note Theoretical Results are Under constant PSI, While Experimental are not
Orifice Diameter in inch
Under gravitational force
Experimental testing
Theoretical results
Theoretical results h= .2, c=.559, using a program written in Mathematica
1/32 = Diameter
It took 6 hours and 20 minutes for one gallon of water to drain. Q=60/380 = This was done in Jackson, MS
From Internet:
Q= , with c=.7
Time to drain one gallon : hr
(Note, P1= , p2= )
Checked again, same answer
Q= gph
3/64=.0469 Diameter
In Jackson, on 9/24 took 3:30 hours for one gallon of water to drain, Q=60/210=.2857
Q= , which took about 3 hours to drain
Q=.6732
1/16 = Diameter
It took 82 minutes for the water to drain, one tenth ounce of liquid was left. Q=60/82=.7317 gph
This was done on 9/25/2016 in Oxford
From Internet: Q= gph
Checked again, Same answer
Also test these Under Mathematica Program
1.131 gph
1/16 =.0625 Diameter
Gasoline Testing: It took 41 minutes for one gallon of gas to drain: Q=60/41 = 1.46 gph, So gas drains almost twice as fast as water, under the same condition.
The reason these values are high is because the head is variable and here it is assumed to be constant at .2 ft

23. Experimental and Theoretical Results of Leaks about 6 PSI
Orifice Diameter in inch
Theoretical Results from Mathematica, psi=6, c=.559
Experimental using air pressure to generate pressure of 6.0 psi
1/32 = Diameter
Theoretical Results with psi=6, 2r=1/32=.0312, c=.559. s= 5.*10^-6 From Mathematica Q=1.481 gpu
Not Performed
3/64=.0469 Diameter
From Mathematica psi = r= 3/64= , c=0.559
S=1.2566*10^-05, Q= gph
1/16 = Diameter
From Mathematica, psi= 6.0, c=.559 2r=1/16= , s= *10^-5
Q = gph
It took 10 minutes for a gallon of water to drain. So, Q = 6.00 gph gallons. So the experimental and the theoretical methods are almost the same
The reason these values are high is because the head is variable and here it is assumed to be constant at .2 ft

24. Set Up of the Experimental Method Using Air Pressure

25. Larger Gage Reads up to 15 psi, the Smaller Gage Is Graded up to 240 psi

26. How to Build a Graph to Represent Continuous Range of Pressure Similar to Graph Above
Measure the psi using a column of either gas or water 8’ high and observe the leakage at that rate
Measure the leakage for psi obtained from 7’ to 1’
Now with having 8 points for psi and 8 point for leakage at a given rate e.g. 1/16 a graph could be constructed to give the leakage rate anywhere from 1 foot to 8’ for a given orifice
The values obtained are accurate since we exactly know the psi and the height. The graph will be similar to graph above
Then we can obtain any leak for a given orifice and pressure

27. Graph of Setting Up the Experiment To Measure Leaks at Different heights to Obtain a Graph Similar to Slide # 11 Above

28. Leask Calculator From Internet

29. Parameters Are h=6ft, c=.559, s=.0000215ft^2 or 0.0625’, Flow(cfs)=0.000236*3600*7.47=6.3465gph

30. Conclusion Surprising and Interesting Result
Under the gravitational force gasoline drains twice as fast as water. That is because the density of gas is lower than the density of water. For example, honey and heavy oil have a higher density than water and drain slower than water
Under 25 psi water runs out of an orifice of 1/32 about 8.42 gph, if the analysis of gas running twice as fast water at 25 psi still holds at 25 psi, then in one hour a line having an orifice of 1/16 will discharge gallons of gas in to the atmosphere
This is way higher than 3 gph

31. Conclusion
For the First experiment Results of 3 methods were close but the method could be improved. My analysis uses bernoulli Equation, some others authors use empirical equation
These were results obtained from the internet, theoretical and analytical results obtained myself
Results showed even with a leak as small as 1/32 inch could produce a large leak of more than 8 gph if the line is under 25 psi of pressure.
This is the first try, to get a more accurate results, some parts of experimental study should be repeated