Fall 2009
Appendix C. Calculation of Airfoil Drag Force Using the Momentum Integral Method
Consider an experiment in which the
re is
drag force on an airfoil that is immersed in a steady
incompressible flow.
The drag force can be determined from the measurement of velocity
distributions far upstream and downstream of the airfoil body (figure below).
1.
Velocity far upstream is the uniform flow .
2.
Velocity in the wake of the body is measured with hotwire/Pitot probe to be , which is
less than
due to the drag of the airfoil.
3.
Objective: Find the drag force
per unit length (span wise) of the airfoil.
Method 1: Choose a control volume following the flow streamline.
Fig. 1 Control volume following the flow streamline.
Solution:
Find relation between
and
using the mass conservation
Since we choose the streamline as the control volume (
CV
), there is no mass flow across it.
For
the
CV
,
is the unit normal vector and it is assumed that the
CV
has a unit depth.
()
()
Thus,
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 Fall '10
 FredrickStern
 Force, Momentum, Aerodynamics, Yi, momentum integral method

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