This interplay between the far field momentum balances and the local blade forces requires one to solve the momentum equations and the airfoil equations simultaneously.
42.
The simplest and most widely used equations are those that consider wake rotation with the momentum equation but ignore the pressure drop from wake rotation.
43.
With Newton s second law, Newtonian fluids assumption and Stokes hypothesis, the original fluid momentum equations are derived as the Navier-Stokes equations.
44.
In these instances, HEC-RAS will use a form of the momentum equation to solve for the water surface elevation at an unknown location.
45.
Since this equation must hold for any control volume, it must be true that the integrand is zero, from this the Cauchy momentum equation follows.
46.
By contrast this is not as easy in RQM; the energy momentum equation is quadratic in energy " and " momentum leading to difficulties.
47.
Taking the z-and x-derivatives of the x-and z-momentum equation, and subtracting, the pressure p can be eliminated:
48.
*The y-momentum equation implies that the pressure in the boundary layer must be equal to that of the free stream for any given x coordinate.
49.
This produces a force that can be expressed in the Navier Stokes or momentum equation governing fluid flow as the " Kelvin body force ( KBF ) ".
50.
In Computational Fluid Dynamics, solving the partial differential momentum equations mentioned above with discretized algebraic equations is the most important procedure to study flow characteristics in different applications.
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