ME 310 Chap.10 External Flow: Boundary Layers, Lift and Drag
External Flow: Boundary Layers, Lift and Drag
Closing a question from week one
In an early lecture the course sets up a water droplet falling through air, uses it to show every part of the force balance, and leaves the calculation until drag can be predicted. External flow provides that piece.
The first homework solutions add that the drag coefficient is often close to one for objects as different as an airplane and a golf ball, so a first estimate is possible before looking up an exact value.
Lift and drag
The force of a fluid on an immersed body splits into drag along the oncoming flow and lift across it, each written as a coefficient times dynamic pressure times a reference area.
Drag has two sources: shear on the surface, friction drag, and the pressure difference between front and wake, pressure drag. Streamlined shapes minimise the second; thin plates aligned with the flow minimise the first.
Boundary layers
Because of no slip, viscosity matters in a thin layer next to the surface even at high Reynolds number.
On a flat plate the laminar layer thickens with the square root of distance and usually becomes turbulent once the local Reynolds number reaches a few hundred thousand.
The syllabus lists momentum integral analysis here: a control-volume balance across the layer that, with an assumed profile shape, estimates thickness and wall shear closely.
Separation and the drag crisis
Behind the widest point of a body, pressure rises along the surface and slow fluid near the wall can reverse, separating the layer and leaving a low-pressure wake.
Turbulent layers resist separation better, which is why a rough or dimpled sphere can have lower drag than a smooth one at the same speed.
Very slow flow
At Reynolds numbers below about one, inertia is negligible and drag on a sphere is proportional to speed, giving settling speeds of fine particles and droplets directly.
Estimating before looking up
For a bluff body, set the drag coefficient to one and compute half density times speed squared times frontal area.
The result is usually within a factor of two or three of the true drag and shows immediately whether the force is newtons or kilonewtons.
What this chapter covers
- 01
Lift and drag coefficients
- 02
Friction drag and pressure drag
- 03
Laminar boundary-layer growth
- 04
Transition to a turbulent boundary layer
- 05
Momentum integral estimates
- 06
Separation, wakes and streamlining
- 07
Stokes drag on small spheres
Worked example · free
Terminal speed of a skydiver
- 2At terminal speed drag balances weight: ½ρV²(C_D A) = mg; buoyancy in air is negligible.
- 2V² = 2mg / (ρ C_D A) = 2 × 80 × 9.81 / (1.2 × 0.50) = 2616 m²/s².
- 1V = 51 m/s, about 184 km/h.
- 1Check the regime: Re is of order 10⁶, consistent with a drag coefficient of order one.
Key terms
- Boundary Layer
- A boundary layer is the thin region next to a surface where viscous effects slow the flow from the free-stream speed to zero at the wall.
- Drag Coefficient
- The drag coefficient is drag force divided by dynamic pressure times a reference area.
- Flow Separation
- Flow separation is the detachment of a boundary layer from a surface when it cannot advance against a rising pressure.
- Pressure Drag
- Pressure drag is the part of drag caused by the pressure difference between the front of a body and its wake.
External Flow: Boundary Layers, Lift and Drag FAQ
Why does a golf ball have dimples?
Dimples make the boundary layer turbulent earlier. A turbulent layer stays attached further around the ball, the wake narrows, and pressure drag falls, which outweighs the small increase in friction drag.
When can I use the Stokes drag law?
Only when the Reynolds number based on the sphere diameter is below about one, meaning very small, slow or viscous cases such as fine sediment in water or mist droplets. Compute Re after solving to confirm the assumption held.
What is the difference between friction drag and pressure drag?
Friction drag is shear stress integrated over the wetted surface; pressure drag is the net force from higher pressure at the front than in the wake. Streamlining reduces the second at the cost of slightly more of the first.
Why does a laminar boundary layer grow with the square root of distance?
Viscous diffusion spreads the influence of the wall a distance proportional to the square root of time, and a particle moving at the free-stream speed spends a time proportional to distance travelled, so thickness grows with the square root of distance from the leading edge.
Exam move
Every drag answer ends with a Reynolds-number check; practise stating whether the drag law you used was allowed.
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