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Incompressible Flow > Potential Flow > Flashcards

Potential Flow Flashcards

1
Q

Are potential flows limited by non-linear terms in their derivations?

A

No

Ref: Frank White, Ch8, Pg 521

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2
Q

What is an adverse pressure gradient?

A

When the pressure starts to increase.

Ref: Frank White, Ch8, Pg 522

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3
Q

True or False

If viscous effects are neglected, low speed flows are [irrotational] and the velocity potential [exists].

A

Both are true.

Ref: Frank White, Ch8, Pg 522

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4
Q

What are all the conditions needed to use the stream function?

A
  1. Steady
  2. Incompressible
  3. 2D
  4. Satisfy the continuity equation

Ref: Munsen Pg 213 (physical copy)

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5
Q

Lines along which the stream function is constant are called?

A

Streamlines.

Ref: Munsen Pg 214 (physical copy)

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6
Q

The change in the value of psi is related to ______.

A

The volume rate of flow [q].

Ref: Munsen Pg 215 (physical copy)

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7
Q

True or False

In a flow defined by a stream function, the flow can cross streamlines?

A

False. Flow never crosses streamlines because by definition the velocity is tangent to the streamline.

Ref: Munsen Pg 215 (physical copy)

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8
Q

The volume rate of flow [q] between two streamlines is defined as…

A

q = psi_2 - psi_1

Ref: Munsen Pg 225

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9
Q

The stream function is a consequence of ______, whereas the velocity potential is a consequence of _______.

A

Conservation of mass
irrationality of the flow field

Ref: Munsen Pg 225 (physical copy)

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10
Q

For an incompressible fluid the divergence is ____.

A

Zero.

Ref: Munsen Pg 225 (physical copy)

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11
Q

The laplacian of any velocity potential must be ____.

A

Zero

Ref: Munsen Pg 225 (physical copy)

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12
Q

What flow characteristics are governed by the Laplace Equation?

A
  1. Inviscid
  2. incompressible
  3. Irrotational

Ref: Munsen Pg 225 (physical copy)

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13
Q

True or False

If vorticity is present, a flow field cannot be described by the Laplace Equation.

A

True

Ref: Munsen Pg 225 (physical copy)

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14
Q

If a flow is irrotational, the curl will be _____.

A

Zero.

Ref: White, Ch8, Pg 256

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15
Q

Lines of constant phi are called the _____ of the flow.

A

Potential Lines.

Ref: White, Ch8, Pg 256

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16
Q

True or False
Stream Function is 2D only.
Velocity Potential can be 3D.

A

Both are true

Ref: White, Ch8, Pg 257

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17
Q

Lines of constant phi and psi are ______.

A

Orthogonal.

Ref: White, Ch8, Pg 257

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18
Q

If the continuity equation reduces to Laplace’s equation for an arbitrary velocity potential function, then the momentum equation will reduce to ______.

A

Bernoulli’s Equation.

Ref: White, Ch8, Pg 522

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19
Q

For a line source or sink at the origin, is there any circumferential velocity?

A

No

Ref: White, Ch8, Pg 525

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20
Q

The radial outflow for a source or sink is defined as…

A

m = Q/(2pib) where Q if the volumetric flow rate and b is the length of the sink.

Ref: White, Ch8, Pg 525

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21
Q

A double is formed by?

A

Putting a source and sink at the origin.

Ref: Munsen, Pg 235 (physical copy)

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22
Q

True or False

Streamlines can cross at a stagnation point?

A

True

Ref: White Pg 528

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23
Q

True or False

A source or sink creates no circulation.

A

True

Ref: White Pg 531

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24
Q

What is a “favorable” pressure gradient?

A

Pressure decreases along a surface.

Ref: White Pg 532

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25
Q

True or False

The Rankine half-body is not found in a real fluid because of boundary layer separation.

A

True

Ref: White Pg 532

26
Q

What is the formula for the maximum surface speed on a Rankine half oval?

A

umax=U*1.26

Ref: White Pg 528

27
Q

What is the formula for the maximum surface speed on a Rankine Oval?

A

umax=1.74U

Ref: White Pg 538

28
Q

What potential flows are needed to model flow past a circular cylinder with circulation.

A
  1. Uniform Stream
  2. Doublet
  3. Vortex

Ref: White Pg 539

29
Q

What is the Magnus-Robins force?

A

For a cylinder in a uniform flow with circulation, there tends to be an inviscid downward lift normal to the free stream.

Ref: White Pg 540

30
Q

The drag on a cylinder with circulation in inviscid flow has ____ drag.

A

Zero

Ref: White Pg 541

31
Q

State the full KJ lift theory.

A

According to inviscid theory, the lift per unit depth of any cylinder of any shape immersed in a uniform stream equals the density times the upstream velocity times the circulation. Where the circulation is the total net circulation contained within the body shape. The direction of the lift is ninety degrees from the stream direction, rotating opposite to the circulation.

Ref: White Pg 541

32
Q

What is the value of circulation about any closed path that does not enclose the origin?

A

Zero. The key word is “closed.”

Ref: White Solutions manual Problem 8.12

33
Q

If the flow is steady, the acceleration is ________.

A

Convective.

Ref: White Solutions Manual Problem 8.13.

34
Q

For a Rankine half body, does the point of max acceleration occur before or after the point of maximum velocity?

A

Before

Ref: White Solutions Manual Problem 8.13

35
Q

Where does the maximum pressure lie in a vortex?

A

At the origin (r = 0)

Ref: White Solutions Manual Problem 8.14

36
Q

On a Rankine 1/2 oval; at the point on the upper surface where the velocity is equal to the free stream, what is the pressure?

A

The free stream pressure.

Ref: White Solutions Manual Problem 8.17

37
Q

What are the units for the strength of both a vortex and source/sink?

A

m^2/s

Ref: White Solutions Manual

38
Q

For a Rankine oval, where is the maximum velocity found?

A

Theta = 90 (top and bottom of the oval)

Ref: White Solutions Manual

39
Q

For a cylinder in a uniform free stream that is not rotating, where is the lowest pressure?

A

The top and bottom of the cylinder. (Theta = 90, 270)

Ref: White Solutions Manual

40
Q

For a cylinder rotating in a uniform flow, as the circulation (Gamma) increases, how is the velocity on the top and bottom of the cylinder change?

A

On top it gets slower and on the bottom it gets faster.

Ref: White Pg. 539

41
Q

Euler’s’ Equations of motion apply to an ____ flow field.

A

Inviscid.

Ref: Munsen, Pg. 220 (physical copy)

42
Q

What is the definition of vorticity?

A

The curl of the velocity. (Del X V).

Ref: Munsen, Pg. 222 (physical copy)

43
Q

For an inviscid fluid, the are no _____ stresses. The only forces acting on a fluid element is _____, and _______.

A

Shear
Weight
Pressure

Ref: Munsen, Pg. 223 (physical copy)

44
Q

True or False

The BE can be applied between any tow points in a rotational flow field.

A

False, the flow must be irrotational.

Ref: Munsen, Pg. 224 (physical copy)

45
Q

True or False

If the curl of the vector field for a certain flow is not zero, the velocity potential exists.

A

False, the curl of the velocity field gives the vorticity. If the vorticity is not zero (irrotational flow) then the flow is rotational and the velocity potential (phi) does not exist.

Ref: Munsen, Pg. 224 (physical copy)

46
Q

How can the velocity vector for a given flow field be expressed in terms of a velocity potential? What condition(s) must apply?

A

> V = Del(phi)
Irrotational Flow

Ref: Munsen, Pg. 225 (physical copy)

47
Q

True or False

For a 3-D problem, either a velocity potential or stream function can be used.

A

False, a stream function is restricted to two dimensional flows. A velocity potential can be used for either 2 or 3D flows.

Ref: Munsen, Pg. 225 (physical copy)

48
Q

Give the general definition of a potential flow.

A

Inviscid, incompressible, irrotational flow fields that conform to the Laplace Equation.

Ref: Munsen, Pg. 225 (physical copy)

49
Q

True or False

The velocity potential can be applied to both steady and unsteady flow.

A

True.

Ref: Munsen, Pg. 225 (physical copy)

50
Q

True or False

If vorticity is present, a flow cannot be described by the Laplace Equation.

A

True

Ref: Munsen, Pg. 225 (physical copy)

51
Q

Two lines are orthogonal if the products of their slopes is ____.

A

Negative one.

Ref: Munsen, Pg. 228 (physical copy)

52
Q

Give the velocity potential and stream function for uniform flow in the x-direction.

A 
Phi = Ux
Psi = Uy

Ref: Equation Sheet

53
Q

Give the velocity potential and stream function for a source/sink.

A 
Phi = m*ln(r)
Psi = m*theta

Ref: Equation Sheet

54
Q

Give the velocity potential and stream function for a point vortex.

A 
Phi = K*theta
Psi = -K*ln(r)

Ref: Equation Sheet

55
Q

Give the appropriate potential function combinations to crate a Rankine half body. State the stream function.

A

A uniform stream in the x direction and a source.

Psi = Ursin(theta) + m*theta

Ref: Equation Sheet

56
Q

Give the appropriate potential function combinations to crate a Doublet. State the stream function.

A

A source sink pair at the origin.

Psi = -K*sin(theta)/r

Ref: Munsen Pg. 235 (physical copy)

57
Q

Give the appropriate potential function combinations to crate a Rankine Oval. State the stream function.

A

A source sink pair aligned parallel to a uniform stream.

Psi = Ursin(theta) + m*(theta1 + theta2)

Ref: White Pg 537

58
Q

Give the appropriate potential function combinations to crate flow around a non-rotating cylinder. Give the stream function for flow around a non-rotating cylinder.

A

A doublet and a uniform flow.

Psi = Usin(theta)(r - a^2/r)

Ref: White Pg 539

59
Q

Give the definition of circulation applied to a rotating cylinder.

A

Gamma = 2piK

Ref: White Pg 539

60
Q

Give the appropriate potential function combinations to crate flow around a rotating cylinder. Give the stream function for flow around a rotating cylinder.

A

A uniform stream plus a doublet plus a vortex of strength K.

Psi = Usin(theta)(r - a^2/r) - K*ln(r/a)

Ref: White Pg 539

61
Q

Give the formula for the stagnation points for a rotating cylinder in a uniform flow.

A

sin(theta_stag) = K / (2Ua)

Ref: White Pg 539

Incompressible Flow (6 decks)

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