Fluid Mechanics Cheat Sheet

Fluid Mechanics Cheat Sheet - Akram Ayache AUB MECH-314:...

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Unformatted text preview: Akram Ayache AUB MECH-314: Introduction to Fluid Mechanics Final Cheat Sheet Material Derivative: D g2930 = g2930 + (V g4652g1318 g4652g1318 ) Conservation of Mass: 0 = g2930 g3512 d g2288 g2887g2906 + g3518 (V g4652g1318 g2916 / g2887g2903 d g2285 g1318 ) g2887g2903 0 = g2930 + g4652g1318 g3435 V g4652g1318 g3439 0 = g2930 + g4652g1318 V g4652g1318 + V g4652g1318 g3435 g4652g1318 g3439 Using g2930 = 0 and Ma < 0.3 we get incompressible continuity: g4652g1318 V g4652 = 0 Conservation of Linear Momentum: F g4652g1318 = g2930 g3512 V g4652g1318 d g2288 g2887g2906 + g3518 V g4652g1318 (V g4652g1318 g2916 / g2887g2903 d g2285 g1318 ) g2887g2903 g g4652g1318 g4652g1318 P + g4652g1318 g1318 g1318 = D g2930 V g4652g1318 F g4652g1318 g3505 a g4652 g2934g2935 / g2908g2909 dm = g2930 g3512 V g4652g1318 d g2288 g2887g2906 + g3518 V g4652g1318 (V g4652g1318 g2916 / g2887g2903 d g2285 g1318 ) g2887g2903 F g4652g1318 ma g4652 g2934g2935 / g2908g2909 = m g4662 g2925 u g2925 m g4662 g2919 u g2919 g3437 g g2934 g g2935 g g2936 g3441 g4684 g2934 P g2935 P g2936 P g4685 + g4684 g2934 g2934g2934 + g2935 g2935g2934 + g2936 g2936g2934 g2934 g2934g2935 + g2935 g2935g2935 + g2936 g2936g2935 g2934 g2934g2936 + g2935 g2935g2936 + g2936 g2936g2936 g4685 = g4684 g2930 V g2934 + V g2934 g2934 V g2934 + V g2935 g2935 V g2934 + V g2936 g2936 V g2934 g2930 V g2935 + V g2934 g2934 V g2935 + V g2935 g2935 V g2935 + V g2936 g2936 V g2935 g2930 V g2936 + V g2934 g2934 V g2936 + V g2935 g2935 V g2936 + V g2936 g2936 V g2936 g4685 For Newtonian Fluids g1318 g1318 = g4652 V g4652g1318 and g2919g2920 = g2920g2919 = ( g2919 V g2920 + g2920 V g2919 ) thus momentum balance yields the Navier-Stokes Equation: g g4652g1318 g4652g1318 P + g2870 V g4652g1318 = D g2930 V g4652g1318 g3437 g g2934 g g2935 g g2936 g3441 g4684 g2934 P g2935 P g2936 P g4685 + g4684 g2934g2934 g2870 V g2934 + g2935g2935 g2870 V g2934 + g2936g2936 g2870 V g2934 g2934g2934 g2870 V g2935 + g2935g2935 g2870 V g2935 + g2936g2936 g2870 V g2935 g2934g2934 g2870...
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Fluid Mechanics Cheat Sheet - Akram Ayache AUB MECH-314:...

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