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'.(adsbygoogle = window.adsbygoogle || []).push({});

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!!

-Josh

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# Fluid Mechanics: pressure gradient of a tube bifurcation

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