Laws and Properties
What is the name of the law that describes momentum transfer?
Newton's Law (of Viscosity)
What assumption removes "accumulation" from IOGA?
What causes generation of momentum?
Force (or net force)
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 does IOGA mean?
In - Out + Generation = Accumulation
What is the driving force for energy (or heat) transfer?
What needs to be assumed to cancel the pressure gradient (in the direction of movement) from the momentum balance?
Open to atmosphere
What are two models that can be used to find the momentum transfer in non-Newtonian fluids?
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 = 0.00982 lbm/(ft s)
What are the two things "tau" may be considered as?
Shear stress and momentum flux
What is the physical property that relates concentration gradient to mass transfer?
Diffusivity
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 kind of mathematical relationship does a Newtonian fluid have between the momentum flux and velocity gradient?
Linear
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)
Can Wilke's Correlation be used for liquids?
No, only gasses
What are the key property and law related to heat (or energy) transfer?
Thermal conductivity and Fourier's Law
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 type of fluid uses n < 1 in the Power Law Model for shear stress?
Shear thinning
Calculate the viscosity of a gas in Pa*s using the kinetic gas theory model (Chapman-Enskog Equation) 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
What are the two components of combined (energy) flux?
Molecular and convective transport
What are the three terms in Fick's Law?
j = D * (dC/dx)
mass flux = diffusivity * (concentration gradient)
What are 4 things that could be assumed about water open to atmosphere undergoing fully-developed flow across a horizontal plane?
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 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
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) = 2000 kg m-3
MW = 20 g mol-1
mu = 4.612 centipoise
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