Mean flow velocity within pipes with turbulent flow
Key FactsGyroscopic Couple: The rate of change of angular momentum () = (In the limit).
- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.
OverviewThe Chezy equation applied to pipes with turbulent flow is
- i is or head loss due to fiction over the pipe length,
- m is or wetted area divided by the wetted perimeter,
- and C is where f is the coefficient of friction.
TheoryFor the flow of a fluid within a pipe with velocity (v), there will be a reduction in mean pressure with distance, which is usually referred to as "head loss". Frictional resistance is proportional and the wetted area around the circumference of the pipe. Therefore,
- P is the perimeter of the pipe ,
- L is the length of the pipe section
- and f is the coefficient of friction
where m is the hydraulic mean depth
where h is the slope of the hydraulic gradient. Note: C is not a constant since f is a function of Reynolds number