Fluid Mechanics 2

What is the Eulerian frame of reference?

Everything is related back to a fixed point of reference

What is the Lagrangian frame of reference?

The frame of reference moves with a fluid particle.

what does the material derivative find?

Lagrangian rate of change

Incompressible flow definition

Density of a particle is constant

continuity equation, material derivative and cauchy assumptions

continuum

Bridgmann theorem

Physical dimensions can be expressed as the product of fundamental dimensions raised to the power of a real number

what is the number of dimensionless groups?

n-r

what assumptions are used to measure the speed of sound?

c is constant, 1D, inviscid flow, no body forces, compression is infintesimally small

what is a choked nozzle?

When the flow through the nozzle occurs at a Mach number of 1

when is the mass flowrate maximum inside a nozzle?

when the nozzle is choked

Bernoulli equation assumptions

steady flow, inviscid, incompressible, same streamline

isentropic flow assumptions

continuum, steady flow, no body forces, inviscid, perfect gas, isentropic, flow along a streamline, small angles in the nozzle

Euler assumptions

inviscid, continuum

What can particle motion be decomposed into?

Translation, rotation, deformation

Navier stokes assumptions

Incompressible, uniform viscosity, continuum, newtonian

How does velocity change in stokes first problem?

Plate suddenly set into motion at t=0

How does velocity change in stokes second problem?

Plate velocity varies by a certain function

how do bluff bodies cause boundary layer separation?

Adverse pressure gradient causes fluid near the wall to slow and reverse direction, causing the boundary layer to detach from the wall

how does a low Reynolds number affect wake and drag?

no separation, no wake, little drag

how does a high Reynolds number affect wake and drag?

flow separation, turbulent wake, form drag prevalent

how does an even higher Reynolds number affect wake and drag?

huge momentum deficit, smaller wake, higher drag

How are diffusers designed to minimise losses?

Change in cross section

boundary layer assumptions

low mach number, steady flow, no body forces, newtonian fluid, 2D

what additional assumptions are used for the Blasius solution?

d«L, self similarity, pressure gradient is 0

what is skin drag caused by?

wall shear stress

what is form drag caused by?

pressure difference

how are vortexes formed?

acceleration is provided by the pressure gradient, so the radius and pressure increase (lowest pressure is in the centre, causing water level to fall)

how many repeated terms are in dimensional analysis?

r (number of groups- M,L,T)

what is dimensional homogenity?

an equation must have the same units on each side for it to be true

what happens if pressure changes at a given location for incompressible flow?

pressure change affects the entire flow instantaneously (elliptic behaviour)

what happens if pressure changes at a given location for compressible flow?

pressure change propagates at a finite speed throughout the flow field (hyperbolic behaviour)

when is the bernoulli approximation valid?

when M<0.3

why is the stress tensor symetric?

the fluid must satisfy rotational equilibrium

what is Couette flow?

top plate moves, no pressure gradient

what is Poiseuille flow?

plates are both stationary, pressure gradient

what is Hagen Poiseuille flow?

pressure gradient in a pipe

what is Couette-Poiseuille flow?

top plate moves, pressure gradient

why does form drag occur when the boundary layer separates?

separation creates a wake of low pressure behind the object, which creates a net pressure difference

what happens when a flat plate is faced parallel to flow?

thin boundary layer, low drag, mainly skin drag

what happens when a flat plate is faced perpendicular to flow?

immediate separation at the tip, wide wake, high drag, mainly form drag

what does streamlining do?

reduces drag without reducing frontal area

what is the ideal angle for a streamline and why?

<10 degrees to avoid separation

optimum angle for a circular diffuser

2.5 < theta < 3.5 degrees

optimum angle for a rectangular diffuser

3.5 < theta < 5.5 degrees

symptoms of turbulence

unsteadiness and irregularity of flow, range of scales, 3D vortical motion

what is the energy cascade?

large eddies take energy from the mean flow, then break into smaller eddies, transferring energy down the scales, until viscosity dissipates as heat