# Predicting raindrop speed from a given height

1. Apr 4, 2012

### uluru

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.

2. Apr 20, 2012

### Staff: Mentor

Hi uluru! Why don't you write the equation out neatly on paper and scan it? Someone may be able to offer suggestions on making V(t) the subject of the formula.

You may then be able to use a numerical method to evaluate the integral. http://en.wikipedia.org/wiki/Numerical_integration