Physical properties of fluid and fluid transport in piping system
Laminar and turbulent flow in pipe
Friction factor
Flow in pipes and valves theory - full content
Physical values in Darcy formula are very obvious and can be easily obtained when pipe properties are known like D - pipe internal
diameter, L - pipe length and when flow rate is known, velocity can be easily calculated using continuity equation. The only value
that needs to be determined experimentally is friction factor. For laminar flow regime Re<2000, friction factor can be calculated,
but for turbulent flow regime where is Re>4000 experimentally obtained results are used. In the critical zone, where is Reynolds
number between 2000 and 4000, both laminar and turbulent flow regime might occur, so friction factor is indeterminate and has lower
limits for laminar flow, and upper limits based on turbulent flow conditions.
If the flow is laminar and Reynolds number is smaller than 2000, the friction factor may be determined from the equation:
where is:
- f - friction factor
- Re - Reynolds number
When flow is turbulent and Reynolds number is higher than 4000, the friction factor depends on pipe relative roughness
as well as on the Reynolds number. Relative pipe roughness is the roughness of the pipe wall compared to pipe diameter e/D.
Since the internal pipe roughness is actually independent of pipe diameter, pipes with smaller pipe diameter will have higher
relative roughness than pipes with bigger diameter and therefore pipes with smaller diameters will have higher friction factors
than pipes with bigger diameters of the same material.
Most widely accepted and used data for friction factor in Darcy formula is the Moody diagram. On Moody diagram friction factor
can be determined based on the value of Reynolds number and relative roughness.
The pressure drop is the function of internal diameter with the fifth power. With time in service, the interior of the pipe
becomes encrusted with dirt, scale, tubercles and it is often prudent to make allowance for expected diameter changes.
Also roughness may be expected to increase with use due to corrosion or incrustation at a rate determined by the pipe material
and nature of the fluid.
When the thickness of laminar sub layer (laminar boundary layer &delta) is bigger than the pipe roughness e the
flow is called flow in hydraulically smooth pipe and Blasius equation can be used:
where is:
- f - friction factor
- Re - Reynolds number
The boundary layer thickness can be calculated based on the Prandtl equation as:
where is:
- &delta - boundary layer thickness
- D - internal pipe diameter
- Re - Reynolds number
For turbulent flow with Re<100 000 (Prandtl equation) can be used:
For turbulent flow with Re>100 000 (Karman equation) can be used:
where is:
- f - friction factor
- Re - Reynolds number
- D - internal pipe diameter
- kr - pipe roughness
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