Question: Consider fully developed laminar flow of a constant-property fluid in a circular tube. At a particular flow cross section calculate the total axial momentum flux by integration over the entire cross section. Compare this with the momentum flux evaluated by multiplying the mass flow rate times the mean velocity. Explain the difference, then discuss the implications for the last part of Problem.
Problem: Starting with the momentum theorem, develop an equation for the pressure drop for steady flow of a constant-property fluid in a tube of constant cross-sectional shape as a function of the friction coefficient, mean velocity, and tube length. Start with a control volume that is of infinitesimal dimension in the flow direction but that extends across the entire flow section. Then reconsider the problem when fluid density varies in some known manner along the tube but can be considered as effectively constant over the flow cross section. Discuss the implications of the latter assumption.