Lecture 4 Flashcards
(20 cards)
What law does the momentum equation take into account?
Newton’s 2nd Law; F=ma.
What 2 types of forces is the “force” in “F=ma” made up of? What are the definitions of these and give 3 examples of one of them, and 2 types of another.
Body / Volume forces: acting on volumetric mass of fluid element, “at a distance”. Eg. Gravitational; Electric; Magnetic.
Surface forces: act on surface of fluid element. Two types: pressure and viscous (shear/normal) stress.
What are the pressure forces within the surface forces imposed by?
By the outside fluid surrounding the fluid element (“thermodynamic pressure” associated with particle collision at microscopic level).
What are the viscous (shear/normal) stresses associated with the surface forces imposed by? How do these vary from the pressure forces.
Also by outside fluid, where it “tugs” or “pushes” on the surface by means of friction.
Pressure forces are of a thermodynamic nature; viscous stresses are due to viscosity.
How does the shear stress arise in a flow?
Different flows moving at different velocities exert shear stresses on each other.
What are viscous shear and normal stresses related to? What do they depend on?
The time rate of change of the deformation of the fluid element.
Depend on velocity gradients.
Normal vs Shear Stress: what different things are they related to?
Shear: time rate of change of shearing deformation of fluid element.
Normal: time rate of change of volume of fluid element.
Which direction does each stress (normal and shear) deform the fluid element?
How do the magnitudes of normal stresses and shear stresses compare?
Normal stresses are typically smaller
Explain the flow chart that summarises all forces acting on a body for the momentum equation.
What is the notation for the body force acting in the x-direction for the momentum equation?
Roughly outline the surface force diagram for momentum equation in x-direction. IMPORTANT: what’s the convention for labelling directions?
How can you tell whether a stress is normal or shear from the sign convention?
If subscript is the same; normal.
If different; shear.
What is the total LHS (forces) of the equation for momentum equation? What two things is the total force broken down into?
What is on the RHS (ma) of the momentum equation in the x-direction, for the Lagrangian model, and why?
Mass = density * volume
Accel. = Du/Dt because it’s the Lagrangian model, so substantial derivative used due to the moving fluid.
Final form of x-component of momentum equation, before tau simplification.
With the x-direction derived, how would the y and z-directions look? What are these called? What is the next step in the derivation?
Navier-Stokes equation
Still have to substitute to replace the tau (stresses)
What does this equal for incompressible flow and why?
0, because continuity
Final form of momentum equation with accel., force, mass labelled.
Final form of momentum equation with terms labelled.
