Consider an infinitely thin flat plate with a 1 m chord at an angle of attack of
The normal, axial, lift and drag forces, moment about the leading and quarter chord and the centre pressure.
Answer to Problem 1.4P
Normal force
Axial force
Lift force
Drag force
Moment about the leading
Moment about quarter chord
Centre of pressure
Explanation of Solution
Given:
Pressure on upper surface
Pressure on lower surface
Shear stress on upper surface
Shear stress on lower surface
Length of chord
Angle of attack
Calculation:
The normal force per unit span is,
Since the plate is thin
Then, normal force per unit span is,
Now, axial force,
Since the plate is thin
Then, axial force per unit span is,
Lift and drag force:
Lift
Drag
The equation of the moment about leading edge per unit span is,
Here, pu and pl is the pressure upper and below the plate, respectively.
Since the plate is thin,
Since shear stresses are also negligible, therefore,
Then, from above equation the moment about leading edge per unit span is,
Again, the moment about the quarter chord per unit span is,
The equation of location of centre of pressure of the plate is,
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