Characteristics of Fluid Flows

1. Characteristics of Fluid Flows Chapter 2 Henderson, Perry and Young BAE 2023 Physical Properties

2. Laminar and Turbulent Flow • Laminar: fluid flows in parallel elements, velocity remains constant but not always the same as the adjacent element • Turbulent: fluid moves in elemental swirls or eddies…velocity and direction of each element change with time BAE 2023 Physical Properties

3. Figure 2.2 BAE 2023 Physical Properties

4. Velocity is highest at the center • At surface velocity is zero • Reynolds found 4 factors affecting velocity • D V ρ and μ so (pipe dia., average V, density and dynamic viscosity of fluid) • Re = D V ρ /μ • Re< 2130….laminar • Re>4000….turbulent • 2130<Re<4000….impossible to predict exactly BAE 2023 Physical Properties

5. Can be used for other shapes by calculating the “hydraulic diameter” • Dh = 4 (area of cross section)/(wetted perimeter) • For pipe Dh = 4(πD2/4) / (πD) = D BAE 2023 Physical Properties

6. Friction Losses • Darcy F=f(L/D)V2/2g) • f is a function of the Re and relative roughness of the pipe. Table 2.2 • And moody diagram Fig 2.6 • Use either • For Re < 2130 f = 64/Re • For Re>2130 f = 0.25/(log10(ε/3.7D)+2.51/(Re f 0.5)))2 BAE 2023 Physical Properties

7. Example 2.4 pg 24 BAE 2023 Physical Properties

8. Friction loss in fittings • Follows Bernoullis equation… F = K(V2/2g) K = friction loss factor K is empirically determined Table 2-3 BAE 2023 Physical Properties

9. Friction loss in sudden enlargements in pipe • F = (V1 – V2)2 / 2g Fig 2.7 • If expansion is large….velocity 2 becomes 0 and drops from the equation above BAE 2023 Physical Properties

10. Flow of air through particles • Fixed bed of granular material….resistance is a function of • size, • shape, • surface configuration, • size distribution, • Method of placement (affects void space) BAE 2023 Physical Properties

11. Flow of air through particles • Fixed bed of granular material….resistance is a function of • size, • shape, • surface configuration, • size distribution, • Method of placement (affects void space) BAE 2023 Physical Properties

12. Flow of air through particles • Much empirical testing… • F = Δp/ϒ = f(L/Dp)(V2/2g) • (specific weight of fluid or air) • When the particles are not spheres… • Dp = 6vp/sp • particle volume and particle surface area • f = ((1 – εp)/ε3p)(300(1-εp)/(Re + 3.5) • εp= bed voidage BAE 2023 Physical Properties

13. Fluid  Air BAE 2023 Physical Properties

14. Flow of air through particles • Pressure loss • Δp/L = a V2/ln(1+bV) for clean loosely packed material • a and b are constants…see Table 2-5 • Use 1.5 for packed or dirty material • After Δp is calculated… • Bernoullis F = Δp/ϒ BAE 2023 Physical Properties

15. Flow of air through floors • Perforated floors or walls that contain products add energy loss • Floors: F = (1.071)(V/Of)2 / (ρg) see pg 29-30 • With product on the floor: • F = (1.071)(V/Ofεp)2 / (ρg) includes voidage fraction of the material BAE 2023 Physical Properties

16. Aero/Hydrodynamic Properties • Air and water are used to remove foreign material from products • How much air required depends on the drag force FD ( sum of skin friction and pressure drag) • FD affected by density, abs. viscosity, area and velocity (equation 10.1) • Reference Figure 10.1 Dr. C. L. Jones Biosystems and Ag. Engineering BAE 2023 Physical Properties

17. Figure 10.1 BAE 2023 Physical Properties

18. Aero/Hydrodynamic Properties • FD depends on the drag coefficient CD which is quantified using the Reynolds number. • NRe = Vdpρf/η Where: • V = fluid velocity • dp = particle dimension • ρf= fluid density • η = absolute viscosity • NRe<1.0, Stokes flow, FD=3πdpμV (sphere) • NRe<1,000 Laminar flow • NRe >20,000 Turbulent flow Dr. C. L. Jones Biosystems and Ag. Engineering BAE 2023 Physical Properties

19. Aero/Hydrodynamic Properties • Terminal velocity: occurs when drag force balances gravitational force • See Table 10.1 • For a sphere • Fdrag=CD(πd2/4)(ρfv2/2) • CD depends on the Reynold number of the particle: Rep= ρfvd/μ (restated from eqt. 10.1 in different terms) • If Rep<0.2, CD=24/Rep • If Rep>200,000, CD=0.44 • If Repis between 500 and 200,000, • CD=(24/Rep)(1.0 + 0.15(Rep)0.687) Dr. C. L. Jones Biosystems and Ag. Engineering BAE 2023 Physical Properties

20. Lecture 17 – Aero/Hydrodynamic Properties (Ch. 10) Dr. C. L. Jones Biosystems and Ag. Engineering BAE 2023 Physical Properties

21. Aero/Hydrodynamic Properties Read Example Problem 10.1. You will need to be familiar with it. This examples shows how to find a Reynolds number for a particle, the drag coefficient and the terminal velocity Dr. C. L. Jones Biosystems and Ag. Engineering BAE 2023 Physical Properties

22. Aero/Hydrodynamic Properties Application example: Can corn stalks be separated from corn cobs pneumatically? What minimum air velocity can be used? How well will it be separated? How could we improve the separation? Dr. C. L. Jones Biosystems and Ag. Engineering BAE 2023 Physical Properties

23. Aero/Hydrodynamic Properties Application example: A seed company would like to move soybeans through a pipe (5.25” inside diameter) pneumatically. What capacity should the air source (the fan) be rated for? Dr. C. L. Jones Biosystems and Ag. Engineering BAE 2023 Physical Properties