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42 Physics Formulary by ir. J.C.A. Wevers Sr: (non-stationary inertial forces)/(stationary inertial forces) Fr: (stationary inertial forces)/(gravity) Fo: (heat conductance)/(non-stationary change in enthalpy) Pe: (convective heat transport)/(heat conductance) Ec: (viscous dissipation)/(convective heat transport) Ma: (velocity)/(speed of sound): objects moving faster than approximately Ma = 0,8 produce shock- waves which propagate with an angle θ with the velocity of the object. For this angle holds Ma = 1 / arctan( θ ) . Pr and Nu are related to specific materials. Now, the dimensionless Navier-Stokes equation becomes, with x = x/L , v = v/V , grad = L grad, 2 = L 2 2 and t = t ω : Sr v t + ( v · ) v = - grad p + g Fr + 2 v Re 9.5 Tube flows For tube flows holds: they are laminar if Re < 2300 with dimension of length the diameter of the tube, and turbulent if Re is larger. For an incompressible laminar flow through a straight, circular tube holds for the velocity profile: v ( r ) = - 1 4 η dp dx ( R 2 - r 2 ) For the volume flow holds: Φ V = R 0 v ( r )2 π rdr = - π 8 η dp dx R 4 The entrance length L e is given by: 1. 500 < Re D < 2300
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