Sloshing force on a tube in a tank

[Lancea]

Hi everyone,
I have a seismic calculation question.

A tube (19.48 ft, 2 ft diameter) stands in the middle of a 40 diameter 26 ft tall tank, in which the max operating water height is 23 ft.

When calculation the sloshing force on the TUBE, I did the impulsive & convective period of the tank mass (Ti & Tc), the impulsive & convective acceleration of the mass (Ai & Ac), then 0.5*Ti*Ai & 0.5*Tc*Ac are the max imulsive & convective velocity of the mass particles (Vi & Vc). After this, I used the "P = 0.5*density*velocity(square)*A*Cd" to calculate the force acting on the tube ,where the A = diameter of the tube * H (tube height in impulsive / convective mass region).

OK, the above precedure turned out the forces are pretty fractional.
Is this the good way to calculate the sloshing force on the tube??

Please let me know what you are going to do on this real problem.
Anyone's comments will help!

Thanks a lot!!

--Lancea

 

[ishvaaag]

Most likely it will be treated as a mechanical event simulation in one program able to take dynamic input and mechanic of fluids ... well out of my ordinary scope. In any case as long the basic cylindrical shape stands it seems quite logical that the values not grow big on the opposition of the fluid to the other side of the action to be moved. This must help the tube, plus the basic central symmetry; at one side bigger speeds and impacts might eventually be attained on some instability of the dynamic input causing the rotation of the fluid, one would think.

 

[JStephen]

There is a technical paper by Wozniak and Mitchell from 1978 about "Basis for Seismic Provisions" for API-650. If I remember correctly, the appendix to that paper gives equations for the liquid forces on a cylinder in the tank (specifically to calculate loads on support columns). The approach is similar to what you have described above.

 

[DBrian]

Lancea
I believe you are correct that the sloshing (convective) forces will be relatively small (unless you have wave impact loading).

However I would include an impulsive added fluid mass component. Newmark estimated these forces as the mass of water displaced by the tube. For your tube the added impulsive fluid mass will be = (Dia of Tube)^2*pi/4*fluid mass density x height of the tube. This mass can be approximated as a UDL distributed over the full height of the tube (not just the impulsive height). Add this mass to the mass of the tube and any tube contents and calculate seismic forces accordingly.

If you would like more info try the USACE publications on intake towers or refer to Chopra & Goyal (1989)

Regards
DBH

 

[Lancea]

Thank you 3, ishvaaag, JStephen & Brian.
Thank you for your info.

This afternoon I found a mistake in my cals that I forgot to times the gravity "g" after the acceleration obtained from AWWA D-100-05 chapter 13, because those Ai & Ac are just multiples of "g". Added the "g", the results are much more reasonable. ( V = A * T * g )

All your comments are valuable to us.
Thank you again!

--Lancea