♦ Factors that affect lift generation:
• Air Velocity
• Density of air
• Wing area
• Shape of the airfoil
• Angle of attack
since we know that, L∝ρ, L∝s and, L∝v2 ∴L=12ρv2sCL
♦ Effect of AOA(angle of attack) on lift:
Up to a certain AOA of an airfoil, the airflow follows the profile or shape of the airfoil. Up to this AOA, lift increases almost linearly as the AOA increases. At a certain AOA (usually less than 15∘) the airflow begins to separate from the aerofoil and can not follow the shape of the aerofoil. This certain angle is called the stall angle. After stall angel lift decreases gradually with the increase of Angle of Attack (AOA).
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♦ Proof of Bernoulli's Theorem:
we know,
Total Energy = Work done
Total Energy=Work done=Force×Distance=F×d=PAd |[FA=P]=PV
Work done from A1 to A2 per unit volume =(P1−P2)
Total Energy=Kinetic energy + Potential energy=12mv2+mgh=12ρv3+ρvgh∴ Total energy per unit volume=12ρv2+ρgh
from equation (1) & (2) we get,
P1−P2=12ρv2+ρgh⟹ P1−P2=12ρ(v22−v21)+ρg(h2−h1)⟹P1+12ρv21+ρgh1=P2+12ρv22+ρgh2∴P1+12ρv2+ρgh=Constant
h1=h2h=h1−h2and, ρgh=0 P+12ρv2=Const KE=12ρv2=12mv2
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