Hydrodynamik I & II Flashcards
Definition of a fluid
A fluid deforms continuously, no matter whether the stress is large or small. That means that the constituent parts do not have the same velocity.
Fluids are liquids or gases
What are ideal fluids?
- have no viscosity
- no regards to molecules colliding with each other
Definition of newtonian fluids.
is a fluid in which the viscous stresses arising from its flow, at every point, are linearly correlated to the local strain rate—the rate of change of its deformation over time
Definition of viscosity.
RESISTANCE TO FLOW.
is a measure of its resistance to deformation at a given rate.
- for a liquid - the kinematic viscosity decreases with higher temperature
- for a gas - the kinematic viscosity increases with higher temperature
- it expresses interaction between fluid layers that can transfer momentum between them.
Viscous critical force:
F crit= η^2/ ρ
- if Fs>Fcrit = NICHT visköse Medium –> Turbulente Strömung
- if Fs laminare Strömung
Definition of viscous force bzw. Scherkraft.
fs = −η (v ⋅ A )/d
A: size of the plates
v: speed
d: distane between plates
η : viscosity of the medium
What is the newtons law of viscosity?
–>definition of shear stress, the stress on a surface in y- direction due to flow in x-direction
—> dvx/dy : Shear rate (const= newtonian fluid) it is just a gradient of velocity in a flowing material.
Viscosity = const —> Newtonian fluid
n = f (dVx/dy) –> depends on rate of deformation–> NON newtonian fluid
Explain the diferent plots of shear stress / shear rate, and what meaning do they have to the fluid dynamics.
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Explain the no slip condition and boundary layer flow in the two plates experiment.
Experiment: two layers and in between a fluid. The upper layer in moving while the other is static. The fluid is moving on the x axis, whereas the shear force is applied in the opposite direction. A flow profile is created, where the smaller the h (distance between the plates) the linear the correspondace.
- the fluid at boundaries move at same velocity as boundary. Meaning: vx (y=0) = 0 ; vx (y=h) = v.
- je näher an der bewegliche Platte, desto schneller die Bewegung der visköse Fluid ist.
- Für ganz kleine h –> lineare Anstieg, also vx (y)= vy/h
Boundary layer:
the distance z = dL when v = 0.99 v . But, dL gets larger with increasing distance from the leading edge of the plate. With increasing thickness of the layer, it becomes unstable which leads to turbulence. This transition is accompanied by a sudden increasing friction and thickness of the boundary layer (dL ≤dT)
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definition of laminar flow
Laminarefluß ist der parallele Fluss von Partikeln. Es kommt zustande, wenn die Viskosität groß ist und die Strömmung dadurch bestimmt wird.
- The velocity profile resembels a deck of cards. No cross-currents perpendicular to the direction of flow.
- The velocity of flow varies from zero at the walls to a maximum along the cross-sectional centre of the vessel.
- At lower velocities.
- Re > 10^4 transition from laminar –> turbulent flow
- Fs = viskose kritische Kraft =
What is the viscous critical force and what does it measures?
Viscous critical force:
F crit= η^2/ ρ
- if Fs>Fcrit = NICHT visköse Medium –> Turbulente Strömung
- if Fs<fcrit> laminare Strömung</fcrit>
What is the Reynolds number? helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent
The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.
- helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent
- aminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion
Re = ρuL /μ = uL/v
where:
ρ is the density of the fluid (SI units: kg/m3)
u is the flow speed (m/s)
L is a characteristic linear dimension (m)
μ is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/(m·s))
v is the kinematic viscosity of the fluid (m2/s)
Relation between Re , F crit, & laminar/turbulent flow.
- Re small = laminar flow –> Fs < Fcrit => viscous medium
- Re big = turbulent flow –> Fs > Fcrit => not viscous medium
–> Pt : point of transition from laminar to turbulent flow mit zunehmender Länge und Geschwindigkeit. ( Re= 10^4 = 2000)
define kinematic viscosity.
define shear strain
Explain Stockes Law
in a falling sphere viscosimeter;
Wann stoppt ein Bakterium, wenn es aufhört aktiv zu schwimmen?
What distance is it E. coli still swimming after it stops beating the flagellum?
How much POWER is needed to push a bacteria forward?
Erklären Sie den Fluss durch Kapillaren als Fluss durch Konzentrichen Röhren dargestellt wird.
–> The inner cyclinders move faster than the outer ones
- the central cylinder has a driving force. F= π* r^2 * pressure difference.
- there is also a frictional force, Ff= (2πrl)*η* (-dv / dr) , the laste term is the shear rate. => Ff changes with the radius
- Fd = Ff at steady movement => π* r^2 * pressure difference = (2πrl)*η* (-dv / dr)
- Through integration–> velocity profile. v(r) = - (dif. p/ 2πlη) * (1/2*r^2 +C)
- At no slip condition: r= R & v(r) =0 –> goes to zero.
- v(r) = - (dif. p/ 2πlη) * (R^2 -r^2) => PARABOLIC FUNTION
=> vmax is at the center, where r=0, and the flow has the largest distance from the surface.
What is volume flow (Jv) and what is its relation with the Hagen-Poiseuille equation?
Beschriebt die laminare Strömung eines homogenen Newtonsche Fluids durch ein Rohr in abhängigkeit von Eigenschaften vom Fluid und Rohr.
- incompressible fluids
- laminar flow
–> Blood flow!
- der Fluss in den Kapillaren hängt von der 4te Potenz von R ab
- Bei einer Innendurchmesser Verdopplung –> hohen Fluss bzw. hohen Druck
- pressure increase –> Jv will increase
- if the viscosity of blood increases –> Jv will decrease
What is the pulsed speed and which equation describes it?
is the velocity at which the blood pressure pulse propagates through the circulatory system, usually an artery or a combined length of arteries. PWV is used clinically as a measure of arterial stiffness.
Explain the picture.
Um noch laminare Strömungen innerhalb des Blutflusses zu haben, ist es wichtig kleine Verweigungen und demzufolge kleine Winkel, um LAMINARE Strömungen aufrechzuerhalten.
Kritische Reynoldszahl ( ab 2000 gibt es Turbulenzen) ist von den Branching points winkel abhängig.
How does the flagellar propulsion ( in 1-2µm: bacteria, archaea) work?
- Rotary motor turn the flagella relative to the body with the frequency ω.
- Torque (Drehmoment)is generated by rotation and it is opposed by viscous drag, due to counter-rotation of the cell body
- Thrust (Vorstoß) generated by the flagellum is balanced by drag, due to translation of the body.
= the Bacterium rotates in CW motion with a spcf. frequency.
What are the components of the drag in bacterial propulsion ?
FΩ = Reibung im Schwimmrichtung
FΩ´ = Reibungskraft entgegen der Drehrichtung -> WOBLING
- FΩ & FΩ´ = TORQUE- Drehmoment
- Fv and Fv´ = THRUST- Vorstoß
–> Wenn sich FΩ & FΩ´ nicht während der Rotation balancieren ensteht CONICAL WOBLING.
Which modes of flagellar beating exist in eukaryotes?
- UNDULATION MODE
- Flagelattes and mammalia sperm
- no helix, rotation –> Reibung beim Vorstoß
- flagellare Welle nach rechts, dann erfolgt eine Bewegung nach links.
- BREAT STROKE MODE
- aka. Power recovery stroke
- Vorward ( power) =/= Back (recovery) stroke –> Netto Kraftbewegung nach VORNE
- Power stroke = forward movement
- Recovery stroke = brings flagellum in start position
What is the geometric cluth model?
- molecular mechanism how bending of the cilia or flagella
