Problem 4.18: Consider the steady laminar flow of a viscous fluid through a long circular...

Problem 4.18: Consider the steady laminar flow of a viscous fluid through a long circular cylindrical tube. The governing equation is

where is the axial component of velocity, is the viscosity, and is the gradient of pressure (which includes the combined effect of static pressure and gravitational force). The boundary conditions are

Using the symmetry and (a) two linear elements, (b) one quadratic element, determine the velocity field and compare with the exact solution at the nodes: