An incompressible fluid flows downward through a vertical cylindrical pipe under the action of gravity. The flow is fully developed and laminar. Use the Navier– Stokes equations to derive an...

An incompressible fluid flows downward through a vertical cylindrical pipe under the action of gravity. The flow is fully developed and laminar. Use the Navier– Stokes equations to derive an expression for the flowrate for the case of zero pressure gradient along the pipe.