Storage tank defect spray distance

[cornemo]

Dear,

I don't exactly know where to post this question, but as it actually is a fluid flow issue, I thought I post it here.

I have to calculate the spray distance resulting from a small defect (say 10 or 20 mm) in a storage tank shell.

My first assumption was to calculate the outlet velocity using the hydrostatic pressure:
velocity = (2*g*Head)^0.5
where Head = the liquid height above the defect

Then calculate the time it takes for gravitation to get the liquid down:
droptime = (2*height of defect / g)^0.5

Then using droptime * velocity to get the horizontal distance of the spray.

However if I compare my results to the example results I have from someone elses calculation my distances are much larger (about 1.6 times).
I know I calculated the distance with constant horizontal speed of the flow which may not be accurate.

Can any of you help me to get a more accurate calculation method for this problem?

 

[zelgar]

What you've posted is how I would calculate it. Of course, the following items could change the calculation:
1. Pressure (if it's a pressurized tank, the velocity would increase, v = (2*g*Head + pressure/density)^0.5
2. Viscosity, if the fluid is more viscous than water then you may have more losses due to friction.
3. The calculation is assuming no losses occurring at the defect.

All in all, if you are wanting to find the worst case scenario, then your calculation (unless the tank is pressurized) are correct.

 

[Latexman]

I am very familiar with this "pee distance" calculation. If you attach your derivations, we can review and comment on it. There is a defect height that maximizes (i.e. you'll need to differentiate!) the distance to the dike.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[cornemo]

Thanks for the replies.

@Latexman:
I didn't do anything more then using above three formulas (velocity = (2*g*Head)^0.5, droptime = (2*height of defect / g)^0.5 and distance=velocity*droptime) to calculate the distance for multiple defect locations. Then took the highest value from these calculations as maximum distance to be considered.

If there are any other factors I have/can take into account please let me know.

 

[Latexman]

Differentiate the distance=velocity*droptime equation wrt distance. Set it = 0. Solve for the (H_defect)_Max, i.e. height of defect which gives the maximum spray distance. Then, substitute this equation for (H_defect)_Max back into the original distance=velocity*droptime equation. This will allow you to calculate the maximum spray distance directly.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.