| Describe what happens when an ideal fluid moves past a straight smooth solid boundary | Fluid velocity is unaffected by presence of boundary.
Mutual force between fluid and solid is normal to surface.
Drag is zero. |
| Describe what happens when a real fluid moves past a straight smooth solid boundary | Fluid adjacent to boundary is brought to rest (relative to boundary).
Large velocity gradient exists in a thin layer of fluid near boundary, in which velocity increases from zero to free stream velocity, U.
Large velocity gradient means shear stress plays a significant role in BL. Shear stress gives rise to drag force on boundary. |
| Describe the pressure changes across a flat smooth boundary layer. | Since BL is thin, velocity components normal to surface are very small, hence pressure changes across BL are negligible (for flat, smooth surface, not cylinders). |
| Describe the pressure changes across a curved surface, e.g. cylinder. | If the BL is curved, streamline curvature will cause velocity gradients. |
| Describe the thickness of the BL. | As velocity in BL approaches free stream aymptotically, there is no definite thickness of BL.
BL does not have a uniform thickness, but develops in direction of main stream flow.
Nominal thickness is defined, e.g. limit definted as point where when u=0.99u0 |
| Why are BLs important? | BLs influence drag on surface and mass and heat transfer rates.
BLs in velocity gradients can be thought of as analogous to temperature gradients and concentration gradients.
The 3 BL types are distinct from one another.
If physical properties remain constant, then velocity BL will be unaffected by temp & conc BLs. |
| Describe the boundary layer on a flat plate | BL starts with zero thickness at leading edge.
BL increases in downstream direction.
Near leading edge, flow is laminar in BL.
Thickness of BL increases more in turbulent area.
Flow is all BLs begins as laminar, then goes through transition area where large eddies are formed, then develops into turbulent.
All BLs become turbulent if surface is sufficiently long. |
| Describe skin friction in laminar flow | Skin friction is the viscous drag on a surface.
It is proportional to the velocity gradient in the BL evaluated at the surface. |
| What is Inviscid flow? | These are areas of flow where viscous effects are negligible (inviscid assumption or irrotational flow region).
Flow is inviscid/irrotational in regions where velocity has not yet diffused. |
| What are properties of stream functions? | curves of constant Ψ are streamlines of the flow.
Streamlines are tangent to velocity field.
At steady steady: streamlines approx equal path lines.
Difference in value of Ψ from one streamline to another is equal to the volume flow rate per unit width between the two streamlines. |
| What are the conditions of velocity potential? | Must be a solution of laplace equation.
Satisfy boundary conditions (inviscid flow assumption), such as no flux through solid surfaces, uniform flow away from objects.
Flow is determined by kinermatics only, Euler equations are a constraint on the pressure required for the flow.
Can be used for uniform flows, flow around objects (cylinders) or flow around corners. |
| How do real fluids behave at the surface? | No slip conditions at surface, viscous effects generate shear at the surface. |
| What does the thickness, δ, of BL depend on? | Displacement thickness
Momentum thickness
Energy thickness |
| What is displacement thickness? | Displacement thickness is the distance the wall must be placed to keep the same flow rate as the inviscid flow. |
| What is momentum thickness? | Thickness such that rho * u0 *Θ^2 is a direct measure of momentum lost through viscous effects. |
| What are the assumptions for momentum applied to BL? (this is used for deriving force equation) | Steady state flow.
Density constant.
No pressure gradient in flow direction (only for flat plates, not cylinders). |
| What are the two dimensionless coefficients? | Skin friction coefficient, Cf.
Drag coefficient, Cd. |
| What are the BL boundary conditions at y=0? | No slip at boundary surface (u=0).
Shear stress at boundary must be finite (differential is finite).
Equation of motion satisfied (double differential =0). |
| What are the BL boundary conditions at outer edge, y=δ? | No discontinuinity of velocity profile (u=u0).
No "kink" in velocity profile (differential=0).
For smooth transitions, need double differential=0. |
| What are the steps to calculate BL thickness, force, shear stress, etc? | Check BCs.
Get δ* and Θ in terms of δ.
Get δ.
Apply to required parameter. |
| What is the multilayer model? | Multilayer model is an extension of the adaptations made with the viscous sub-layer.
Approximate analysis of turbulent BL made with power law and laminar sub-layer inclusion (however still oversimplified).
Investigate turbulent velocity profile in immediate vicinity of laminar sub-layer (u=δ'). |
| What are the implications of a rough boundary? | Calculations studied assume boundary is smooth.
If boundary is rough, viscous sub-layer becomes disrupted.
If roughness elements are large enough, they completely break up the laminar sub-layer. |
