Assumptions
What assumption removes "accumulation" from IOGA?
What is the name of the law that describes momentum transfer?
Bonus: What is the law (equation)?
Newton's Law (of Viscosity)
Bonus: tau = mu(dv/dx)
Find tau in lbf ft-2 if:
dv/dx = -3 s-1
mu = 2.15 lbm ft-1 s-1
tau = 0.200 lbf ft-2
What causes generation of momentum?
Force (or net force)
What does IOGA mean?
In - Out + Generation = Accumulation
What can be assumed to cancel the pressure gradient (in the direction of movement) from the momentum balance?
Open to atmosphere
What is the driving force for energy (or heat) transfer?
Calculate viscosity in lbm/(ft s) if:
V1 = 14 ft/s
V2 = 0.4 ft/s
F = 0.5 lbf
A = 1 ft^2
deltay = 0.1 in
mu = 0.00987 lbm/(ft s)
What are two models that can be used to find the momentum transfer in non-Newtonian fluids?
What are the two things "tau" may be considered as?
Shear stress and momentum flux
What does "no-slip condition" mean in momentum transfer?
The velocity of the fluid at the boundary of a container is the same as the velocity of the boundary (e.g. moving plates)
What is the physical property that relates concentration gradient to mass transfer?
Diffusivity
Calculate phi1,1 in the equation used to predict mixture viscosities if:
MW1 = 10 g mol-1
MW2 = 15 g mol-1
mu1 = 200 cP
mu2 = 480 cP
phi1,1 = 1
(trick question, i = j)
What kind of mathematical relationship does a Newtonian fluid have between the momentum flux and velocity gradient?
Linear
Can Wilke's Correlation be used for liquids?
Bonus: What can it be used for?
No
Bonus: Gases
What four things need to be assumed about a fluid to use the kinetic gas theory viscosity equation?
mu = (2)(mkT)1/2/(3pi3/2d2)
The particles are rigid, are spheres, are non-attracting, and are at low density
What are the key property and law related to heat (or energy) transfer?
Thermal conductivity and Fourier's Law
Calculate the viscosity of a gas in Pa*s using the kinetic gas theory model if:
d = 0.4 nm
Boltzmann constant = 1.3806 × 10-23 m2 kg s-2 K-1
T = 700 K
MW = 80 g mol-1
mu = 2.6812 * 10-5 Pa*s
What type of fluid uses n < 1 in the Power Law Model for shear stress?
Bonus: What uses n > 1
Shear thinning
Bonus: Shear thickening
What are the two components of combined (energy) flux?
Molecular and convective transport
What are 4 things that could be assumed about water open to atmosphere undergoing fully-developed flow across a horizontal plane?
Bonus: Name seven
Any 4 of the following:
Newtonian fluid, Vy = 0, Vz = 0, Vx =/= f(x), laminar flow, steady state, constant properties rho and mu (or incompressible with no temperature gradient), dP/dx = 0, no end effects (same as Vy = Vz = 0)
What are the three terms in Fick's Law?
j = D * (dC/dx)
mass flux = diffusivity * (concentration gradient)
Estimate the viscosity of liquid X in centipoise at 400 K using the equation from the molecular theory of liquids if:
NA = 6.022 * 1023 mol-1
h = 6.626 * 10-34 m2 kg s-1
Tb = 500 K
rho(400 K) = 500 kg m-3
MW = 20 g mol-1
mu = 1.153 centipoise
What 3 (or 4) variables is viscosity a function of in the simplified molecular theory of liquids?
Specific volume (or molecular weight and density), boiling point, and temperature
DOUBLE JEAPORDY (1000 points)
How do you prove velocity is not a function of the direction it is moving in (not being transferred in)?
Mass balance
Assume steady state
Find mass flow in terms of density, velocity, and cross-sectional area
Take the limit / Find the derivative
Derivative should equal 0