Fluids- Rigid Body Motion, Flow Terminology and Continuity Flashcards
What is the gradient of the pressure profile equation for a fluid at rest?
dP/dz=-ρg
Where P is pressure
Where z-axis goes down to the bottom of the fluid
Describe how pressure varies in a fluid in free fall
The pressure is the same throughout the fluid
Define and describe isobars
They are planes of constant pressure and are always perpendicular to the resultant acceleration. An example of one is a free surface.
What is the sign convention in terms of up, down, left and right?
Up and right are positive. Others are negative.
General equation for the slope of an isobar when a fluid accelerates on a straight path to the right (possibly up or down).
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
Equations for pressure variation in each direction for an accelerating fluid (gradients)
dP/dx=-ρax
dP/dy=0
dP/dz=-ρ(g+az)
Overall equation for pressure variation in an accelerating fluid
P=P0-ρaxx-ρ(g+az)z
Where x and z are the displacements in the x and z direction
Describe what happens when a cylindrical container partially filled with a liquid is rotated about its axis with a constant ω
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.
Equations for pressure variation in a rotating cylindrical container.
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
Formula for z position of an isobar given a horizontal distance from centre of a rotation cylinder.
z=(ω^2/2g)r^2+C1
At the free surface C1 is the lowest point of free surface
Formula for expressing z position of free surface for rotating cylinder in terms of original height of free surface, h0
z=h0-(ω^2/4g)(R^2-2r^2)
What are viscous flows?
Flows in which the frictional effects are significant
What is an inviscid flow?
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.
What is internal flow?
The flow in a pipe or duct if the fluid is completely bounded by solid surfaces
What is external flow?
The flow of an unbounded fluid over a surface such as a plate, a wire or a pipe
What is incompressible flow?
If the density of the flowing fluid remains nearly constant throughout.
What is compressible flow?
If the density of fluid changes during flow
What is laminar flow?
The highly ordered fluid motion characterised by smooth layers of fluid. Typically the flow of high viscosity fluids is laminar.
What is turbulent flow?
The highly disordered fluid motion that typically occurs at high velocities and is characterised by velocity fluctuations and mixing.
What is transitional flow?
A flow that alternates between being laminar and turbulent
Differences between ideal and real flow
Ideal: incompressible, inviscid, steady
Real: compressible, viscous, unsteady
What is forced flow?
When a fluid is forced to flow over a surface or in a pipe by external means such as a pump or a fan
What is natural flow?
Fluid motion due to natural means. Example is the buoyancy effect where warmer fluid rises above cooler fluid.
Name some steady-flow devices
Turbines, compressors, boilers, condensers, heat exchangers. They all operate for long periods of time under the same conditions
What does a profile plot indicate?
How the value of a scalar property varies along some desired direction in the flow field
What determines whether a flow is one, two or three dimensional?
Whether the flow varies in one, two or three dimensions significantly compared to the other dimensions
What is a vector plot?
An array of arrows indicating the magnitude and direction of a vector property at an instant in time.
Is the average airflow over a bullet 1, 2 or 3 dimensional?
2 because the velocity doesn’t vary with the angle around the bullet.
What is a steamline?
A curve that is everywhere tangent to the instantaneous local velocity vector.
What is a streamtube?
A bundle of streamlines
What are pathlines?
The actual path travelled by an individual fluid particle over some time period.
What are streaklines?
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.
When are streaklines, streamlines and pathlines identical?
In steady flow
What is a timeline?
A set of adjacent fluid particles that were marked at the same (earlier) instant in time. Look like waves in a box from above
When is volume conserved?
During incompressible flow
Continuity equation for a single stream
ρ1V1A1=ρ2V2A2
