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EXAMS January 2022 > VFF equations > Flashcards

VFF equations Flashcards

1
Q

What is the material derivitave?

A

-

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2
Q

Express the velocity gradient tensor in terms of the rate of strain tensor and the rate of rotation tensor.

A

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3
Q

How does the rate of rotation tensor relate to the vorticity?

A

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4
Q

What is the continuity equation (differential form) for compressible fluids?

A

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5
Q

What is the continuity equation (differential and integral form) for incompressible fluids?

A

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6
Q

How is the stress related to the stress tensor?

A

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7
Q

What is Cauchy’s equation?

A

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8
Q

What is the constitutive equation for a newtonian fluid?

A

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9
Q

What is a newtonian fluid?

A

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10
Q

How is the kinematic viscosity related to the dynamic viscosity?

A

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11
Q

What are the units of the dynamic viscosity?

A

kg m^-1 s^-1

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12
Q

What are the Navier-Stokes equations?

A

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13
Q

What are the kinematic and dynamic free surface boundary conditions?

A

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14
Q

What is the reynolds number?

A

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15
Q

What is the definition of the streamfunction?

A

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16
Q

How can velocities be obtained from the streamfunction (cartesian)?

A

-

17
Q

How is the stream function related to the vorticity?

A

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18
Q

What form is the CF of a constant coefficients ODE with real and equal roots?

A

(A+Bx)e^(lambda x)

19
Q

What form is the CF of an Euler ODE with real and equal roots?

A

Aln(x) x^(lambda) + B x^(Lambda)

20
Q

What is the form of the CF of an Euler ODE with complex roots?

A

-

21
Q

What is the form of the CF of a constant coefficients ODE with complex roots?

A

-

22
Q

How is the shear rate related to the rate of strain tensor?

What about the extensional rate of strain?

A

-

23
Q

In which direction is traction exerted?

A

exerted onto the fluid

24
Q

What form of ansatz should we use for a periodically varying problem?

A

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25
Q

What form of ansatz should we use for a similarity solution?

A

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26
Q

When can a linearity and homogeneity argument be made?

A

-

27
Q

What are the parallel flow equations (cartesian)?

A

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28
Q

What are the units of the streamfunction?

A

-

29
Q

What are the units of the vorticity?

A

-

30
Q

What are the units of force?

A

-

31
Q

What is the form of the non-dimensional N-S?

A

Everything dimensionless but the material derivative has the reynolds number as its coefficient.

32
Q

In what case can we use the stokes equations?

What are they?

A

-

33
Q

How could we prove the relationship between the cartesian velocity components and the streamfunction?

A

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34
Q

How is the vorticity related to the velocity?

A

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EXAMS January 2022 (7 decks)

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