# Bond number for accelerating flow

The Bond number is a dimensionless number typically used to analyze cases where two fluids of different densities are in contact and subject to gravity only. I'm analyzing a system where gas and liquid are entrained in a pipe (think garden hose with trapped air pockets), and both are subject to high accelerations, much higher than gravity. I'd like to modify the equation for the Bond number to use my known value of acceleration in place of gravitational acceleration, but I can't find any published literature where someone has done this.

What I want to do is this: $$Bo=\frac{\Delta \rho a L^2}{\sigma}$$ where $a$ has replaced $g$ in the traditional equation: $$Bo=\frac{\Delta \rho g L^2}{\sigma}$$ Anyone have experience or at least comments on my approach?

$$Eu = \frac{\Delta p}{\rho v^2}$$ $$We = \frac{\rho v^2 l}{\sigma}$$ $$Eu\cdot We=\frac{\Delta p\cdot l}{\sigma}$$