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f05_fall

# f05_fall - Fluids Lecture 5 Notes 1 Eects of Reynolds...

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Fluids – Lecture 5 Notes 1. Effects of Reynolds Number 2. Effects of Mach Number Reading: Anderson 1.10, 1.11 Dimensional Analysis has identified the important dimensionless parameters (or Π products), which determine the nature of a given aerodynamic ﬂow situation. The main parameters are the Reynolds number and the Mach number, and their values in any given ﬂow situation will determine the nature of the ﬂow (strongly viscous vs. nearly inviscid, low speed vs. high speed) Effects of Reynolds Number Interpretation The Reynolds number can be interpreted as a comparison of the pressure forces and viscous shear forces which act on the body, done by forming their ratio. 2 pressure forces p p ρu 2 ρ V ρ V c = Re shear forces τ µ du/dn µ V /c µ Note that p p is considered rather than p itself, since p is just a large constant bias which produces no net force on a body. The Reynolds number is therefore a measure of the importance of pressure forces relative to viscous shear forces. Hence, if the Reynolds number increases, the viscous effects on the ﬂow get progressively less important. The viscosity of air and water is quite small when expressed in common units. Air @ STP Water @ 15 C µ 1 . 78 × 10 5 kg/m-s 1 . 15 × 10 3 kg/m-s µ/ρ = ν 1 . 45 × 10 5 m 2 /s 1 . 15 × 10 6 m 2 /s The ratio µ/ρ = ν is called the kinematic viscosity . This is more relevant than µ itself, since the ratio is what actually appears in the Reynolds number.

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