Calculating the distance between isobars...?

Question

I know I've done this before, but I can't for the life of me recall how. Given a change in pressure, a velocity of an air parcel moving across the gradient, and the density of the air, I need to find the distance between the isobars. This is extremely idealized so we're assuming everything remains the same across the gradient.

Any suggestions? I'll play around with units and see if I can figure it out dimensionally but if anyone has any hints that would be greatly appreciated.

Thanks much!

Answer 1

Why not use the horizontal equation of motion and assume no change in v along the gradient. This gives dp/dx = -rho(f)(v) where rho is the density (given), the velocity, v (given), and the change in pressure dp (given) solve for dx.