Lecture 2 Flashcards
What are two approaches to solving transport problems
Theoretical and empirical
What is dimensional analysis
It is a way to reduce complex problems to simpler forms
Used to understand and simplify complex physical problems by expressing the relationship between different physical quantities through their fundamental units (such as length, time, and mass).
It focuses on how changing one variable affects others and helps ensure that formulas and equations are dimensionally consistent.
Scaling
Procedure to reduce the number of parameters in the transport problem
We want to non-dimensionnalize by dividing the variable by the max value of the variable in the problem (like x* = x/L)
Geometric similarity
All dimensions of model and original have same ratio (same shape, dif size)
What is convective transport related to in flow
high reynolds numbers, inertial transport
What is molecular transport related to in flow
low reynolds number, viscous flow
What is Reynolds number
Re(L) = p(v)L/µ
What is Froude number
Fr = v^2/gD
What is schmidt number
Sc = v/D
How to scale pressure
P = P* x rho x (average v)^2
How can we interpret reynolds number for flow
Re can be interpreted as the ratio of inertial forces to viscous forces in the fluid.
At high Reynolds numbers, inertial terms dominate and the flow may tend to become turbulent or chaotic.
At low Reynolds numbers, viscous effects will dominate and flow will be laminar.
Inertial flow is related to
high reynolds numbers, low impact of viscosity
Convective transport of momentum (rho)*( v^2)
(mass transport)
Viscous flow is related to
low reynolds number, low impact of inertial forces
Molecular transport of momentum
-µ*delvx/dely
(shear)
