1. Pipe Components,
Piping System

2. PART I
Minor Loss
Loss Coefficient

3. Major Loss, PL,minor
As shown in Chapter 6, major Loss, i.e. the pressure drop when fluid flows across a straight pipe, can be calculated by E6-22 or E6-22a:
(E6-22)
(E6-22a)
where the friction factor f for turbulent can be obtained from the Moody chart. For laminar can be calculated using formulas

4. Minor Loss, PL,minor
Minor Loss is due to pressure drop when fluid flows across a pipe component.
Typical pipe components include:
Entrance and exit
Enlargements and contractions
Bends
Pipe fittings such as tees, elbows, unions and flow controlling devices (valves)

5. 1 2 3 5 4

6. Flow Through a Valve A pipe component has a very complex geometry;
Flow through it has a very complex pattern;
Analytical analysis is not possible
we need to have a unified easy-to-use methodology for the calculation of minor losses of all components for practical applications.

7. Loss Coefficient, KL We can define a dimensionless loss coefficient as
We can then calculate minor loss as
(E7-1)
(E7-2)
(E7-2a)

8. Loss Coefficient, KL
Equations E7-2 and E7-2a are for all pipe components;
Loss coefficient KL becomes very important in solving engineering problems.
Our job now is to find the value of KL for each type of pipe components;
Typically, values of KL can only be estimated by experiments.

9. Dynamic pressure
Friction factor
Pipe geometry factor
Major loss is a function of friction factor ( f ) pipe geometry (L/D), and dynamic pressure.

10. Loss coefficient
Dynamic pressure
Minor loss is a function of loss coefficient (KL) and dynamic pressure.
Friction factor and geometry factor are very difficult to be quantified for pipe components so that the two parameters are accumulated into a single loss coefficient, KL.

11. Loss Coefficients of Various Pipe Components
PART II
Loss Coefficients of Various Pipe Components

12. Entrance (1)
Re-entrant
Sharp-Edged
Rounded

14. Entrance (2)
At point 1 far from the entrance, the fluid is stationary (V1 = 0) with static pressure P1.
Near the pipe entrance, the fluid starts to accelerate while it enters into the pipe entrance from all directions.
Because the flow direction is not entirely in the axial direction, the radial inward velocity of the fluid leads to the formation of a narrowed neck (also called the vena contracta) just downstream of the entrance.

15. Entrance (3)
As the flow is separated at the corner of the entrance, a collar of separated fluid surrounds the neck, where the fluid velocity continues to accelerate (the fluid pressure continued to decrease) until it reaches maximum velocity V2 at point 2.
Once passing through the neck, the fluid will decelerate to some point, where the flow practically becomes uniform over the cross section of the pipe.

16. Entrance (4)
From point 2 to point 3, the fluid slows down from relatively high velocity V2 and high kinetic energy to relatively low velocity V3 and low kinetic energy.
The kinetic energy can not be fully recovered as increased pressure because part of the kinetic energy becomes friction loss (i.e. minor loss at entrance) and is dissipated into the fluid due to fluid mixing and eddy transport.

17. Entrance (5)
Experimental data indicate that KL value of a sharp-edged entrance is 0.5.
The entrance loss strongly depends on the entrance geometry.
We can reduce the entrance loss by carefully designing its geometry.

18. KL depends on roundness, see Table 7-1
Entrance (6)
Rounded
KL depends on roundness, see Table 7-1
Re-entrant
KL = 0.78
Sharp-Edged
KL = 0.5

19. Exit
When fluid flows from a pipe into a tank, it mixes with the fluid in the tank and eventually comes to rest. The exit loss is the entire fluid kinetic energy, i.e. KL = 1.0.
Re-entrant
KL = 1.0
Sharp-Edged
KL = 1.0
Rounded
KL = 1.0

20. Entrance and Exit

21. Enlargements and Contractions
We can calculate the loss coefficients, KL, of enlargements and contractions as
Entrances and exits are special cases of enlargements and contractions
(E7-3)

22. Loss coefficient, KL
KL based experiments L
A1 V1
A2 V2

23. Enlargements and Contractions

24. Pipe Bends and Fittings
In most fluid systems, we must consider the pressure drop due to
Pipe bends
pipe fittings, including bends, elbows, tees, valves and union etc.
Flows in pipe fittings are more complex than those through pipe enlargements and exits as the flow path is generally much complicated.

25. 900 Bend
450 Elbow
900 Elbow
Tees-line flow
Tees-branch flow

26. Pipe Bends and Fittings
We can use two methods to deal with pipe bends and fittings
Loss coefficient, KL
Equivalent pipe length

27. Equivalent Pipe Length
Equivalent pipe length of fittings is dimensionless and defined as the number of pipe diameters needed to have the same friction loss as the fittings, i.e.

28. Equivalent Pipe Length
The equivalent pipe length is obtained from the correlations of experimental data.
With equivalent pipe length, we can
calculate the pressure drop; or
add this length to the actual length of the pipe to find an adjusted length, which gives practically the same friction effect as does the actual pipe including pipe components.

29. Equivalent Pipe Length

30. What Are the Differences between KL and Equivalent Pipe Length?
The same pipe component may have the values of both equivalent pipe length and loss coefficient.
Either equivalent pipe length or loss coefficient can be used to calculate the pressure drop. They may end up with results of differences.
Both equivalent pipe length and loss coefficient are empirical correlations, we should not try to match theoretical significance to the two.
Both equivalent pipe length and loss coefficient are merely simple results of carefully-designed tests, arranged in a way that is used to predict the pressure drop across the same fittings in new systems.

31. Valves
Gate valve
Angle valve
Globe valve
Ball valve

32. Loss Coefficient, KL
Loss coefficient is often used for Valves.

33. In minor loss calculations:
The values of friction factor is always depend on the geometry of: entrance, exit bends, tees and valves.
Bends 90 degree: is the only one you need to know the flow properties (i.e. laminar or turbulent to find f)

34. PART III
Piping Systems

35. Pipe Systems

36. Series Pipe Systems
Governed by mass conservation law, the flow rate through series pipe systems should be same in each pipe.
The total pressure drop (from point A to point B) should be the sum of the pressure drop in each pipe.

37. Parallel Pipe Systems
The fluid will take any of the three pipes to travel from A to B. Therefore the total flow rate is equal to the sum of the flow rates in each pipe.
By writing an energy equation between points A and B, it is found that the pressure drop experienced by any fluid travelling between these locations is the same, independent of the path taken.

38. Pipe Flow Problems with Examples
PART IV
Pipe Flow Problems with Examples

39. Pipe Flow Problems
There are commonly THREE types of pipe flow problems:
Type I: Determine the pressure drop (or head loss) through a pipe system, given the kind and size of pipes, pipe components included, and the flow rate.
Type II: Determine the flow rate through a pipe system, given the pressure drop (or head loss), kind and size of pipes, pipe components included.
Type III: Determine the size of pipe needed to carry the flow, given the kind of pipe, pressure drop (or head loss), pipe components included and flow rate.

40. Type I Pipe Flow Problems
Type I: Determine the pressure drop (or head loss) through a pipe system, given the kind and size of pipes, pipe components included, and the flow rate.

44. Type II Pipe Flow Problems
Type II: Determine the flow rate through a pipe system, given the pressure drop (or head loss), kind and size of pipes, pipe components included.

49. Type III Pipe Flow Problems
Type III: Determine the size of pipe needed to carry the flow, given the kind of pipe, pressure drop (or head loss), pipe components included and flow rate.

54. Self study problem Problem
bend
bend