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gas dynamics > CH7: Eq. of Frictionless Flow > Flashcards

CH7: Eq. of Frictionless Flow Flashcards

1
Q

Nonviscous or inviscid flow requires the absence of what two phenomena?

A

The flow must be:
1. Frictionless
2. Non-conducting (no currents)

Elements of GD, Roshko, Pg. 178

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2
Q

True or False
Vorticity cannot exist in one-dimensional flow.

A

True.

Elements of GD, Roshko, Pg. 178

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3
Q

Stress is a tensor of ______ order.

A

2nd

Elements of GD, Roshko, Pg. 179

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4
Q

A vector is a tensor of ______ order.

A

First.

Elements of GD, Roshko, Pg. 179

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5
Q

Differentiation of a tensor yields a tensor of _______ order.

A

one higher

Elements of GD, Roshko, Pg. 179

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6
Q

True or False
The gradient of a scaler quantity yields a vector.

A

True.

Elements of GD, Roshko, Pg. 179

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7
Q

True or False
The gradient of a vector is a tensor of third order.

A

False. The gradient of a vector yields a tensor of second order. Differentiation yields a result of one order higher.

Elements of GD, Roshko, Pg. 179

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8
Q

Divergence of a vector is a ________.

A

Scaler.

Elements of GD, Roshko, Pg. 180

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9
Q

Give the mathematical definition of divergence.

A

Grad dot (x) where x is an arbitrary vector.

The result is a scaler.

Elements of GD, Roshko, Pg. 180

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10
Q

State Gauss’ theorem from vector calculus.

A

For any volume V in a vector field b, the normal component (b dot n), integrated over the enclosing surface area A, is equal to the divergence (grad dot b), integrated over the volume.

Elements of GD, Roshko, Pg. 180

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11
Q

What is the physical principle upon which the continuity equation is derived?

A

The flux of matter through a fixed control surface is constant.

Elements of GD, Roshko, Pg. 180

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12
Q

In deriving the continuity equation, the surface area A must be __________.

A

Closed.

Elements of GD, Roshko, Pg. 180

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13
Q

In deriving the continuity equation, the component of velocity which carries matter through the surface is defined by _________.

Hint: What is the mathematical expression that defines the component that travels normal to the surface.

A

u dot n

Where:
u = the velocity vector
n = the unit normal to the surface

Elements of GD, Roshko, Pg. 180

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14
Q

In the continuity equation, the non-stationary term is due to ____________________.

Hint: Non-stationary implies time dependant or unsteady term(s).

A

The fact that the fluid density in the control volume changes if the flow is non-stationary.

Elements of GD, Roshko, Pg. 181

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15
Q

What is the convective term’s physical significance in the continuity equation?

A

This term expresses the fact that the flow carries mass into and out of the control volume.

Extra Notes: The fluid which flows into and out of the control volume transports not only mass but also various characteristics associated with the fluid, such as momentum, energy, entropy, etc.

Elements of GD, Roshko, Pg. 181 - 182

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16
Q

What is the primary use of gauss’s theorem in deriving the equations of motion?

A

Gauss’s theorem is used to rewrite surface integrals as volume integrals.

This is helpful because using control volumes to derive the equations is relatively straightforward.

Elements of GD, Roshko, Pg. 182

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17
Q

True or False
By the momentum equation, the net force acting on the fluid in the control volume is equal to the rate of change in momentum of the fluid in the control volume.

A

True

Elements of GD, Roshko, Pg. 182

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18
Q

True or False
Under steady conditions, momentum cannot accumulate in a control volume.

A

True.

Elements of GD, Roshko, Pg. 183

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19
Q

What are the two kinds of forces involved in the derivation of the momentum equation?

A

Surface and volume forces.

Elements of GD, Roshko, Pg. 183

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20
Q

In general, the surface forces are due to _______________.

A

Whatever medium is adjacent to the surface area, for example, a solid wall or simply the adjacent fluid.

Elements of GD, Roshko, Pg. 183

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21
Q

In a non-viscous flow, what is the only possible surface force?

A

Normal Pressure forces.

Elements of GD, Roshko, Pg. 183

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22
Q

True or False
In non-viscous flow, there are tangential forces adjacent to a surface that accompany normal pressure forces.

A

False. There are only normal pressure forces in non-viscous flow.

Elements of GD, Roshko, Pg. 183

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23
Q

Give some examples of volume or body forces?

A
  1. Inertial forces
  2. Gravitational forces
  3. Electromagnetic forces

Elements of GD, Roshko, Pg. 183

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24
Q

Body forces are proportional to _____.

A

Mass

Elements of GD, Roshko, Pg. 183

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25
Q

The energy law, applied to a given fluid in a control volume can be expressed as ________ + _________ = ___________.

A

heat added + work done on the fluid = increase in energy

Elements of GD, Roshko, Pg. 185

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26
Q

For a flowing fluid through a control volume the rate of change of energy can be written as ___________ + ____________ = __________.

A

Rate of heat addition + rate of work done on the fluid = rate of increase in energy of the fluid.

Elements of GD, Roshko, Pg. 186

27
Q

What symbol denotes the rate of heat addition per unit mass?

A

q

Elements of GD, Roshko, Pg. 186

28
Q

True or False
The heat addition per unit mass (q) only includes the heat that is added externally and is not already latent in the fluid.

A

True

Elements of GD, Roshko, Pg. 186

29
Q

True or False
The heat released by a transformation of the fluid is not included in q, but heat absorbed from external radiation is included.

A

True

Elements of GD, Roshko, Pg. 186

30
Q

The heat addition per unit mass (q) is a _______ term, and does not include heat that is transferred by _________ from one part of the fluid to the other.

A

Volume
Conduction

Elements of GD, Roshko, Pg. 186

31
Q

Heat that is transferred by conduction from one part of the fluid to the other is a ______ term.

A

Surface

Elements of GD, Roshko, Pg. 186

32
Q

The rate of work on the fluid is due to the _______ forces and _______.

A

volume
pressure (surface)

Note: For inviscid flow, only pressure forces are present.

Elements of GD, Roshko, Pg. 186

33
Q

The rate at which the energy is changing inside a control volume has a ________ and a _________ part.

A

non-stationary (unsteady time dependant)
convective

Elements of GD, Roshko, Pg. 186

34
Q

True or False
Any characteristic or property associated with the fluid may be expressed as a field.

A

True

Elements of GD, Roshko, Pg. 186

35
Q

According to the Eulerian derivative, the rate of change of any characteristic for a particle fluid is due to two effects. What are these two effects?

A

Convective and nonstationary effects (unsteady time dependant effects)

Elements of GD, Roshko, Pg. 187

36
Q

Euler’s equation is by definition, equivalent to the differential ___________ equation.

A

Momentum

Elements of GD, Roshko, Pg. 188

37
Q

Whenever an extensive property such as the momentum per unit volume is associated with an intensive property such as the velocity, the continuity equation may be ___________.

A

Subtracted out.

Elements of GD, Roshko, Pg. 188

38
Q

For a conservative system, the kinetic energy is interchangeable with _______________.

A

Work due to pressure (surface) and body forces.

Elements of GD, Roshko, Pg. 189

39
Q

For an inviscid flow in chemical equilibrium, if there is no heat addition (q = 0), the changes in the state of the fluid particles are _____________.

A

Isentropic

Elements of GD, Roshko, Pg. 189

40
Q

True or False
With regard to the energy equation, the effect of friction and conduction is to create dissipation terms which are always negative.

A

False, dissipation terms are always positive because they contribute to entropy production.

Elements of GD, Roshko, Pg. 189

41
Q

In steady flow particle paths coincide with _____________.

A

Streamlines

Elements of GD, Roshko, Pg. 190

42
Q

In steady flow, entropy along streamlines is __________.

A

Constant

Elements of GD, Roshko, Pg. 190

43
Q

For steady adiabatic flow, the total enthalpy is the same at all ______________ of a streamline.

A

Equilibrium sections

Elements of GD, Roshko, Pg. 190

44
Q

Both entropy and total enthalpy are conserved along streamlines, provided what conditions are met?

A

The flow is steady, and it is also frictionless, non-conducting, and adiabatic (isentropic).

Elements of GD, Roshko, Pg. 191

45
Q

What is the natural coordinate system?

A

A coordinate system in which one coordinate lies along a streamline and the other coordinate is orthogonal to the streamline.

Elements of GD, Roshko, Pg. 191

46
Q

True or False
In the natural coordinate system, the coordinates are said to be curvilinear.

A

True

Elements of GD, Roshko, Pg. 191

47
Q

What is a stream tube?

A

A region in a flow which is bounded by two streamlines.

Elements of GD, Roshko, Pg. 191 & 192

48
Q

What is shown by Crocco’s Theorem?

A

How entropy varies normal to streamlines.

Elements of GD, Roshko, Pg. 193

49
Q

If entropy is the same on different streamlines, the flow is said to be ____________ throughout.

A

Isentropic

Elements of GD, Roshko, Pg. 193

50
Q

True or False
A flow in which the entropy on different streamlines is the same must be frictionless.

A

True.

Elements of GD, Roshko, Pg. 193

51
Q

Vorticity is directly related to the ____________ across streamlines.

A

entropy gradient

Elements of GD, Roshko, Pg. 193

52
Q

Zero vorticity implies uniform _________ provided h0 is uniform.

A

entropy

Elements of GD, Roshko, Pg. 193

53
Q

What is the equation that relates vorticity with angular velocity?

A

zeta = 2*omega

Where:
zeta = vorticity
omega = angular velocity

Elements of GD, Roshko, Pg. 195

54
Q

True or False
In general, there are two components of vorticity.

A

False. There are three.

Elements of GD, Roshko, Pg. 195

55
Q

A flow is irrotational only if ________ are zero.

A

All three components of vorticity.

Elements of GD, Roshko, Pg. 196

56
Q

Irrotational flow is also called _______ flow.

A

Potential

Elements of GD, Roshko, Pg. 197

57
Q

True or False
According to Crocco’s theorem, adiabatic, irrotational flows are non-isentropic.

A

False, they are Isentropic.

Elements of GD, Roshko, Pg. 197

58
Q

True or False
All potential flows will satisfy the Laplace Equation.

A

True.

Elements of GD, Roshko, Pg. 199

59
Q

For a perfect gas, vorticity is a measure of the variation of ___________________.

A

Stagnation pressure across streamlines.

Recall that stagnation pressure is directly related to the change in entropy (or the entropy gradient).

Chapter 7 lectures slides, Pg 13

60
Q

Vorticity is a _______ order tensor.

A

2nd

Chapter 7 lecture slides, Pg 17

61
Q

True or False
Circulation is a scaler.

A

True

Chapter 7 lecture slides, Pg 17

62
Q

Use of the ____________ theorem allows circulation to be related to 3D vorticity.

A

Stokes

Chapter 7 lecture slides, Pg 17

63
Q

True or False
Vorticity is considered a pseudo vector.

A

True.

Chapter 7 lecture slides, Pg 18

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