Chapter 4 Flashcards
What does a field representation of a fluid flow provide?
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
What are the three components of the velocity vector?
u, v, and w
Ref: Pg 113
Give the equation for the speed of the fluid.
abs(V) = (u^2 + v^2 + w^2)^0.5
Ref: Pg 113
A change in acceleration may be due to ____.
Change in speed or a change in direction (or both).
Ref: Pg 113
Describe the Eulerian method.
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
Describe the Lagrangian Method.
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
True or False
Either Eulerian or Lagrangian methods can be used to describe flow fields.
True
Ref: Pg 115
True or False
No matter how much Lagrangian information can be accumulated, you can never derive Eularian data from it (or vice versa).
False. If sufficient information is present you can convert between either method.
Ref: Pg 115
In FM, which is usually easier to use; Eulerian or Lagrangian?
Eulerian.
Ref: Pg 115
Most flow fields are ______.
3-D
Ref: Pg 116
Give the definition of “steady flow.”
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)
True or False
In reality, almost all fluid flows are unsteady to some degree.
True
Ref: Pg 117
What are the three general types of unsteady flow?
- Non-periodic
- Periodic
- Random
Ref: Pg 117
Describe turbulent flow.
The unsteady character of a flow is seemingly random. There is no repeatable sequence or regular variation to the unsteadiness.
Ref: Pg 117
Define “streamline.”
A streamline is a line that is everywhere tangent to the velocity vector throughout a flow field.
Ref: Pg 74 and 118 (Print Version)
True or False
For unsteady flow, the streamlines do not change shape.
False
Ref: Pg 118
How does one go about obtaining the information necessary to plot streamlines?
Streamlines can be obtained analytically by integrating the equation defining lines tangent to the velocity field.
dy/dx = v/u
Ref: Pg 118
Give the definition of a “streakline.”
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
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.
True
Ref: Pg 119
Define “pathline.”
A pathline is the line traced out by a given particle as it flows from one point to another.
Ref: Pg 119
True or False
For unsteady flow, a pathline will directly correspond to a streamline of the same particle.
False, the flow must be steady for this condition to be satisfied.
Ref: Pg 119
True or False
Pathlines, streaklines, and streamlines are the same for steady flow.
True.
Ref: Pg 119
Accleration is the ________ for a given particle.
The time rate of change of velocity.
Ref: Pg 121
True or False
The “substantial” derivative is analogous to the “material” derivative.
True
Ref: Pg 122
The material derivative involves what two types of terms?
One time derivative and three spatial derivatives.
Ref: Pg 124
What is the “local derivative?”
The time derivative portion of the material derivative.
Ref: Pg 124
True or False
The acceleration field is analogous to the material derivative.
True
Ref: Pg 122
The local derivative is a result of _______.
The unsteadiness of the flow.
Ref: Pg 124
For steady flow, the local derivative is ___.
Zero.
Ref: Pg 124
What is the convective derivative?
The portion of the material derivative that involves spatial derivatives.
Ref: Pg 124
What is the “convective” acceleration component?
The portion of the material derivative given by the term (V dot Del)(V).
Ref: Pg 124
Describe the streamline coordinate system.
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
In the streamline coordinate system, the flow plane is covered by _________.
An orthogonal curved net of coordinate lines.
Ref: Pg 128
What is the major advantage of using the streamline coordinate system as opposed to the cartesian coordinate system?
The velocity vectors are always tangent to the s direction (e.g., V = Vs^)
Ref: Pg 128 (Print Version)
True or False
The orientation of the unit vector along the streamline changes with distance along the streamline.
True
Ref: Pg 129
What is the definition of a “system” with respect to FM analysis?
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
What is the definition of a “control volume” with respect to FM analysis?
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
True or False
A system is a specific, identifiable quantity of matter.
True
Ref: Pg 130
True or False
The control volume itself is a specific geometric entity, independent of the flowing fluid.
True
Ref: Pg 130
What is the “control surface.”
The geometric surface of the control volume.
Ref: Pg 130
True or False
A “system” approach to a fluid mechanics problem involves Lagrangian description.
True
Ref: Pg 131
True or False
A “Control Volume” approach involves the Eulerian method.
True
Ref: Pg 131
All of the laws governing the motion of a fluid can be stated in their basic form in terms of ______.
A systems approach.
Ref: Pg 131
How do we re-cast the governing fluid laws in a control volume setting?
The Reynolds Transport Theorem
What is an “intensive property?”
A property of matter that is independent of mass.
Ref: Chem for Engineers 1st Ed, Rogers
What is an “extensive property?”
A property of matter which is mass dependant.
Ref: Chem for Engineers 1st Ed, Rogers
The amount of an extensive property that a system possesses at a given instant, can be determined by _________.
Adding up the amount associated with each fluid particle in the system.
Ref: Pg 131
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.
True
Ref: Pg 132
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?
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
True or False
The time rate of change of a system property is a Lagrangian concept.
True
Ref: Pg 134
True or False
The time derivative associated with a system will always be the same as that of a control volume.
False, the two can be different.
Ref: Pg 135
For the general Reynolds transport theorem, the term on the left side of the equation has what physical interpretation?
The time rate of change of an arbitrary extensive parameter of a system. The parameter depends on the choice of B.
Ref: Pg 138
For the general Reynolds transport theorem, the first term on the right-hand side of the equation has what physical interpretation?
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
For the general Reynolds transport theorem, the last term on the right-hand side of the equation has what physical interpretation?
This term (through a surface integral) represents the net flow rate of the parameter B across the entire control surface.
Ref: Pg 138
Give the physical interpretation of the material derivative.
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
What is the mathematical relationship between the Reynolds transport theorem and the material derivative?
The Reynolds transport theorem is the integral counterpart of the material derivative.
Ref: Pg 138
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.
True
Ref: Pg 139
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?
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)
True or False
The Reynolds transport theorem involves both steady and unsteady flow.
True
Ref: Pg 140
What is the main difference between the fixed and moving control volumes?
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
The relative velocity is defined as …?
The difference between the absolute velocity and the velocity of the control volume.
