Unsteady laminar flow in a circular pipe
Barrett, Robert Russell
Beckmann, Herbert K.
Master of Science
An exact solution of unsteady laminar flow of an incompressible fluid in a circular pipe is presented. The flow is taken to be axially symmetric and parallel to the pipe axis. The equation of motion in two independent variables is transformed, by a Laplace Transformation, to an ordinary differential equation independent of time. The solution to the differential equation is then transformed to include the variable t, by means of the Complex Inversion Theorem. It is shown that once the pressure gradient is known as a function of time, a solution for the velocity is available, provided the Laplace transform of the pressure gradient exists.