Newtonian Flow through a Capillary

Equation 4-3b may be regarded as the basic equation of capillary viscometry. The properties of the liquid enter the equation by way of the rheological function which expresses the relation between rate of shear and shear stress. For Newtonian flow from Eqn 4-2 we get 

On integrating with respect to a. and using the boundary condition w when = R, we get 

It is evident that the velocity function with respect to a is parabolic, with maximum velocity where a = 0. 

The volumetric flow rate Q. can be obtained by a second integration 2 

This is the Hagen-Poiseuille law for laminar flow in tubes. Its conversion to a form applicable to experimental measurements will be given later. For the present we note that the quantities R, aP and I can all be obtained by direct measurement and Eqn 4-8 therefore can be used in the absolute experimental method for the determination of the viscosity of a liquid in any physically rational system of units. When the 

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