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Fluid Mechanics > Chapter 4 > Flashcards

Chapter 4 Flashcards

1
Q

What does a field representation of a fluid flow provide?

A

The field representation provides information on the flow’s parameters such as temperature, pressure, or velocity/acceleration as a function of spatial coordinates as well as time.

Ref: Pg 112

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2
Q

What are the three components of the velocity vector?

A

u, v, and w

Ref: Pg 113

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3
Q

Give the equation for the speed of the fluid.

A

abs(V) = (u^2 + v^2 + w^2)^0.5

Ref: Pg 113

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4
Q

A change in acceleration may be due to ____.

A

Change in speed or a change in direction (or both).

Ref: Pg 113

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5
Q

Describe the Eulerian method.

A

The Eulerian method used the field concept. In this case, the fluid motion is given by completely prescribing the necessary properties (pressure, density, velocity, etc) as functions of space and time. From this method, we obtain information about the flow in terms of what happens at fixed points in space as the fluid flows through those points.

Ref: Pg 115

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6
Q

Describe the Lagrangian Method.

A

This method involves following individual fluid particles as they move about and determining how the fluid properties associated with these particles change as a function of time.

Ref: Pg 115

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7
Q

True or False

Either Eulerian or Lagrangian methods can be used to describe flow fields.

A

True

Ref: Pg 115

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8
Q

True or False
No matter how much Lagrangian information can be accumulated, you can never derive Eularian data from it (or vice versa).

A

False. If sufficient information is present you can convert between either method.

Ref: Pg 115

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9
Q

In FM, which is usually easier to use; Eulerian or Lagrangian?

A

Eulerian.

Ref: Pg 115

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10
Q

Most flow fields are ______.

A

3-D

Ref: Pg 116

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11
Q

Give the definition of “steady flow.”

A

The velocity of a fluid particle at a given point in space doesn’t vary with time.

Extra Notes: This is listed by the index as the definition but it is used in looser terms in other areas of the book.

Ref: Pg 117 (Print Version)

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12
Q

True or False

In reality, almost all fluid flows are unsteady to some degree.

A

True

Ref: Pg 117

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13
Q

What are the three general types of unsteady flow?

A
  1. Non-periodic
  2. Periodic
  3. Random

Ref: Pg 117

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14
Q

Describe turbulent flow.

A

The unsteady character of a flow is seemingly random. There is no repeatable sequence or regular variation to the unsteadiness.

Ref: Pg 117

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15
Q

Define “streamline.”

A

A streamline is a line that is everywhere tangent to the velocity vector throughout a flow field.

Ref: Pg 74 and 118 (Print Version)

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16
Q

True or False

For unsteady flow, the streamlines do not change shape.

A

False

Ref: Pg 118

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17
Q

How does one go about obtaining the information necessary to plot streamlines?

A

Streamlines can be obtained analytically by integrating the equation defining lines tangent to the velocity field.

dy/dx = v/u

Ref: Pg 118

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18
Q

Give the definition of a “streakline.”

A

A streakline consists of all particles in a flow that have previously passed through a common point.

Extra Notes: These are much more commonly used as a laboratory tool rather than an analytical tool.

Ref: Pg 119

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19
Q

True or False
If the flow is steady, each successively injected particle follows precisely behind the previous one, forming a steady streakline that is exactly the same as the streamline through the injection point.

A

True

Ref: Pg 119

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20
Q

Define “pathline.”

A

A pathline is the line traced out by a given particle as it flows from one point to another.

Ref: Pg 119

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21
Q

True or False

For unsteady flow, a pathline will directly correspond to a streamline of the same particle.

A

False, the flow must be steady for this condition to be satisfied.

Ref: Pg 119

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22
Q

True or False

Pathlines, streaklines, and streamlines are the same for steady flow.

A

True.

Ref: Pg 119

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23
Q

Accleration is the ________ for a given particle.

A

The time rate of change of velocity.

Ref: Pg 121

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24
Q

True or False

The “substantial” derivative is analogous to the “material” derivative.

A

True

Ref: Pg 122

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25
Q

The material derivative involves what two types of terms?

A

One time derivative and three spatial derivatives.

Ref: Pg 124

26
Q

What is the “local derivative?”

A

The time derivative portion of the material derivative.

Ref: Pg 124

27
Q

True or False

The acceleration field is analogous to the material derivative.

A

True

Ref: Pg 122

28
Q

The local derivative is a result of _______.

A

The unsteadiness of the flow.

Ref: Pg 124

29
Q

For steady flow, the local derivative is ___.

A

Zero.

Ref: Pg 124

30
Q

What is the convective derivative?

A

The portion of the material derivative that involves spatial derivatives.

Ref: Pg 124

31
Q

What is the “convective” acceleration component?

A

The portion of the material derivative given by the term (V dot Del)(V).

Ref: Pg 124

32
Q

Describe the streamline coordinate system.

A

The flow is described in terms of one coordinate along the streamlines (denoted s) and the second coordinate normal to the streamlines (denoted as n). Unit vectors for these two coordinates are s^ and n^ respectively.

Ref: Pg 127

33
Q

In the streamline coordinate system, the flow plane is covered by _________.

A

An orthogonal curved net of coordinate lines.

Ref: Pg 128

34
Q

What is the major advantage of using the streamline coordinate system as opposed to the cartesian coordinate system?

A

The velocity vectors are always tangent to the s direction (e.g., V = Vs^)

Ref: Pg 128 (Print Version)

35
Q

True or False

The orientation of the unit vector along the streamline changes with distance along the streamline.

A

True

Ref: Pg 129

36
Q

What is the definition of a “system” with respect to FM analysis?

A

A system is a collection of matter of fixed identity (always the same atoms or fluid particle), which may move, flow, and interact with its surroundings.

Ref: Pg 130

37
Q

What is the definition of a “control volume” with respect to FM analysis?

A

A control volume is a volume in space (a geometric entity that is independent of mass) through which the fluid may flow.

Ref: Pg 130

38
Q

True or False

A system is a specific, identifiable quantity of matter.

A

True

Ref: Pg 130

39
Q

True or False

The control volume itself is a specific geometric entity, independent of the flowing fluid.

A

True

Ref: Pg 130

40
Q

What is the “control surface.”

A

The geometric surface of the control volume.

Ref: Pg 130

41
Q

True or False

A “system” approach to a fluid mechanics problem involves Lagrangian description.

A

True

Ref: Pg 131

42
Q

True or False

A “Control Volume” approach involves the Eulerian method.

A

True

Ref: Pg 131

43
Q

All of the laws governing the motion of a fluid can be stated in their basic form in terms of ______.

A

A systems approach.

Ref: Pg 131

44
Q

How do we re-cast the governing fluid laws in a control volume setting?

A

The Reynolds Transport Theorem

45
Q

What is an “intensive property?”

A

A property of matter that is independent of mass.

Ref: Chem for Engineers 1st Ed, Rogers

46
Q

What is an “extensive property?”

A

A property of matter which is mass dependant.

Ref: Chem for Engineers 1st Ed, Rogers

47
Q

The amount of an extensive property that a system possesses at a given instant, can be determined by _________.

A

Adding up the amount associated with each fluid particle in the system.

Ref: Pg 131

48
Q

True or False
Most of the laws governing fluid motion involve the time rate of change of an extensive property of a fluid system–the rate at which the momentum of a system changes with time, the rate at which the mass of a system changes with time, and so on.

A

True

Ref: Pg 132

49
Q

In terms of the equations describing the change in the extensive properties of a system with respect to time vs. a control volume with respect to time; what is the major mathematical difference?

A

The boundary limits on the integrals. One set of bounds are for the control volume and the other is for the system.

Ref: Pg 132

50
Q

True or False

The time rate of change of a system property is a Lagrangian concept.

A

True

Ref: Pg 134

51
Q

True or False

The time derivative associated with a system will always be the same as that of a control volume.

A

False, the two can be different.

Ref: Pg 135

52
Q

For the general Reynolds transport theorem, the term on the left side of the equation has what physical interpretation?

A

The time rate of change of an arbitrary extensive parameter of a system. The parameter depends on the choice of B.

Ref: Pg 138

53
Q

For the general Reynolds transport theorem, the first term on the right-hand side of the equation has what physical interpretation?

A

The rate of change of B within the control volume as the fluid flows through it.

Extra Notes: It is B not b. This is because brhodVolume = B. The same applies to the second right hand term.

Ref: Pg 138

54
Q

For the general Reynolds transport theorem, the last term on the right-hand side of the equation has what physical interpretation?

A

This term (through a surface integral) represents the net flow rate of the parameter B across the entire control surface.

Ref: Pg 138

55
Q

Give the physical interpretation of the material derivative.

A

The material derivative provides the time rate of change of a fluid’s properties (temp, pressure, velocity, etc) associated with a particular fluid particle as it flows.

Ref: Pg 138

56
Q

What is the mathematical relationship between the Reynolds transport theorem and the material derivative?

A

The Reynolds transport theorem is the integral counterpart of the material derivative.

Ref: Pg 138

57
Q

True or False
Both the material derivative and the Reynolds transport theorem equations represent ways to transfer from the Lagrangian viewpoint to the Eulerian viewpoint.

A

True

Ref: Pg 139

58
Q

For steady effects, the Reynolds transport theorem reduces to equation 4.20 in the book. What is the physical interpretation of the integral term on the right-hand side of the equation?

A

The amount of parameter B that exists within a system is changing with time. It may be accumulating or discharging but it is not a constant.

Ref: Pg 139 (Print Version)

59
Q

True or False

The Reynolds transport theorem involves both steady and unsteady flow.

A

True

Ref: Pg 140

60
Q

What is the main difference between the fixed and moving control volumes?

A

The relative velocity, W, that carries fluid across the moving control surface, whereas it is the absolute velocity, V, that carries the fluid across the fixed control surface.

Ref: Pg 141

61
Q

The relative velocity is defined as …?

A

The difference between the absolute velocity and the velocity of the control volume.

Fluid Mechanics (7 decks)

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