1. Key Boundary Layer Equations Normal transition from Laminar to Turbulent x Boundary layer thickness (m) at distance x down plate = Shear stress on plate at distance x down plate U 0 free stream vel. kinematic visco. Rough tip –induced turbulence

2. Shear Resistance due to flow of a viscous fluid of density  and free stream vel = U o Over a plate Length L Breath B

3. Flow in Conduits --Pipes + - Head IN from pump Note pump power Head OUT from Turbine Note power recovered Q discharge 0<  <1 efficiency Heat Loss 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  = 1 If we select the points [a] and [b] to be at the top of the tanks Eq. 1 Simplifies to (1) We can not measure H BUT we can estimate the head loss h L

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

9. In current problem Three components for head loss

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

11. See Table 10.3 in Crowe, Elger and Robinson

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

13. =0 by continuity Rearrange (1) (2) Wetted perimeter (1) And (2) 

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

15. Friction Factor

16. Friction Factor Turbulent Flow

21. Friction Factor