42Physics 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 angleθwith 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, withx=x/L,v=v/V, grad=Lgrad,∇2=L2∇2andt=tω:Sr∂v∂t+ (v·∇)v=-gradp+gFr+∇2vRe9.5Tube flowsFor tube flows holds: they are laminar if Re<2300with dimension of length the diameter of the tube, andturbulent if Re is larger. For an incompressible laminar flow through a straight, circular tube holds for thevelocity profile:v(r) =-14ηdpdx(R2-r2)For the volume flow holds:ΦV=R0v(r)2πrdr=-π8ηdpdxR4Theentrance lengthLeis given by:1.500<ReD<2300
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