Key Boundary Layer Equations

1. Key Boundary Layer Equations Boundary layer thickness (m) at distance x down plate = U0 free stream vel. kinematic visco. Shear stress on plate at distance x down plate n Normal transition from Laminar to Turbulent Rough tip –induced turbulence x

2. Shear Resistance due to flow of a viscous fluid of density r and free stream vel = Uo Over a plate Length L Breath B

3. Flow in Conduits --Pipes - + Head IN from pump Note pump power Heat Loss Head OUT from Turbine Note power recovered Q discharge 0< h <1 efficiency Our concern is to calculate this term

4. The nature of Flow in Pipes

5. Development of flow in a pipe

7. We use energy Eq.—assume a = 1 (1) If we select the points [a] and [b] to be at the top of the tanks Eq. 1 Simplifies to We can not measure H BUT we can estimate the head loss hL

8. There are a number of items that contribute to the head loss hL

9. In current problem Three components for head loss

10. Minor Losses In Example problem Note form Dimensionless No X V2/2g

11. See Table 10.3 in Crowe, Elger and Robinson

12. Head loss in a pipe In this case reduces to

13. Head loss in a pipe (1) =0 by continuity Wetted perimeter Rearrange (2) (1) And (2) 

14. Head loss in a pipe Introduce a Dimensionless friction factor Then In a full circular pipe So to find head loss hL Need to find friction factor f

15. Friction Factor

16. Friction Factor Turbulent Flow

17. Friction Factor Turbulent Flow

18. Friction Factor Turbulent Flow

19. Friction Factor Turbulent Flow

20. Friction Factor Turbulent Flow

21. Friction Factor