### Characteristics of External Flow

• Define external flow and contrast it with internal flow.

• Explain the difference between developing flow and fully-developed flow.

• Understand qualitatively how external flow around objects affects drag and will be able to calculate drag forces and terminal velocities.

• Solve simple engineering problems involving the effects of External (open) flows on bodies of various shapes.

• Apply laminar and turbulent flow concepts to external flows.

• The stagnation point is the point where the free stream flow divides itself.

• The fluid at the body takes the velocity of the body (no-slip condition).

• A boundary layer is formed at the upper and lower surface of the airfoil.

• The flow in the boundary layer is initially laminar and the transition to turbulence takes place at downstream of the stagnation point, depending on the free stream conditions.

• The turbulent boundary layer grows more rapidly than the laminar layer, thus thickening the boundary layer on the body surface. So, the flow experiences a thicker body compared to original one.

• In the region of increasing pressure (adverse pressure gradient), the flow separation may occur. The fluid inside the boundary layer forms a viscous wake behind the separated points.

### Solved Example:

#### 64-1-01

The displacement thickness is:

### Solved Example:

#### 64-1-02

A streamlined body in which: (DSSSB AE Civil Sept 2021)

The velocity distribution in a turbulent boundary layer is given by: $\dfrac{u}{ \cup } = {\left( {\dfrac{y}{\delta }} \right)^{\dfrac{1}{7}}}$ What is the displacement thickness $\delta^*$? (ISRO Scientist ME 2014)