Steady pressure-driven flow through a circular pipe has the parabolic profile
For and independent small errors, . Independent pressure errors add in quadrature before dividing by the pressure difference. Bounded worst-case errors instead add absolute derivative contributions.
For a parabolic profile in a pipe of radius , the mean speed is and . With pressure drop over length and kinematic viscosity , , so . This is not the pressure-work dissipation .

Articles by others on the same topic (1)

The Hagen–Poiseuille equation is a fundamental equation in fluid mechanics that describes the laminar flow of an incompressible and Newtonian fluid through a cylindrical pipe. It is used to calculate the volumetric flow rate of the fluid based on a few key parameters.