Fluids- Rigid Body Motion, Flow Terminology and Continuity

Question 1

What is the gradient of the pressure profile equation for a fluid at rest?

Answer 1

dP/dz=-ρg
Where P is pressure
Where z-axis goes down to the bottom of the fluid

Question 2

Describe how pressure varies in a fluid in free fall

Answer 2

The pressure is the same throughout the fluid

Question 3

Define and describe isobars

Answer 3

They are planes of constant pressure and are always perpendicular to the resultant acceleration. An example of one is a free surface.

Question 4

What is the sign convention in terms of up, down, left and right?

Answer 4

Up and right are positive. Others are negative.

Question 5

General equation for the slope of an isobar when a fluid accelerates on a straight path to the right (possibly up or down).

Answer 5

dz/dx= -ax/(g+az)=-tanθ
x and z after a is subscript
ax is acceleration horizontally
az is acceleration vertically
θ is angle between free surface and horizontal

Question 6

Equations for pressure variation in each direction for an accelerating fluid (gradients)

Answer 6

dP/dx=-ρax
dP/dy=0
dP/dz=-ρ(g+az)

Question 7

Overall equation for pressure variation in an accelerating fluid

Answer 7

P=P0-ρaxx-ρ(g+az)z

Where x and z are the displacements in the x and z direction

Question 8

Describe what happens when a cylindrical container partially filled with a liquid is rotated about its axis with a constant ω

Answer 8

After some time, the liquid moves as a rigid body together with the container. Every fluid particle moves with the same angular velocity so there’s is no relative motion and no shear stress. The free surface formed is in the shape of a dome.

Question 9

Equations for pressure variation in a rotating cylindrical container.

Answer 9

dP/dθ=0
dP/dz=-ρg
dP/dr=ρrω^2
dP=ρrω^2dr-ρgdz
Where r is the horizontal distance from centre to the point in question
Use curly ds for dP/dr and dP/dz and dP/dθ

Question 10

Formula for z position of an isobar given a horizontal distance from centre of a rotation cylinder.

Answer 10

z=(ω^2/2g)r^2+C1

At the free surface C1 is the lowest point of free surface

Question 11

Formula for expressing z position of free surface for rotating cylinder in terms of original height of free surface, h0

Answer 11

z=h0-(ω^2/4g)(R^2-2r^2)

Question 12

What are viscous flows?

Answer 12

Flows in which the frictional effects are significant

Question 13

What is an inviscid flow?

Answer 13

Flows in regions where viscous forces are negligibly small compared to the inertial or pressure forces for practical interest. Often these regions are not close to solid surfaces.

Question 14

What is internal flow?

Answer 14

The flow in a pipe or duct if the fluid is completely bounded by solid surfaces

Question 15

What is external flow?

Answer 15

The flow of an unbounded fluid over a surface such as a plate, a wire or a pipe

Question 16

What is incompressible flow?

Answer 16

If the density of the flowing fluid remains nearly constant throughout.

Question 17

What is compressible flow?

Answer 17

If the density of fluid changes during flow

Question 18

What is laminar flow?

Answer 18

The highly ordered fluid motion characterised by smooth layers of fluid. Typically the flow of high viscosity fluids is laminar.

Question 19

What is turbulent flow?

Answer 19

The highly disordered fluid motion that typically occurs at high velocities and is characterised by velocity fluctuations and mixing.

Question 20

What is transitional flow?

Answer 20

A flow that alternates between being laminar and turbulent

Question 21

Differences between ideal and real flow

Answer 21

Ideal: incompressible, inviscid, steady
Real: compressible, viscous, unsteady

Question 22

What is forced flow?

Answer 22

When a fluid is forced to flow over a surface or in a pipe by external means such as a pump or a fan

Question 23

What is natural flow?

Answer 23

Fluid motion due to natural means. Example is the buoyancy effect where warmer fluid rises above cooler fluid.

Question 24

Name some steady-flow devices

Answer 24

Turbines, compressors, boilers, condensers, heat exchangers. They all operate for long periods of time under the same conditions

Question 25

What does a profile plot indicate?

Answer 25

How the value of a scalar property varies along some desired direction in the flow field

Question 26

What determines whether a flow is one, two or three dimensional?

Answer 26

Whether the flow varies in one, two or three dimensions significantly compared to the other dimensions

Question 27

What is a vector plot?

Answer 27

An array of arrows indicating the magnitude and direction of a vector property at an instant in time.

Question 28

Is the average airflow over a bullet 1, 2 or 3 dimensional?

Answer 28

2 because the velocity doesn’t vary with the angle around the bullet.

Question 29

What is a steamline?

Answer 29

A curve that is everywhere tangent to the instantaneous local velocity vector.

Question 30

What is a streamtube?

Answer 30

A bundle of streamlines

Question 31

What are pathlines?

Answer 31

The actual path travelled by an individual fluid particle over some time period.

Question 32

What are streaklines?

Answer 32

The locus of fluid particles that have passed sequentially through a prescribed point in the flow. Most common flow pattern generated in a physical experiment.

Question 33

When are streaklines, streamlines and pathlines identical?

Answer 33

In steady flow

Question 34

What is a timeline?

Answer 34

A set of adjacent fluid particles that were marked at the same (earlier) instant in time. Look like waves in a box from above

Question 35

When is volume conserved?

Answer 35

During incompressible flow

Question 36

Continuity equation for a single stream

Answer 36

ρ1V1A1=ρ2V2A2