Section 1: Fluid flow, boundary layers, velocity profiles, drag (Reynolds number) Flashcards
SI base units of density
ρ= kg m-3
SI base unit of velocity
u= m s-1
SI base unit of acceleration
a= m s-1
Newton’s first law of motion
Unless a force acts on a body, its velocity will not change. If F = 0 then Du = 0 provides an intuitive meaning of force: a force is that agent which changes the velocity of a body
Newton’s second law of motion
The rate of change of momentum (mu) of a body, is proportional to the force that acts on it
F = m*a Force = mass x acceleration
Newton’s third law of motion
For any force exerted, there is an equal force in the opposite direction
SI base unit of viscosity
μ= kg m-1 s-1
Common method for observation of fluid dynamics
Smoke generation in air
Dye injection into water and other fluids
Define streamlines
A line that is tangential to the instantaneous velocity direction
At anyone point its tangential to the path
Fluid does not cross this line and streamlines cannot cross
Define pathlines
The trajectory or path of a given fluid particle
A record of the path a fluid particle has take (its history)
Pathlines may intersect since different particles may follow different paths at different times
Define streaklines
A streakline is the instantaneous locus or trace of all the fluid particles that pass through a given fixed point in space.
If we injected dye continuously from a fixed point – the dye would form a streakline as it passed down stream
Streaklines cannot intersect because two particles cannot occupy the same space at the same instant
What occurs to the lines of movement in steady flow
When velocity is not changing with time (steady flow) then streamlines, pathlines and streaklines are identical
Define timelines
A time line is the instantaneous location of a line of fluid particles in the flow usually the initial formed line is perpendicular to the flow boundary
Deformed timelines
If one end of the line is ahead of the other, fluid is moving faster
Changes in shape of the line tells use about relative changes in velocity
Define streamtube
A streamtube is an imaginary tube whose walls are streamlines. It may be envisaged as a bundle of streamlines
The boundary of the stream tube can’t be crossed
Just as streamlines cannot cross so the boundary of the streamtube cannot be crossed
Outside streamlines form duct boundary
Key features to form turbulence
Disorder (irreproducible in detail)
Efficient mixing
Vorticity (irregularly distributed in 3 dimensions) - eddies on varies scales included
What is turbulence ‘energy cascade’
Largest eddies have biggest kinetic energy
Continuous but irregular
Progressively decay into smaller eddies until ‘smeared out’ by viscosity
Energy reflects size of the system
Forces dominant in a high Reynolds number world
Inertial forces are dominant
Forces dominant in a low Reynolds number world
Viscous forces dominant
When velocity doesn’t change, what distribution will the flow be
Uniform flow will have a parabolic velocity distribution
Stress in Laminar flow
Viscous shear stress is transmitted through the fluid
Stress in Turbulent flow
Turbulent shear stress dominates
Define boundary layer
region of fluid next to the boundary across which the velocity of the fluid grades from that of the boundary to that of the unaffected part of the flow
Define free stream
Unaffected part of the flow
