Boundary layer (2) von Karman momentum integral equation

In boundary layer studies, an important principle is the momentum integral equation which is derived from the integration of the Navier-Stokes equation to a large control volume encompassing a vertical slice of both the boundary layer and ideal fluid flow regions. This fundamental equation is valid for both laminar and turbulent boundary layers.
Let us consider the boundary layer developing along the flat plate and apply the equation of conservation of momentum in its integral form to the control volume. The integration of the momentum principle may be combined with the differential form of the Bernoulli equation for the ideal fluid flow. After some re-arrangement, an abbreviated form of the momentum integral equation is obtained.
The von Karman momentum integral equation may be used to solve a boundary layer problem by assuming a particular velocity distribution. In modern times, the momentum integral equation is rarely used for laminar boundary layer flows, but it is more commonly applied to turbulent boundary layer flows (Chanson 2014). The von Karman momentum equation, also called momentum integral equation, is a very important equation. It is valid for both laminar and turbulent incompressible boundary layer flows. It was first developed by Theodore von Karman (1921).
The application of the momentum integral equation to a boundary layer is a fundamental concept in applied fluid mechanics and fluid dynamics. It is valid for both laminar and turbulent flows.
A basic understanding of the physical fluid dynamic processes is critical in many real-word applications and discussed in a number of relevant RUclips video movies in the same Playlist at:
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Fluid mechanics and hydraulics in Hubert Chanson RUclips channel { / @hubert_chanson }
Applied hydrodynamics [Playlist]
Advanced hydraulics of open channel flows [Playlist]
Fundamentals of open channel hydraulics [Playlist]
Environmental hydraulics of open channel flows [Playlist]
Streamlines { • Streamlines }
Reynolds number { • Reynolds number }
Laminar and turbulent flows { • Laminar and turbulent ... }
Turbulent boundary layer (1) Presentation { • Boundary layer (1) Pre... }
Acknowledgements
Professor Colin J. APELT
USGS EROS Data Center Satellite Systems Branch
NASA Earth Observatory
References
KARMAN, T. von (1921). "Uber laminare und Zeitschrift für angewante Mathematik und Mechanik turbulente Reibung." Zeitschrift für angewandte Mathematik und Mechanik (ZAMM), Vol. 1. (English translation: NACA Tech. Memo. No. 1092, 1946.)
SCHLICHTING, H. (1979). "Boundary Layer Theory." McGraw-Hill, New York, USA, 7th edition.
CHANSON, H. (2014). "Applied Hydrodynamics: An Introduction." CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 448 pages & 21 video movies (ISBN 978-1-138-00093-3).