1. Characteristics of Fluid Flows Chapter 2 Henderson, Perry and Young BAE 2023 Physical Properties1

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 Properties2

3. Figure 2.2 BAE 2023 Physical Properties3

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 Properties4

5. Can be used for other shapes by calculating the “hydraulic diameter” D h = 4 (area of cross section)/(wetted perimeter) For pipe D h = 4(πD 2 /4) / (πD) = D BAE 2023 Physical Properties5

6. Friction Losses DarcyF=f(L/D)V 2 /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/(log 10 (ε/3.7D)+2.51/(Re f 0.5 ))) 2 BAE 2023 Physical Properties6

7. Example 2.4 pg 24 BAE 2023 Physical Properties7

8. Friction loss in fittings Follows Bernoullis equation… F = K(V 2 /2g)K = friction loss factor K is empirically determined Table 2-3 BAE 2023 Physical Properties8

9. Friction loss in sudden enlargements in pipe F = (V 1 – V 2 ) 2 / 2gFig 2.7 If expansion is large….velocity 2 becomes 0 and drops from the equation above BAE 2023 Physical Properties9

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 Properties10

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 Properties11

12. Flow of air through particles Much empirical testing… –F = Δp/ ϒ = f(L/D p )(V 2 /2g) (specific weight of fluid or air) –When the particles are not spheres… D p = 6v p /s p –particle volume and particle surface area –f = ((1 – ε p )/ε 3 p )(300(1-ε p )/(Re + 3.5) ε p = bed voidage BAE 2023 Physical Properties12

13. Fluid  Air BAE 2023 Physical Properties13

14. Flow of air through particles Pressure loss –Δp/L = a V 2 /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 Properties14

15. Flow of air through floors Perforated floors or walls that contain products add energy loss Floors: F = (1.071)(V/O f ) 2 / (ρg) see pg 29-30 With product on the floor: –F = (1.071)(V/O f ε p ) 2 / (ρg) includes voidage fraction of the material BAE 2023 Physical Properties15

16. BAE 2023 Physical Properties16 Dr. C. L. Jones Biosystems and Ag. Engineering Air and water are used to remove foreign material from products How much air required depends on the drag force F D ( sum of skin friction and pressure drag) F D affected by density, abs. viscosity, area and velocity (equation 10.1) Reference Figure 10.1 Aero/Hydrodynamic Properties

17. BAE 2023 Physical Properties17 Figure 10.1

18. BAE 2023 Physical Properties18 Dr. C. L. Jones Biosystems and Ag. Engineering F D depends on the drag coefficient C D which is quantified using the Reynolds number. N Re = Vd p ρ f /ηWhere: »V = fluid velocity »d p = particle dimension »ρ f = fluid density »η = absolute viscosity N Re <1.0, Stokes flow, F D =3πd p μV (sphere) N Re <1,000 Laminar flow N Re >20,000 Turbulent flow Aero/Hydrodynamic Properties

19. BAE 2023 Physical Properties19 Dr. C. L. Jones Biosystems and Ag. Engineering Terminal velocity: occurs when drag force balances gravitational force See Table 10.1 For a sphere –F drag =C D (πd 2 /4)(ρ f v 2 /2) C D depends on the Reynold number of the particle: Re p = ρ f vd/μ (restated from eqt. 10.1 in different terms) If Re p <0.2, C D =24/Re p If Re p >200,000, C D =0.44 If Re p is between 500 and 200,000, C D =(24/Re p )(1.0 + 0.15(Re p ) 0.687 ) Aero/Hydrodynamic Properties

20. BAE 2023 Physical Properties20 Dr. C. L. Jones Biosystems and Ag. Engineering Lecture 17 – Aero/Hydrodynamic Properties (Ch. 10)

21. BAE 2023 Physical Properties21 Dr. C. L. Jones Biosystems and Ag. Engineering 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 Aero/Hydrodynamic Properties

22. BAE 2023 Physical Properties22 Dr. C. L. Jones Biosystems and Ag. Engineering 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? Aero/Hydrodynamic Properties

23. BAE 2023 Physical Properties23 Dr. C. L. Jones Biosystems and Ag. Engineering 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? Aero/Hydrodynamic Properties