Fluid Mechanics: pressure gradient of a tube bifurcation
The question is as follows: A circular tube of radius 'a' bifurcates into two tubes with equal radii 'ka', where k is a dimensionless coefficient. Derive an expression for the ratio of the pressure gradient in each bifurcated tube to that in the initial tube in terms of 'k'.
I'm not sure how to approach the problem. I believe I might need to use the Navier-Stokes equation, but we haven't covered Reynold's numbers in class. The only other way I can think of approaching the derivation problem is by first describing the jump in pressure across the three-dimensional interface (the splitting point) as being equal to the product of the surface tension and twice the mean curvature of the surface (cylindrical).
Thanks in advance!!