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Marcus N 1753
Postad: 18 feb 16:55

Internal flow

In internal flow, a pipe is completely filled with a fluid. Laminar flow is characterized by smooth streamlines and highly ordered motion, and turbulent flow is characterized by unsteady disorderly velocity fluctuations and highly disordered motion. The Reynolds number is defined asLh.

Re=Intertial forcesViscous forces=VavgDv=ρVavgDμ

Under most practical conditions, the flow in a pipe is laminar at Re < 2300, turbulent at Re > 4000, and transitional in between.


The region of the flow in which the effects of the viscous shearing forces are felt is called the velocity boundary layer. The region from the pipe inlet to the point at which the flow becomes fully developed is called the hydrodynamic entrance region, and the length of this region is called the hydrodynamic entry length Lh. It is given by:

Lh,lamninarD0.05 Re and Lh,turbulentD10

The friction coefficient in the fully developed flow region is constant. The maximum and average velocities in fully developed laminar flow in a circular pipe are:

umax=2Vavg  and  Vavg=PD232μL

The volume flow rate and the pressure drop for lamninar flow in a horizontal pipe are


The pressure loss and head loss for all types of internal flows (laminar or turbulent, in circular or noncircular pipes, smooth or rough surfaces) are expressed as


where ρV22is the dynamic pressure and the dimensionless quantity f is the friction factor. For fully developed laminar flow in a round pipe, the friction factor is f=64/Re.

For noncircular pipes, the diameter in the previous relations is replaced by the hydraulic diameter defined as Dh=4Ac/p, where Ac is the cross-sectional area of the pipe and p is its wetted perimeter.

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