University:
Duke University
Course:
PHYSICS 151L9D | Introductory Mechanics (Discussion Component)
Academic year:

2023
Views:

284

Pages:

2
Author:

Pemuda H

Chapter 2 Open System-mass can flow through it Control Volume: - volume doesn't change Boundary: 26** Closed Surface surface Closed System Can deform the surface; controlled mass Time Derivatives ← C(x,y,z,t)-concentration of fish in river (x(t), y(t), 2 (t)) - (XYZ) number of fish seen in a certain amount of time C + 2c dx axe de + dt dza dt de +22 dt moving up and down the river over a certain amount of time while counting fish 20 +22 k dx dy = + 20 Material/Substantial Derivative Dc 24 = at + C. where is the river's velocity (go w/ the flow). Reynold's Transport Theoret - Control Volume: dex(x,y,z,t)d= + 6* x(x,y,z,t). 260* -Control Mass: Ex(x,y,z,t) = x(x,y,z,t)d+ √x(x,y,z,t) Jondo d dt mov Lt mem=0 = min-mout << 90° mout 2 > 90° min mev = Spd mass, flux Spindo = in direction of surface σ do d dt mov d dt PTñdo = 0 I form of: 26=0 mass conservation Using Reynold's T.T. pvon do If you say that these two egs. were equal at some point then - [(-)n]do For *=0 then Using Gauss's Theorem: [ade = fando "Divergence Theorem" So you get P+ Δ for any volume, which means the inside must equal zero 2 Steady Incompressible + Sidenote: Another notation for this is: Pit (pui=0 ↓ V=

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