Quiz 3

Question 1

what are the 4 assumptions that must be made to use Bernoulli’s Equation?

Answer 1

The flow is:

1) steady

2)Incompressible

3)Inviscid

4) The flow occurs along a streamline

Question 2

When is Bernoulli’s equation valid between any two points, and not just along any streamline?

Answer 2

When the flow is irrotational

Question 3

If the coefficient of pressure is equal to 1 (Cp = 1), What is this indicative of?

Answer 3

There exist a stagnation point. Also, 1 is the highest possible value that can exist for a pressure coefficient

Question 4

What is the dilatation rate?

Answer 4

Rate at which the volume of the fluid changes. It is the divergence of the fluid’s velocity vector

Question 5

What does it mean when the differential Operator is squared? (D^2)

Answer 5

This is the Laplacian Operator, which is defined as the divergence of a gradient of a scalar

Question 6

What Principle allows one to combine several solutions to Laplace’s Equations to generate yet another solution?

Answer 6

Superposition

Question 7

Why would it be useful to define (V) in terms of velocity potential or of the stream function?

Answer 7

We would have to use the Laplacian to simplify the velocity equation to one equation and one unknown

Question 8

Write the continuity equation in terms of a stream function

Answer 8

See image(If asked for the velocity potential, change psi to phi)

Question 9

What conditions exist for source flow?

Answer 9

All streamlines are perfectly straight that eliminate from a singular, central point. in other words, incompressible flow is physically possible everywhere except the origin. Furthermore, source flow is irrotational at every point.

Question 10

What is the circulation of a source flow?(A Number)

Answer 10

Naught(0).

Question 11

What is Sink?

Answer 11

Exist when all streamlines are perfectly straight lines that head towards a singular, central point. Like Source flow, incompressible flow is physically possible everywhere except the origin. Furthermore, source flow is irrotational at every point

Question 12

What does capital lambda,(Upside down V), represent in aerodynamics?

Answer 12

The source strength, which is the rate of volume flow per unit depth

Question 13

When does the Rankine oval form?

Answer 13

when there is a uniform, source and sink present flow present at the same time. ( A closed body will form)

Question 14

In the shown stream function, label the terms indicative of uniform flow and the terms indicative of source and sink flow.

Answer 14

See Image

Question 15

Describe doublet flow

Answer 15

Occurs when a source for flow and sink for are spaced out by distance of zilch. The source and the sink are on top of each other. Note that kappa is the doublet strength

Question 16

Define Vortex Flow

Answer 16

A flow where the velocities along any given circular streamline are constant, but the velocities vary from streamline to streamline and they vary intensely with the distance from the common center. Note, velocities only vary circumferentially and not radially

Question 17

In the shown stream function, label the terms indicative of uniform flow and terms of doublet flow.

Answer 17

See Image

Question 18

Write out the stream function for Vortex Flow

Answer 18

See Image

Question 19

On a stationary Cylinder placed in a fluid flow that is inviscid, where do the two stagnation points exist?

Answer 19

Stagnations points exist at the leading edge of the cylinder and at the trailing edge of the cylinder

Question 20

Imagine a cylinder starts to spin. What happens to the stagnation points on the cylinder?

Answer 20

The stagnation points will move toward one another when the cylinder starts to spin. Once they coincide, the stagnation points separate vertically, even jumping off the cylinder’s edge.

Question 21

When the cylinder is stationary and placed in an inviscid fluid flow, how long can the pressure coefficient go to?

Answer 21

The lowest pressure coefficient value would be -3

Question 22

Under what parameters can the pressure coefficient go lower than-3?

Answer 22

If and only if the cylinder is rotating.(The pressure will Never exceed a maximum of 1)

Question 23

In the diagram describe the phenomenons

Answer 23

a. Creeping Flow is happening here. This occurs between Reynold’s Numbers of 0-4

b. We witness a standing vortex, and these occur between Reynold’s numbers of 4-40.

c. We observe a Von Karman Vortex Street, which occurs betwixt Re values of 40-100000

d. Laminar Boundary Layer flow separation occurs here, on Re values of about 100000.

e. Turbulent Boundary Layer flow separation occurs, and this occurs above RE values of 3x10^5

Question 24

when a cylinder is placed in laminar (subcritical) flow, what does the pressure distribution on the cylinder look like?

Answer 24

the pressure distribution( which is always acting perpendicular and onto a surface) is at a maximum at the leading edge of a cylinder, and then it starts to decrease, to the point that at 90 at 270 degrees, the pressure is at a minimum. Due to the flow separation, the recovers little to no pressure

Question 25

when a cylinder is placed in a Turbulent (supercritical) flow, what does the pressure distribution on the cylinder look like?

Answer 25

At a maximum at the leading edge of the cylinder, and then it starts to decrease, to the point at 90 at 270 degrees, the pressure is at a minimum. It starts t climb back up, recovering a noticeable fraction of the pressure loss, but due to flow separation, the pressure will not fully recover by the instance where the flow reaches the trailing edge of the cylinder

Question 26

Why is there a greater pressure recovery as flow passes over a cylinder for turbulent flows as opposed to laminar flows?

Answer 26

According to the velocity profiles, the velocity of the turbulent flow is greater than that of a laminar flow as the flow gets closer to the wall. As a result, there is a higher momentum for the turbulent flow.

Question 27

This recovery in pressure for turbulent and laminar flows impacts a certain aerodynamic value. What is the value, and how is the value impacted?

Answer 27

the Reynolds numbers are affected. When compared with laminar flow, the drag coefficient is higher because not as much pressure was recovered

Question 28

What is the Kutta-Joukowski-Theorem useful for?

Answer 28

Relating lift to circulation

Question 29

Write out the Kutta-Joukowski theorem.

Answer 29

see image

Question 30

Write out stream function for vortex flow.

Answer 30

See Image