Aerofoils, or aerodynamic wings, used in race car design produce down-thrust. Ai

Question

Aerofoils, or aerodynamic wings, used in race car design produce down-thrust. Air flows at different speeds over the two sides of the aerofoil, resulting in a pressure difference, a physical rule known as Bernoulli's Principle based on the bulk modulus of elasticity: dp= partial differential p/partial differential p|_T + partial differential p/partial differential T|_p Air (110 degree F, 14.7 psia) flowing over the aerofoil encounters a pressure drop of 1.0 psia and a temperature drop of 20 degree F. Estimate the density change (as a percentage of undisturbed air density). Is the assumption of an incompressible fluid justified?

Explanation / Answer

Here given that,

p1 = 14.7 psia = 101.352 kPa

T1 = (273+37.777) = 310.777 K

p2 = 13.7 psia = 94.4581 kPa

T2 = (273+32.222) = 305.222 K

density1 = p1/(R*T1) = 101.352*1000/(287.058*310.777) = 1.1360

density2 = p2/(R*T2) = 94.4581*1000/(287.058*305.222) = 1.0780

Change in density = (density1-density2)/density1*100 = 5.10%

Here, density is varying therefor assumption of incompressible flow are not applicable.

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