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Unformatted text preview: ENG 103 Fluid Mechanics EQUATION SHEET [FINAL EXAM VERSION] Ideal Gas Law p/ = RT, R = R o /M, R o = 8314 kg . m 2 / (kmol . s 2 . K) Shear Stress in a Newtonian Fluid (1D) = du dy Flow Patterns Streamlines: dx u = dy v = dz w Pathlines: x = Z udt ; y = Z v dt ; z = Z w dt Total differential When a differential equation has the form: P ( x,y ) dx + Q ( x,y ) dy = 0 If P/y = Q/x , then there is a function F ( x,y ) such that dF = P ( x,y ) dx + Q ( x,y ) dy (= 0) The original differential equation can then be integrated as F = constant with F x = P ( x,y ) and F y = Q ( x,y ) Pressure Variation in a Fluid with Rigid-Body Motion- ~ p- g ~ k = ~a Note: ~a is the acceleration and ~ k is the unit vector aligned with gravity but pointing up. Hydrostatic force on a flat surface (coordinates of the center of pressure) y CP = y CG- I x x sin p CG A , x CP = x CG- I x y sin p CG A where, CG denotes the centroid of the flat surface, is the angle betweeb the flat surface and the horizontal, I x x is the second moment of area of the flat surface and I x y is the product of area of the flat surface. Note that the signs in these equations depend on the direction of the y axis. Here it is assumed that the y axis is directed upward. Reynolds Theorem For a control volume moving at constant velocity dB dt sys = d dt Z C . V ....
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