Weber number

[hsolid100]

The weber number equals to density x velocity^2 x diameter/surface tension. Could someone please tell if this density is of the droplet or the fluid surrounding the droplet. Also what is the unit of the surface tension in this calculation?

Thanks

 

[zdas04]

In US Customary units units of surface tension are lbf/ft. Density and velocity are of the minor phase (i.e., the droplet), diameter is of the flow conduit. In U.S. customary units you also need a g_c to get the lbf and lbm to cancel. I've never needed to calculate this value in SI so I don't know the units there.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[hsolid100]

Thanks for your reply, I think it is incorrect though. One thing I am sure of is that the diameter is the droplet diameter. I am unsure of what the density should be (liquid droplet's density or that of the gas surrounding it). I have seen some research papers in which scholars have used both the liquid and the gas densities for their "own" definitions of the Weber number such as the collision weber number, or crossflow weber number.

Could you explain if possible?

 

[zdas04]

Interesting that I've been using it "incorrectly" for 25 years. Your post does clear up one thing for me--I've seen research where the number was very small, and other research where it was much larger. In other words it doesn't seem to matter what diameter you use as long as you are using it consistently to apply to varying configurations of your experiment (rather than relying on an absolute value like we do for Reynolds Number). I have several patents that represent products that were designed based on my definition of Weber Number. I have written programs that manufacturers have used to successfully evaluate candidates for a commercial product based on my definition of Weber Number. Guess it is "incorrect" in a useful way.

In terms of usefulness I must wonder exactly how someone assigns a droplet diameter when in real flows that parameter varies a couple of orders of magnitude from one end of a pipe to the other, but when you're making crap up (like you must do to determine a droplet size) I guess it is OK to make up whatever you want.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist