Fluid dynamics continued Comments about flow viz lab Conservation of energy, continued Examples Other forms Example of rotation, if possible

Lab – visualization experiments Laminar/turbulent pipe flow Flow moves from left to right in pipe Dye is continuously injected at the left while flow velocity steadily increases; –Re  –Watch transition to turbulence

Lab – visualization experiments Streaklines (streamlines if steady) over shapes Flow moves from right to left Dye is continuously injected at points on the right –First cylinders –Then, airfoil Watch dependence on “attack angle”

Visualization helps us understand natural phenomena Movies shown: Flow past cylinder Oscillating sign

Back to conservation of energy Conservation of momentum Conservation of energy

Pulling cons. of energy together: e = energy/mass = net heat into system / control volume (cv) = net work by system / cv on surroundings

Visualization

Back to conservation of energy For steady state flow With no work/heat in or out And no internal change of energy (change in temperature, etc.)

Careful energy treatment across pipe with viscosity Consider a bit more “honest” (mathematically correct) form: (CS=control surface)

Careful energy treatment across pipe with viscosity Consider a bit more “honest” (mathematically correct) form: (CS=control surface)

Careful energy treatment across pipe with viscosity Consider a bit more “honest” (mathematically correct) form: (CS=control surface)