1. Losses due to Fluid Friction
Chapter 6
Losses due to Fluid Friction

2. Objectives
To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate.
To correlate this in terms of the friction factor and Reynolds number.
To compare results with available theories and correlations.
To determine the influence of pipe fittings on pressure drop
To show the relation between flow area, pressure drop and loss as a function of flow rate for Venturi meter and Orifice meter.

3. Losses due to Friction (6.13) (6.14)
Mechanical energy equation between locations 1 and 2 in the absence of shaft work:
where
=Friction head/unit mass
For flow in a horizontal pipe and no diameter change (V1=V2), then : OR
F in J/kg
Hagen-Poiseuille Law-E5.10
Because of (5.4) :
Thus, the shear stress at the wall is responsible for the losses due to friction
and
(6.13)
(6.14)
Or F/g= hLoss= 128μQL/(πρgD4)

4. Losses due to Friction
Total head loss , hL (=F/g), is regarded as the sum of
major losses and minor losses
hL major, due to frictional effects in fully developed flow in
constant area tubes,
hL minor, resulting from entrance, fitting, area changes,
and so on.

5. Losses due to Friction/The Friction Factor
In order to determine an expression for the losses due to friction we must resort to experimentation.
where L=length of the pipe,
D=diameter of the pipe,
V=velocity,
By introducing the friction factor, f:
(6.15)
where or
f is called Darcy friction factor

6. Friction Factor The Darcy friction factor f is defined as
later
now
The Darcy friction factor f is defined as
We know the wall shear stress
and
(E6-21)
The friction factor is the ratio between wall shear stress
and flow inertial force.

7. Major Loss and Friction Factor
With the introduction of friction factor, we can calculate major loss by
(E6-22)
Friction factor
Pipe geometry factor
Dynamic pressure
Therefore, our job now is find the friction factor f for various flows.

8. Friction Factor - Laminar Pipe Flow
For a pipe with a length of L, the pressure gradient is constant, the pressure drop based on Hagen-Poiseuille Law ,
Divided both sides by the dynamic pressure V2/2 and L/D
We have

9. Major Loss and Friction Factor
The mechanical energy equation can be written in terms of heads :
(6.17)
Knowledge of the friction factor allows us to estimate the loss term in the energy equation.
This head loss can also be calculated using H-B equation

11. Example 1
losses in

13. Example 2

15. Case 2: Turbulent Flow
When fluid flow at higher flow rates, the streamlines are not steady, not straight and the flow is not laminar.
Generally, the flow field will vary in both space and time with fluctuations that comprise "turbulence”
When the flow is turbulent the velocity and pressure fluctuate very rapidly. The velocity components at a point in a turbulent flow field fluctuate about a mean value.
Time-averaged velocity profile can be expressed in terms of the power law equation, n =7 is a good approximation.

16. Friction Factor-Turbulent Pipe Flow
For a laminar flow, the friction factor can be analytically derived.
It is impossible to do so for a turbulent flow so that we can only obtain the friction factor from empirical results.
For turbulent flow, it is impossible to analytically derive the friction factor f, which can ONLY be obtained from experimental data.
In addition, most pipes, except glass tubing, have rough surfaces.
The pipe surface roughness is quantified by a dimensionless number, relative pipe roughness (ε / D ), where ε is pipe roughness and D is pipe diameter.
For laminar pipe flow, the flow is dominated by viscous effects hence surface roughness is not a consideration.
However, for turbulent flow, the surface roughness may protrude beyond the laminar sublayer and affect the flow to a certain degree. Therefore, the friction factor f can be generally written as a function of Reynolds number and pipe relative roughness
There are several theoretical models available for the prediction of shear stresses in turbulent flow.

17. Surface Roughness Additional dimensionless group /D
need to be characterize
Thus more than one curve on friction factor-Reynolds number plot
Fanning diagram or Moody diagram
Depending on the laminar region.
If, at the lowest Reynolds numbers, the laminar portion corresponds to f =16/Re Fanning Chart
(or f = 64/Re Moody chart)

18. Friction Factor and Pipe Roughness
Most pipes, except glass tubing, have rough surfaces
- Pipe surface roughness,
- Relative pipe roughness,
The surface roughness may affect the friction factor. Generally, we have

19. Pipe Surface Roughness

20. Friction Factor of Turbulent Flow
If the surface protrusions are within the viscous layer, the pipe is hydraulically smooth;
If the surface protrusions extend into the buffer layer, f is a function of both Re and /D;
For large protrusions into the turbulent core, f is only a function of /D.

21. Friction Factor for Smooth, Transition, and Rough Turbulent flow
Smooth pipe, Re>3000 Or
Rough pipe, [ (D/ε)/(Re√ƒ) <0.01]
Transition function for both smooth and rough pipe

22. Fanning Diagram
f =16/Re

23. Friction Factor – The Moody Chart

24. Example: Comparison of Laminar or Turbulent pressure Drop
Air under standard conditions flows through a 4.0-mm-diameter drawn tubing with an average velocity of V = 50 m/s. For such conditions the flow would normally be turbulent. However, if precautions are taken to eliminate disturbances to the flow (the entrance to the tube is very smooth, the air is dust free, the tube does not vibrate, etc.), it may be possible to maintain laminar flow.
(a) Determine the pressure drop in a 0.1-m section of the tube
if the flow is laminar.
(b) Repeat the calculations if the flow is turbulent.
Straight and horizontal pipe and same diameters give same velocity:
Z1=Z2= V1=V2 and thus

25. Solution1/2 f=64/Re=`…=0.00467 F=16/Re=`…=0.001167
Under standard temperature and pressure conditions
Ρ=1.23kg/m3, μ=1.7910-5Ns/m
The Reynolds number r
If the flow were laminar and using Darcy friction
f=64/Re=`…=
If the flow were laminar and using Fanning friction
F=16/Re=`…=

26. Solution2/2 From Moody chart f=Φ(Re, smooth pipe) =0.028
If the flow were turbulent
From Moody chart f=Φ(Re, smooth pipe) =0.028
From Fanning chart f=Φ(Re, smooth pipe) =0.007

27. Example
Straight and horizontal pipe and same diameters give same velocity:
Z1=Z2= V1=V2 and thus

30. Example
0.04 m

33. for fanning

34. Example: Determine Head Loss
Crude oil at 140°F with γ=53.7 lb/ft3 and μ= 810-5 lb·s/ft2 (about four times the viscosity of water) is pumped across Alaska through the Alaska pipeline, a 799-mile-along, 4-ft-diameter steel pipe, at a maximum rate of Q = 2.4 million barrel/day = 117ft3/s, or V=Q/A=9.31 ft/s. Determine the horsepower needed for the pumps that drive this large system.

35. Solution1/2 The energy equation between points (1) and (2)
hP is the head provided to the oil by the pump.
Assume that z1=z2, p1=p2=V1=V2=0 (large, open tank)
Minor losses are negligible because of the large length-to-diameter ratio of the relatively straight, uninterrupted pipe.
f= from chart ε/D=( ft)/(4ft), Re=…..

36. Solution2/2 The actual power supplied to the fluid power=Q∆P =Qρgh
unit of power (SI): Watt =N.m/s=J/s

37. Minor Losses 1/5
Most pipe systems consist of considerably more than straight pipes. These additional components (valves, bends, tees, and the like) add to the overall head loss of the system.
Such losses are termed MINOR LOSS.
The flow pattern through a valve

38. 900 Bend
450 Elbow
900 Elbow
Tees-line flow
Tees-branch flow

39. Valves
Gate valve
Angle valve
Globe valve
Ball valve

40. Minor Losses 2/5
The theoretical analysis to predict the details of flow pattern (through these additional components) is not, as yet, possible.
The head loss information for essentially all components is given in dimensionless form and based on experimental data.
The most common method used to determine these head losses or pressure drops is to specify the loss coefficient, KL

41. Minor Losses 3/5
Minor losses are sometimes given in terms of an equivalent length leq
The actual value of KL is strongly dependent on the geometry of the component considered. It may also dependent on the fluid properties. That is

42. Minor Losses 4/5
For many practical applications the Reynolds number is large enough so that the flow through the component is dominated by inertial effects, with viscous effects being of secondary importance.
In a flow that is dominated by inertia effects rather than viscous effects, it is usually found that pressure drops and head losses correlate directly with the dynamic pressure.
This is the reason why the friction factor for very large Reynolds number, fully developed pipe flow is independent of the Reynolds number.

43. Minor Losses 5/5 This is true for flow through pipe components.
Thus, in most cases of practical interest the loss coefficients for components are a function of geometry only,

44. Minor Losses Coefficient For Example Entrance flow
Entrance flow condition and loss coefficient
(a) re-entrant, KL = 0.8
(b) sharp-edged, KL = 0.5
(c) slightly rounded,
KL = 0.2
(d) well-rounded,
KL = 0.04

45. Summary of Minor Losses
Major losses: Associated with the friction in the straight portions of the pipes
Minor losses: Due to additional components (pipe fittings, valves, bends, tees etc.) and to changes in flow area (contractions or expansions)
Method 1: We try to express the head loss due to minor losses in terms of a loss coefficient, KL:
Values of KL can be found in the literature (for example, see Table next ppt, for losses due to pipe components.

46. Minor Losses Component KL Elbows Regular 90°, flanged 0.3
Regular 90°, threaded
1.5
Long radius 90°, flanged
0.2
Long radius 90°, threaded
0.7
Long radius 45°, flanged
Regular 45°, threaded
0.4
180° return bends
180° return bend, threaded
180° return bend, flanged
Tees
Line flow, flanged
Line flow, threaded
0.9
Branch flow, flanged
1.0
Branch flow, threaded
2.0
Component KL
Union, threaded
0.8
Valves
Globe, fully open 10
Angle, fully open 2
Gate, fully open
0.15
Gate, ¼ closed
0.26
Gate, ½ closed
2.1
Gate, ¾ closed 17
Ball valve, fully open
0.05
Ball valve, 1/3 closed
5.5
Ball valve, 2/3 closed
210

47. Minor Losses
The mechanical energy equation can be written:
(6.22)

48. Minor Losses
Method 2:
Using the concept of equivalent length, which is the equivalent length of pipe which would have the same friction effect as the fitting.
(6.23)
Values of equivalent length (L/D) can be found in the literature

49. Example: Determine Pressure Drop
Water at 60°F flows from the basement to the second floor through the 0.75-in. diameter copper pipe (a drawn tubing) at a rate of Q = 12.0 gal/min (= ft3/s) and exits through a faucet of diameter 0.50 in. as shown in Figure
Determine the pressure at point (1) if: (a) all losses are neglected, (b) the only losses included are major losses, or (c) all losses are included.

50. Solution1/4 The flow is turbulent The energy equation
Head loss is different for each of the three cases.

51. Solution2/4 (a) If all losses are neglected (hL=0)
(b) If the only losses included are the major losses, the head loss is
chart
f =

52. Solution3/4
(c) If major and minor losses are included

55. Noncircular Ducts
The empirical correlations for pipe flow may be used for computations involving noncircular ducts, provided their cross sections are not too exaggerated.
The correlation for turbulent pipe flow are extended for use with noncircular geometries by introducing the hydraulic diameter, Dh, defined as
Where A is cross-sectional area, and
P is wetted perimeter.

56. Noncircular Ducts 3/4
The friction factor can be written as f=C/Reh, where the constant C depends on the particular shape of the duct, and Reh is the Reynolds number based on the hydraulic diameter.
The hydraulic diameter is also used in the definition of the friction factor, , and the relative roughness /Dh.

57. Non circular conduits Define hydraulic diameter, Dh:
Then use Reynolds number based on hydraulic diameter, Dh:

58. Non circular conduits Pipe of circular cross-section
Annulus (inside diameter D1, outside D2)
Rectangular conduit (area ab)

59. Example
Solved before

61. Multiple Pipe Systems
Pipes in series

62. Multiple Pipe Systems
Parallel pipes