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Derive the equation of force and moment coefficients with the help of given equations.
Explanation of Solution
Given:
The equation of normal force is,
The equation of axial force is,
The equation of the moment about leading edge per unit span is,
Here, pu and pl is the pressure upper and below the surface of the body and
Calculation:
The calculation for coefficient of normal force (1.15) is as follows:
The equation of normal force is
Fig:
Nomenclature for the integration of pressure and shear stress distributions over a two-dimensional body surface.
From figure:
Then, normal force per unit span is
Now, divide by
Here,
Normal force coefficient
Pressure coefficient
Skin friction coefficient
Thus, the equation can be written as:
Now the calculation for coefficient of axial force (1.16) is as follows:
The equation of axial force is
From figure:
Then,
Divide by
Here,
Axial force coefficient
Pressure coefficient
Skin friction coefficient
Then, the above equation can be written as:
And, the calculation for coefficient of moment force (1.17) is as follows:
The equation of the moment about leading edge per unit span is,
Divide by
Here,
Coefficient of moment
Pressure coefficient
Skin friction coefficient
Then, the above equation can be written as:
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Chapter 1 Solutions
Loose Leaf for Fundamentals of Aerodynamics
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