Exam 2 Flashcards
Bernoulli Principle is conservation of:
Force, energy, and momentum
Steady vs unsteady flows
Steady flows are not time-dependent
Stagnation points
Velocity (all components) = 0
Speed
Absolute value of velocity vector (square root of velocity dotted with itself)
Streamlines
Lines tangent to flow field, defined by dy/dx = vy/vx
Irrotational flows
Cross product of gradient and velocity (curl) is zero
Incompressible flows
Dot product of gradient and velocity (divergence) is zero
Sources
Divergence of velocity is greater than zero
Sinks
Divergence of velocity is less than zero
Acceleration
Total derivative of velocity
Composition of total derivative
local derivative (wrt/ time) and convective derivative (wrt/ space)
Stream function existence condition
Incompressible fluid
Potential function existence condition
Irrotational fluid
Streamlines and equipotential lines are:
perpendicular
Flow rate integral
Integral of velocity over an area, can be set equal to the difference in stream functions between points A and B
Inviscid flows
Incompressible and irrotational
Uniform flow
Horizontal lines, only x-component of velocity exists (v = k*x)
Sources and sinks
+/- m/(2pir) in the r direction, irrotational
Steady shear flow
v=cy in the x direction, rotational flow
Free body vortex
v = k/r in the theta direction), irrotational
Rigid body rotation
v = wr in the theta direction, rotational ldw
Key assumptions for Bernoulli
Steady, incompressible, inviscid
Conservation of mass for incompressible fluids
du/dx + dv/dy + dw/dz = 0
