18. Review of Fluid Dynamics
 Air is virtually incompressible for V <100 m/s
 Conservation of Energy – Bernoulli's Equation
 Conservation of Momentum
 Viscosity
 Turbulence
 Friction in Pipe Flow
 Lift and Drag Forces – Fluid & Turbine Machinery

19. Conservation of Energy
P.E. lost + W.D. by Pressure Forces = Gain in K.E. + Frictional Losses

20. Bernoulli's Equation (Frictionless fluid)
Or (Head of fluid)
Ideal Fluid – Zero Viscosity, Thermal Conductivity & Compressibility
When power Pth is added to the fluid and Q= Au (volume
flow rate) and (c m T – c m T ) is the net heat gained

21. Conservation of Momentum
(A1 u1 Δt) (ρu1) / Δt = A1 u1
2
ρ = Momentum / sec
Force = (A2 u2
2
– A1 u1
2
)ρ = m•
(u2 – u1)

22. Viscosity – Flow between two parallel plates
Shear Stress = Force / Area = τ = µ (∂u / ∂y)
µ = Dynamic Viscosity
v = µ / ρ = Kinetic Viscosity Diffusivity

23. Turbulence
Reynolds Number = R = u D / v, D = pipe diameter
R > 2300 Turbulent
Turbulence increases heat transfer

24. Friction in Pipe Flow
f‘ = 4f = pipe friction coefficients
Pipe Roughness parameter ξ

25. Friction coefficient f for pipe flow

26. From graph
From
Table

27. Lift and Drag Forces

28. Power Coefficient Versus Tip Speed

29. Axial Force on Wind Turbines
Actuator Disc – Bernoulli's Principle
neglecting changes
in ρ and z

30. Axial Forces

32. Axial Forces

33. Torque

37. Blade Element Theory – Stream Tube Theory