Theory of flow through pipes, valves and fittings
Theory of flow through valves and fittings
Resistance coefficient K, equivalent length L/D
Flow in pipes and valves theory - full content
Pressure drop or head loss is proportional to the velocity in valve or fitting. For the most engineering practices it can be assumed
that pressure drop or head loss due to flow of fluids in turbulent range through valves and fittings is proportional to square of velocity.
To avoid expensive testing of every valve and every fitting that are installed on pipeline, the experimental data are used. For that purpose
resistance coefficient K, equivalent length L/D and flow coefficient Cv, Kv are used. These values are available from different sources like
tables and diagrams from different authors and from valve manufacturers as well.
Kinetic energy, which is represented as head due to velocity is generated from static head and increase or decrease in velocity directly
is proportional with static head loss or gain. "Velocity head" is:
where is:
- hL - head loss
- v - velocity
- gn - acceleration of gravity
The number of velocity heads lost due to resistance of valves and fittings is:
where is:
- hL - head loss
- K - resistance coefficient
- v - velocity
- gn - acceleration of gravity
The head loss due to resistance in valves and fittings are always associated with the diameter on which velocity occurs.
The resistance coefficient K is considered to be constant for any defined valve or fitting in all flow conditions, as the head
loss due to friction is minor compared to the head loss due to change in direction of flow, obstructions and sudden or gradual
changes in cross section and shape of flow.
Head loss due to friction in straight pipe is expressed by the Darcy equation:
where is:
- hL - head loss
- f - friction factor
- L - length
- D - internal diameter
- v - velocity
- gn - acceleration of gravity
It follows that:
where is:
- K - resistance coefficient
- f - friction factor
- L - lengt
- D - internal diameter
The ratio L/D is equivalent length in pipe diameters of straight pipe that will cause the same pressure drop or
head loss as the valve or fitting under the same flow conditions. As the resistance coefficient is K is constant
the equivalent length L/D will vary inversely with the change in friction factor for different flow conditions.
For geometrically similar valves and fittings, the resistance coefficient would be constant. Actually there are
always smaller or bigger geometrical non similarity in valves and fittings of different nominal size, so the
resistance coefficient is not constant. The resistance coefficient K for a given type of valve or fitting,
tends to vary with size as does friction factor for straight clean commercial steel pipe at the same flow conditions.
Some resistances in piping like sudden or gradual contractions and enlargements, as well as pipe entrances or exists
are geometrically similar. Therefore the resistance coefficient is for these items independent of size.
The values for resistance coefficient are always associated with internal pipe diameter where the resistance is occurring.
If the resistance factor should be used for different internal pipe diameter than the diameter for which existing values
can be found following relationship can be used:
where is:
- K - resistance coefficient
- D - internal diameter
where subscript "a" defines K and d with the reference to internal pipe diameter, and subscript "b" defines K and d with
the reference to the internal diameter for which values of K can be found in tables or diagrams.
This equation can also be used if the piping system has more than one size of valves and fittings to express the resistance
coefficient in terms of one size.
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