midterm 2 Flashcards
what is conservation of angular momentum
mass x radius squared x angular velocity
universal rule: angular momentum must be conserved
if r decreases then angular velocity must increase
velocity varies inversely with radius. Each bit of fluid mass has the same angular momentum
How do vortieces form?
involve shearing of concentric rings of fluild
at low Re, viscous forces dominate, so vortices hace large rotational cores
shear streams of viscous fluid past one another requires energy
absence of energy this gets disipated into heat…
What dominates life at low Reynolds numbers?
viscous forces
If Reynolds number is bery low what happens to fluid touching hairs
viscosity will go up and will be lodged in hairs and other fluid will go around it
Increasing Reynolds number for «1 to ~10 what happens
intertial forces > viscous forces stagnent fluid dislodged and fluid flows between hairs
Scallop theorem
At high Re, dreag (Fd) is proportional to v^2 x time (Fi= pSv^2)
At low RE (RE<1), Fd proportional to v x time (Fv= u(v/l) * S)
An organism with only 1 articulation cannot travel when Re«1, since the swimming motion will always repeat itself in reverse: flows are completely reversible- so motion is too!
How to travel at low Re
use non time-reversible mechanisms for locomotion
eg: flagellum
corkscrew motion
Drag
drag refers to those forces acting opposite to the relative motion of any obgject moving with respect to a surrounding fluid
D’Alambert’s Paradox
an object in a steady fluid flow will experience zero drag
what is Inviscid flow and what it total energy along streamline in it
no loss of energy to friction
total energy along streamlines = constant
this is reasoning for Dlamberts paradox, which is incorrect due to viscosity actually being a thing
An object in a steady fluid flow must experience
drag! But how and where does this drag arise?
viscosity in most of the fluid can be ignored but the thin layer near the object (boundary layer) you need to consider as viscosity is having a large affect (no slip condition due to shearing)
viscosity important but only on a very local field
What does adverse pressure gradient do in a viscid boundary layer
it causes reversal of flow at the bottom of the boundary layer
Separation of flow
Profoundl implications of fluid dynamics
dramatically inc the drag on an object by producing a diff in pressure around the object= pressure drag
separation of flow doesn’t have to be turbulent
Frictional drag
occurs tangential to the surface of the object( ie opposite to the direction of fluid sheering)
Occurs as a direct result of the viscosity of the fluid
Pressure drag
s normal to the
surface of the object. Occurs as an
indirect result of the viscosity of the
fluid reducing the momentum of the
fluid, leading to flow separation
Quantifying drag
Friction drag
arises due to the shearing of fluid in the boundary layer adjacent to the surface
friction drag directly proportional to velocity(c):
friction drag= u(v/l)*S
Pressure drag
the push exerted…
Drag force vs velocity
Higher the velocity 4 fold more drag
How do we normalize the fluid flow conditions on the x axis
use renolds number. htis ratio combines densty, velocity, viscosity, and length one dimensionlss variable. Saves making multiole graphs
How do we normalize the measurement Fd on he y axis?
Convert Fd to another dimensonless coefficent: the coefficient of drag (Cd)
coefficient of drag
reference area
S= reference are of the object
generally just the projected foward-facing area (for high drag bodies) eg for a shpere S= pir^2 and not 1/2 of 4pir^2
its different reference for object/ shape
reference area
S= reference are of the object
generally just the projected forward-facing area (for high drag bodies) eg for a sphere S= pir^2 and not 1/2 of 4pir^2
its different reference for object/ shape
Cd with pressure drag only
What is the universal rule of conservation and continuity laws
In a closed system, mass, momentum (i.e, mass x velocity), and energy must be the same over time, i.e conserved
Potential energy
PE= mass x gravity x height
Kinetic energy
KE= 1/2mass x velocity^2
What happens in a pendulum
it converts Potential energy into kinetic energy and vise versa. With no friction total energy = sum of PE and KE
What energy is in a fluid? moving fluids?
-potential energy (mgh)
-Kinetic energy (1/2mv^2)
-Pressure energy (Px volume)
moving fluids:
PE (pgh)
KE (1/2pv^2)
Pressure energy (Px volume/ volume (static pressure)
Bernoulli’s theorem
describes how total energy of a moving fluid is equal to the sum of the pressure, potential and kinetic energies
- total fluid energy= potential +dynamic +static energy = constant
= P+ pgh + 1/2pv^2
To use Bernoulli’s to determine how different components of a fluids energy must change to satisfy the law of conservation of energy in a moving fluid, you must make some simplifying assumptions about the fluid, what are they?
- flow is inviscid (moves without drag/friction)
- flow is incompressible (low velocity)
- flow is constant (volume/time)
-flow is laminar (no turnulence)
flow rate
m^3/s= Cs area (m^2) x velocity (m/s)
Law of continuity
Volume of fluid passing through each pipe segment per unit time (volume/time ie m^3/s) is the same
The velocity of the fluid as it passes through each pipe segment (distance moved/time ) is different
As CS are decreases the velocity of the fluid increases
fluid velocity inversely proportional to CS (S)
What is true about fluid in a pipe in a real world example (viscid)
energy loss to friction causes the pressure in the pipe to fall along its length.
Fluid in the pipe flows down a pressure(energy) gradient
work must be done on the fluid to keep it moving
The Hagen-Poiseuille equation
relates the rate of laminar flow through a pipe to the pressure gradient driving the flow, the viscosity of the fluid, and the radius and length of the pipe
Q= change of pressure(Pa) * pi * r4/ L* 8* fluid dynamic viscosity (Pa*S)
how does a manometer measure pressure
when pressure is applied to one side of the manometer, the fluid inside will flow, changing in height (h) until the pressure exerted by the raised column of fluid is equal to the applied pressure
can be calculated using relationship between density (rho) gravity(g) and heigh (h) of the fluid column
Reference for gauge pressure is? which means
Atmospheric pressure
gauge pressure can be negative
Patm+Pgauge = Pabs
Reference for absolute pressure is ?
a complete vacuum
P=0
Venturi meter
measures the velocity of a fluid by passing it from a tube with a large cross-sectional area into a constriction (smaller cross-sectional area). A manometer filled with liquid is placed with one arm connected to the large tube and the other to the small tube. When fluid flows from large to small tube the velocity increases and its pressure drops , causing a pressure differential across he manometer which draws fluid up towards the lower pressure in the small tube.
What is the velocity of air (V1) flowing into the venturi meter? What information do we have to solve this?
Area of S1 and S2
change of h= h2-h1
change of P= rho g change of h (where rho= monometer fluid density)
Density of air (rho) flowing through the meter
Bernoulli states: P1 + rho g h + 1/2 rho v^2 = P1 + rho g h + 1/2 rho v^2
assuming continuous airflow through the pipe
Venturi effect by prairie dogs
The same principle observed in venturi meter is used by prairie dogs to ventilate their burrows
their burrows have two openings, one at top of a raised mound and one flush with ground. As air flows over ground t hits mound and is forced to flow up and over top. This causes flow to be constricted forcing it to accelerate and drop in pressure. Thus the burrow is like the manometer, while the raised mound of earth acts like the constriction of the smaller tube in the venturi meter. The low pressure at the opening of the raised burrow draws air through the burrow, down a pressure gradient, from higher pressure at the other burrow entrance flush with the ground
what does a Pitot tube measure?
dynamic pressure of a fluid, which is proportional to the velocity of the fluid and therefore a pitot tube can be used to measure fluid velocity.
How does a pitot tube work?
Has a tube with an opening that faces directly into oncoming fluid flow. The moving fluid is forced to a stop when it hits the opening (stagnation point) this converts fluids dynamic pressure into static pressure. The stagnation pressure will be both dynamic and static pressure of fluid flow combined. A second opening is parallel to fluids flow is called the static port and is used to measure the static pressure of the fluid.
How do fluids flow against a pressure gradient in a pipe
Height of water in vortical tubes can show Static pressure and look like there is an up down up pressure gradient difference in different sections of a pipe but does not show dynamic pressure. A fluid flowing through a constriction will convert static pressure to dynamic pressure. Static pressure may be lower in the constriction the total energy of the fluid (all static, dynamic and potential pressures) is still higher than the next section. Fluid will continue to flow down energy gradient from A to B to C..
A pipe of constant cross sectional area is connected to a pump which maintains a constant pressure head. The pipe runs along the ground then goes up and over a hill.
Describe the changes (if any) in static, dynamic or potential energy, velocity, and rate of flow as the water in the pipe flows over the hill.
If the cross-sectional area of the pipe is constant and the pressure gradient is constant then flow velocity must also be constant.
If velocity is constant, dynamic pressure is
constant.
As the pipe goes over the hill, the vertical position of the pipe, and of the water within it, will increase. Therefore, the potential energy of the water in the pipe will increase,
but according to Bernoulli’s principle, the static pressure energy will decrease
Define Reynolds number
gives the ratio of the inertial forces in a fluid(related to fluid density, velocity and characteristic length) and the viscous forces in a fluid (dynamic viscosity).
It is dimensionless number used to predict whether flow is laminar (low Re) or turbulent (high Re)
What features characterize laminar flow
ordered movement of fluids along streamlines.
It s reversible in time and does not involve mixing
What features characterize turbulent flow?
disordered, non-reversible flow in which there is mixing and vorticity
What is dynamic viscosity of a fluid
mnew (u)
is a measure of relationship between the shear stress applied to a fluid and the resulting shear strain rate.
Its units are Pascal seconds (Pa s)
What is kinematic viscosity of a fluid?
The ratio of dynamic viscosity of a fluid to its density
has units Stokes (St)
What is Lift?
Lift is a force generated perpendicular to the direction of fluid flow
What is the coefficient of lift CL?
is a dimensionlesss number that relates the lift (FL) generated by structure (aerofoil, wing, animal, aircraft) to the reference area (S) of the lift generating surface (generally the planform area of the wings) and dynamic pressure (1/2pv^2) experienced by the structure due to the velocity and density of the fluid flow past it.
CL= 2FL/(rho x v^2 x S)
What is Drag
Is a force generated parallel and in same direction of fluid flow.
What is the coefficient of drag Cd?
A dimensionless number that relates the drag (Fd) generated by a structure to the reference area (S) of the structure and dynamic pressure (1/2 rho v^2) experienced by the structure due to the velocity and density of the fluid flow past it.
Cd =2/Fd/ (rho * v^2 * S)
What is the magus effect?
The magnus effect is the effect by whch a rpptating object (cylinder/ sphere, etc) can generate lift. A rotating object placed in a fluid flow accelerates the fluid on the side of the object where the fluids direction of travel and the objects direction of rotation coincide. The fluid flow that encounters the opposite side of the rotating object is slowed down.
How can Magnus effect generate lift?
Bernoulli states that high velocity air has low pressures, while low velocity air has higher pressure. Thus the object rotation combined with fluid flow creates a pressure difference on opposite sides of the object, producing a force at right angles to the direction of fluid flow = lift!
What is the critical angle of attack?
Critical angle of attack s the angle between the chord of the aerofoil and the relative wind that produces the maximum lift (proportional to the coefficient of lift).
What happens to the magnitude of lift and drag once critical angle of attack s exceeded? Why? What is phenomenon called?
Once critical angle of attack is exceeded the boundary layer of air flowing across the top surface of the wing begins to separate. This is caused by the air in the boundary layer over the top of the wing being unable to flow to the trailing edge due to an inc angle of attack.
Once boundary layer separates from the surface of the wing, a turbulent wake is formed behind the wing. This dramatically reduces the lift and inc the pressure drag produced by wing. This is called a stall
Induced drag
is a by-product of lift production, which produces low pressure above wing and high pressure below. At the wingtip the high pressure air flows up and around the wingtip to the low pressure region above the wing, producing wingtip vortices. These vortices produce an area of downward moving air directly behind the trailing edge of the wing. this downwash causes the relative wind to be pushed down at the trailing edge of the wing. This creates an effective relative wind that is at an angle halfway between the angle of wind in the downwash and the oncoming relative wind. Since lift is generated perpendicular to the effective relative wind, it is tilted rearward and directs more force rearwards. This backwards directed force is induced drag.
What is parasite drag
Parasite drag is the combined drag caused by the skin friction, pressure and interference drag produced by the non-lift producing surfaces of a flying animal or aircraft
