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Fluid Mechanics > Chapter Summaries > Flashcards

Chapter Summaries Flashcards

1
Q

What is a vortex?

A

A coherent motion of fluid particles around some common axis

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2
Q

What is rotational and irrotational flow?

A

Rotational flow is a flow where the fluid particles rotate around their individual axes, irrotational is the converse

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3
Q

Is a solid body vortex rotational?

A

yes

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4
Q

Is a potential vortex rotational?

A

No, except on axis

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5
Q

What is circulation?

A

An integral measure of the velocity or the vorticity field connected by Stokes theorem

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6
Q

What are vortex lines?

A

Integral curves of vorticity field

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7
Q

What is the Biot-Sarvat Law?

A

It allows us to compute the velocity at an arbritrary pint induced by a simply connected path of vorticity

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8
Q

What do the velocities in a straight vortex tube depend on?

A

We obtain rotationally symmetric velocities that depend inversely proportionally on the normal distance and on the two aspect angles

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9
Q

What do induced velocities in an infinite straight vortex tube depend on?

A

Only inversely proportionally on the normal distance

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10
Q

What is a general vortex sheet?

A

An infinite or finite arrangement of infinite or finite parallel straight or curved potential vortices

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11
Q

What are the properties of velocities for an infinite vortex sheet?

A

The velocities above and below are uniform and have a jump across

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12
Q

What is the mirror principle?

A

The mirror principle serve to generate suitable streamlines /surfaces as models for walls in inviscid flows

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13
Q

How can vorticity be produced and destroyed?

A

By positive or negative vortex stretching and by baroclinic production

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14
Q

What is Prandtl’s hypothesis?

A

Prandtl’s hypothesis enables to split flow domain into potential flow and boundary layer

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15
Q

What is potential flow?

A

Potential flow is a flow whose velocity field is irrotational and thus can be generated by a gradient of scalar potential functions

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16
Q

What is the superposition principle?

A

The superposition principle arises from linearity of the Laplace equation and allows to generate new potentials from summation of potentials

17
Q

Where does the normal derivative of potentials vanish?

A

At impermeable walls

18
Q

For what kind of Flows is the Bernoulli equation valid?

A

For potential flows with irrotational velocity (except at isolated singularities), constant density, and volume forces with potential with a unique Bernoulli constant for the entire field

19
Q

How is the divergence free condition satisfied?

A

By using the streamfunction

20
Q

What is the volume flux between two streamlines equal to?

A

The difference in respective stream functions at iso level

21
Q

What is a property of streamlines and Equipotential lines?

A

They are orthogonal to one another except at singularities

22
Q

What is a property of conformal mapping?

A

It is angle preserving

23
Q

What do real and imaginary parts of complex potential represent?

A

Real part is potential function, imaginary part is stream function

24
Q

How can complex vorticity be derived from complex potential?

A

By taking the first derivative

25
Q

What are the components of complex circulation?

A

Real part is circulation, imaginary part is volume flux along closed integration part

26
Q

What is parallel flow characterized by?

A

Velocity vectors of constant direction and magnitude

27
Q

What is source / sink flow characterized by?

A

Velocity vectors pointing radially from / into origin with magnitude decaying inversely proportionally to distance

28
Q

What is potential vortex flow characterized by?

A

Velocity vectors pointing tangentially to circumcircles around the origin with magnitude decaying inversely proportionally to distance

29
Q

How does a dipole flow occur?

A

From the distinguished limit of superimposing source and sink where their strength increases inversely proportionally to their distance

30
Q

What does a wedge flow represent?

A

A wedge flow can represent a whole range of interior/ exterior flows in and around corners, limit cases are flat plate and sharp tip

31
Q

What do free stream and source result in?

A

An open body to compensate for the source volume flux rate which is fed into the body

32
Q

How can a body be closed?

A

By adding a sink of equal and opposite strength

33
Q

What is constructed using superposition of dipole and parallel flow?

A

A potential flow around an infinitely long straight cylinder with circular cross section

34
Q

What is the Kutta-Joukowski theorem?

A

The resulting force in a 2D potential flow around a closed body is proportional to circulation, density and incoming velocity

35
Q

What is the Joukowski map?

A

It maps a circle onto a flat plate

36
Q

Are potential flow solutions around closed bodies unique?

A

No

37
Q
A

Fluid Mechanics (6 decks)

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