Question

In the flow around a cylinder, boundary layer separation occurs due to (SELECT CORRECT ANSWER)

	energy losses in the boundary layer that prevent it from remaining attached.
	the Mach number being too high
	the surface being rough
	a low buoyancy force.

A boundary layer is

	a) a region of flow close to a surface where viscous effects dominate the physics of the flow.
	b) a region of flow that has high turbulence.
	c) important in providing a slip condition at the wall.
	d) increases the velocity of the flow towards the wall

Two flows may be classified as having dynamic similarity if

	a) both cases have equal drag force
	b) both geometries and key dimensionless parameters (i.e. Reynolds numbers) are the same.
	c) both velocities of the flow are the same.
	d) both cases have identical geometry but different size.

Answer 1

Solution:

1)

Separation takes place due to excessive momentum loss near the wall in a boundary layer trying to move downstream against increasing pressure, i.e., , which is called adverse pressure gradient.

So long as no viscous effect is considered, the situation does not cause any sensation.
In the viscid region (near the solid boundary),

1. Up to , the viscous force opposes the combined pressure force and the force due to acceleration. Fluid particles overcome this viscous resistance due to continuous conversion of pressure force into kinetic energy.

2. Beyond , within the viscous zone, the flow structure becomes different. It is seen that the force due to acceleration is opposed by both the viscous force and pressure force.

Depending upon the magnitude of adverse pressure gradient, somewhere around , the fluid particles, in the boundary layer are separated from the wall and driven in the upstream direction. Therefore the correct option would be energy losses in the boundary layer that prevent it from remaining attached as pressure energy doesn't get converted in the required Kinetic Energy to hold the flow stable and attached.

2)

Boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. Therefore the correct option is A, a region of flow close to a surface where viscous effects dominate the physics of the flow

3)

Dynamic similarity is the phenomenon that when there are two geometrically similar vessels (same shape, different sizes) with the same boundary conditions (e.g., no-slip, center-line velocity) and the same Reynolds and Womersley numbers, then the fluid flows will be identical. Therefore the correct answer is b) both geometries and key dimensionless parameters (i.e. Reynolds numbers) are the same.

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