Deriving the Kutta-Joukowsky Equation and Some of Its Generalizations Using Momentum Balances

Author(s)
D. H. Wood

ABSTRACT

Momentum balances are used to derive the Kutta-Joukowsky equation for an infinite cascade of aerofoils and an isolated aerofoil. These derivations are simpler than those based on the Blasius theorem or more complex unsteady control volumes, and show the close relationship between a single aerofoil and an infinite cascade. The modification of lift due to the presence of another lifting body is similarly derived for a wing in ground effect, a biplane, and tandem aerofoils. The results are identical to those derived from the vector form of the Kutta-Joukowsky equation.

Momentum balances are used to derive the Kutta-Joukowsky equation for an infinite cascade of aerofoils and an isolated aerofoil. These derivations are simpler than those based on the Blasius theorem or more complex unsteady control volumes, and show the close relationship between a single aerofoil and an infinite cascade. The modification of lift due to the presence of another lifting body is similarly derived for a wing in ground effect, a biplane, and tandem aerofoils. The results are identical to those derived from the vector form of the Kutta-Joukowsky equation.

KEYWORDS

Lift, Vorticity, Kutta-Joukowsky Equation, Aerofoils, Cascades, Biplane, Ground Effect, Tandem Aerofoils

Lift, Vorticity, Kutta-Joukowsky Equation, Aerofoils, Cascades, Biplane, Ground Effect, Tandem Aerofoils

Cite this paper

nullD. Wood, "Deriving the Kutta-Joukowsky Equation and Some of Its Generalizations Using Momentum Balances,"*Open Journal of Fluid Dynamics*, Vol. 1 No. 1, 2011, pp. 12-16. doi: 10.4236/ojfd.2011.11002.

nullD. Wood, "Deriving the Kutta-Joukowsky Equation and Some of Its Generalizations Using Momentum Balances,"

References

[1] F. M. White, “Fluid Mechanics,” 7th Edition, McGraw- Hill, New York, 2011.

[2] R. L. Panton, “Incompressible Flow,” 3rd Edition, John Wiley & Sons, New York, 2005.

[3] G. K. Batchelor, “An Introduction to Fluid Dynamics,” Cambridge University Press, Cambridge, 1967.

[4] P. G. Saffman, “Vortex Dynamics,” Cambridge University Press, Cambridge, 1992.

[5] D. Crowdy, “Calculating the Lift on a Finite Stack of Cylindrical Aerofoils,” Proceedings of the Royal Society A, Vol. 462, 2006, pp. 1387-1407. doi:10.1098/rspa.2005.1631

[6] H. Glauert, “The Elements of Aerofoil and Airscrew Theory,” 2nd Edition, Cambridge University Press, Cambridge, 1947.

[7] J. Katz and A. Plotkin, “Low Speed Aerodynamics,” 2nd Edition, Cambridge University Press, Cambridge, 2001.

[8] B. Thwaites, “Incompressible Aerodynamics,” Clarendon Press, Oxford, 1960.

[1] F. M. White, “Fluid Mechanics,” 7th Edition, McGraw- Hill, New York, 2011.

[2] R. L. Panton, “Incompressible Flow,” 3rd Edition, John Wiley & Sons, New York, 2005.

[3] G. K. Batchelor, “An Introduction to Fluid Dynamics,” Cambridge University Press, Cambridge, 1967.

[4] P. G. Saffman, “Vortex Dynamics,” Cambridge University Press, Cambridge, 1992.

[5] D. Crowdy, “Calculating the Lift on a Finite Stack of Cylindrical Aerofoils,” Proceedings of the Royal Society A, Vol. 462, 2006, pp. 1387-1407. doi:10.1098/rspa.2005.1631

[6] H. Glauert, “The Elements of Aerofoil and Airscrew Theory,” 2nd Edition, Cambridge University Press, Cambridge, 1947.

[7] J. Katz and A. Plotkin, “Low Speed Aerodynamics,” 2nd Edition, Cambridge University Press, Cambridge, 2001.

[8] B. Thwaites, “Incompressible Aerodynamics,” Clarendon Press, Oxford, 1960.