uluru
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hi everybody,
so I'm working on a project where I'm trying to measure raindrop parameters, and one thing I'm looking at is the sub-terminal speed of drops released from a certain height. The equation that I'm using is from http://staff.science.uva.nl/~jboxel/Publications/PDFs/Gent_98.pdf
The gist of the equation that I was considering is:
F = g*ρw*∏*d^3/6 - 3*∏*d*μ*V*Ct*Cd
where Ct = 1+0.16*Re^(2/3)
and Re = ρVD/μ;
and Cd = 1+a(We+b)^c - ab^c
where a,b,c are empirically derived constants and We = ρ*V^2*d/σ
Basically, when I put everything together and try to calculate fall velocity, I get stuck with a disgusting integral, because I use
V(t)=∫a(t) = (1/m)*∫F(t)
Does anybody have suggestions for how to approach this? I just want to make a model in matlab.. it seems like I could do some kind of step approach, because I looked at the integral and it's really nasty, but I don't know what to do, because I have V(t) on both sides...
Or if anybody knows of a simpler model presented in a paper, I could use that too. I just want to compare my data with a preexisting model; it's not critical to my project, but I think it's important.
so I'm working on a project where I'm trying to measure raindrop parameters, and one thing I'm looking at is the sub-terminal speed of drops released from a certain height. The equation that I'm using is from http://staff.science.uva.nl/~jboxel/Publications/PDFs/Gent_98.pdf
The gist of the equation that I was considering is:
F = g*ρw*∏*d^3/6 - 3*∏*d*μ*V*Ct*Cd
where Ct = 1+0.16*Re^(2/3)
and Re = ρVD/μ;
and Cd = 1+a(We+b)^c - ab^c
where a,b,c are empirically derived constants and We = ρ*V^2*d/σ
Basically, when I put everything together and try to calculate fall velocity, I get stuck with a disgusting integral, because I use
V(t)=∫a(t) = (1/m)*∫F(t)
Does anybody have suggestions for how to approach this? I just want to make a model in matlab.. it seems like I could do some kind of step approach, because I looked at the integral and it's really nasty, but I don't know what to do, because I have V(t) on both sides...
Or if anybody knows of a simpler model presented in a paper, I could use that too. I just want to compare my data with a preexisting model; it's not critical to my project, but I think it's important.