Aero Handbook: Difference between revisions
From GTMS
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Imagine air passing through a sealed tube. The amount of mass passing through two cross sections of the tube must be equal. This is because mass cannot be created or destroyed. The mass flow, or mass of air passing through per time, at section A1 must equal section A2, giving the equation ρ_1 A_1 V_1= ρ_2 A_2 V_2. Because we assume incompressible flow, the density (ρ) may be dropped, and the equation then gives the conservation of volumetric flow in volume per time. To balance the equation, V2 must be greater than V1 because A1 is greater than A2. Conversely, if A2 were greater than A1, as in a diffuser, the air would slow down. This equation for conservation of mass may be derived from Reynold’s Transport Theorem if you are interested. | Imagine air passing through a sealed tube. The amount of mass passing through two cross sections of the tube must be equal. This is because mass cannot be created or destroyed. The mass flow, or mass of air passing through per time, at section A1 must equal section A2, giving the equation ρ_1 A_1 V_1= ρ_2 A_2 V_2. Because we assume incompressible flow, the density (ρ) may be dropped, and the equation then gives the conservation of volumetric flow in volume per time. To balance the equation, V2 must be greater than V1 because A1 is greater than A2. Conversely, if A2 were greater than A1, as in a diffuser, the air would slow down. This equation for conservation of mass may be derived from Reynold’s Transport Theorem if you are interested. | ||
====Conservation of Momentum==== | ====Conservation of Momentum==== | ||
Newton’s Third Law provides a simple way to intuit aerodynamics: conservation of momentum. For every action, there is an equal and opposite reaction. When the car pushes air up, the air pushes the car down and creates downforce – momentum transfer. This can be derived from Reynold’s Transport Theorem for Momentum, which, for a control volume with one inlet and one outlet at constant density, simplifies to | Newton’s Third Law provides a simple way to intuit aerodynamics: conservation of momentum. For every action, there is an equal and opposite reaction. When the car pushes air up, the air pushes the car down and creates downforce – momentum transfer. This can be derived from Reynold’s Transport Theorem for Momentum, which, for a control volume with one inlet and one outlet at constant density, simplifies to <math> F_{net} = \rho(V_{out}^2 A_{out} - V_{in}^2 A_{in}) = (\dot{m}_{out})V_{out} - (\dot{m}_{in})V_{in} </math>, where F and V are vectors. | ||
=Design Methods= | =Design Methods= | ||
