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

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

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 T2 – c m T1) is the net heat gained

Conservation of Momentum

(A1 u1 Δt) (ρu1) / Δt = A1 u12 ρ = Momentum / sec

Force = (A2 u22 – A1 u1

2)ρ = m• (u2 – u1)

Viscosity – Flow between two parallel plates

Shear Stress = Force / Area = τ = µ (∂u / ∂y)

µ = Dynamic Viscosity

v = µ / ρ = Kinetic Viscosity Diffusivity

Turbulence

Reynolds Number = R = u D / v, D = pipe diameter

R > 2300 Turbulent

Turbulence increases heat transfer

Friction in Pipe Flow

f‘ = 4f = pipe friction coefficients

Pipe Roughness parameter ξ

Friction coefficient f for pipe flow

From graphFrom Table

Lift and Drag Forces

Power Coefficient Versus Tip Speed

Axial Force on Wind Turbines

Actuator Disc – Bernoulli's Principle

neglecting changes

in ρ and z

Static Pressure Difference = Dynamic Pressure Difference

Axial Forces

Axial Forces

Torque

Blade Element Theory – Stream Tube Theory