Flow in a Tube of Arbitrary Cross-Section

VISCOUS FLOW IN A TUBE OF ARBITRARY CROSS-SECTION 

It is well known that the velocity 11(17, 0 for viscous flow in a straight pipe satisfies the equations 

Combining this equation with equation (39), and putting i/t = 1, we have the equations for f , 

As an illustration of this a tube of elliptical cross-section may be considered. If the major and minor semi-axes are a and b respectively 

Taking a as the characteristic length it may be shown, after a certain amount of algebraic labour, that 

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