Presentation is loading. Please wait.

Presentation is loading. Please wait.

California State University, Chico

Similar presentations

Presentation on theme: "California State University, Chico"— Presentation transcript:

1 California State University, Chico
CE 150 Fluid Mechanics G.A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University, Chico CE 150

2 Reading: Munson, et al., Chapter 8
Viscous Flow in Pipes Reading: Munson, et al., Chapter 8 CE 150

3 Introduction Pipe Flow – important application
Pipe: circular cross section Duct: noncircular cross section Piping system may contain pipes of various diameters valves & fittings nozzles (pipe contraction) diffusers (pipe expansion) pumps, turbines, compressors, fans, blowers heat exchangers, mixing chambers reservoirs CE 150

4 Introduction Typical assumptions
pipe is completely filled with a single fluid (gas or liquid) phase change possible but course focus is single phase pipe flow is primarily driven by a pressure difference rather than gravity steady, incompressible flow uniform (average) flow at all cross sections extended Bernoulli equation (EBE) is applicable CE 150

5 Characteristics of Pipe Flow
Laminar vs. turbulent laminar: Re  2100 transitional:  Re  4000 turbulent: Re  4000 CE 150

6 Characteristics of Pipe Flow
Entrance region flow - typically between D ; depends on Re: Fully developed flow - occurs beyond entrance region; velocity profile is independent of x CE 150

7 Pipe Flow Problems Laminar flow Turbulent flow
Applications: blood flow, bearing lubrication, compact heat exchangers, solar collectors, MEMS fluid devices Fully-developed flow: exact analysis possible Entrance region flow: analysis complex; requires numerical methods Turbulent flow Applications: nearly all flows Defies analysis CE 150

8 Pressure and Viscous Forces in Pipe Flow
Entrance region Flow is accelerating at centerline, or pressure forces > viscous (shear) forces Flow is decelerating at wall, or viscous forces > pressure forces Fully-developed region Non-accelerating flow Pressure forces equal viscous forces Work done by pressure forces equals viscous dissipation of energy (into heat) CE 150

9 Fully Developed Laminar Flow
Velocity profile Volume flow rate CE 150

10 Fully Developed Laminar Flow
Pressure drop Friction factor CE 150

11 Turbulent Flow Occurs Re  4000 Velocity at given location: CE 150

12 Characteristics of Turbulent Flow
Laminar flow: microscopic (molecular scale) randomness Turbulent flow: macroscopic randomness (3-D “eddies”) Turbulence enhances mixing enhances heat & mass transfer increases pressure drop in pipes increases drag on airfoils CE 150

13 Characteristics of Turbulent Flow
Velocity fluctuation averages: Turbulence intensity: CE 150

14 Turbulent Shear Stress
Turbulent eddies enhance momentum transfer and shear stress: Mixing length model: Eddy viscosity: CE 150

15 Turbulent Shear Stress
Shear stress distribution: Mean velocity distribution: CE 150

16 Turbulent Pipe Flow Velocity Profile
For fully-developed flow, the mean velocity profile has been obtained by dimensional analysis and experiments for accurate analysis, equations are available for each layer for approximate analysis, the power-law velocity profile is often used: where n ranges between 6-10 (see Figure 8.17); n = 7 corresponds to many typical turbulent flows CE 150

17 Dimensional Analysis of Pipe Flow
Pressure drop where  = average roughness height of pipe wall; has no effect in laminar flow; can have significant effect in turbulent flow if it protrudes beyond viscous sublayer (see Table 8.1) Typical pi terms CE 150

18 Dimensional Analysis of Pipe Flow
Pressure drop is known to be linearly proportional to pipe length, thus: Recall friction factor: Pressure drop in terms of f : CE 150

19 Summary of Friction Factors for Pipe Flow
Laminar flow Turbulent flow in smooth pipes Turbulent flow in rough pipes CE 150

20 The Moody Chart CE 150

21 Friction Head Loss in Pipe Flow
For a constant-diameter horizontal pipe, the extended Bernoulli equation yields Head loss due to friction: If elevations changes are present: CE 150

22 Minor Head Losses in Pipe Flow
Minor losses are those due to pipe bends, fittings, valves, contractions, expansions, etc. (Note: they are not always “minor” when compared to friction losses) Minor head losses are expressed in terms of a dimensionless loss coefficient, KL: CE 150

23 Minor Head Losses in Pipe Flow
The loss coefficient strongly depends on the component geometry Entrance: Figures 8.22, 8.24 Exits: Figure 8.25 Sudden contraction: Figure 8.26 Sudden expansion: Figure 8.27 Conical diffuser: Figure 8.29 90º bends: Figures 8.30, 8.31 Pipe fittings: Table 8.2 CE 150

24 Noncircular Conduits Friction factors for are usually expressed as
where Reh is the Reynolds number based on the hydraulic diameter (Dh): Friction factor constants (C) are given in Figure 8.3 for annuli and rectangular cross sections CE 150

25 Common Types of Pipe Flow Problems
CE 150

26 Multiple Pipe Systems Analogy to electrical circuits:
Electrical circuits:  e = iR Pipe flow:  p = Q2 R( f,KL) Series path: Q = constant,  p’s are additive Parallel path:  p = constant, Q’s are additive CE 150

27 Pipe Flowrate Measurement
Orifice meter Venturi meter Rotameter Turbine and paddlewheel Nutating disk meter Bellows meter CE 150

Download ppt "California State University, Chico"

Similar presentations

Ads by Google