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KevinW July 22, 2013 02:12

A question on Fluid Dynamics
 
"From basic fluid mechanics it is known that a pressure gradient, ∂p/∂r=rho*V^2/r, is necessary to curve the streamlines; r is the curvature of the streamline and V is the speed. This pressure gradient acts like the centripetal force known from the circular motion of a particle." ------Quoted from a book on wind turbine aerodynamics.
Please do me a favor and explain more in detail the philosophy underlying the equation. I guess it can be derived from F= m*v^2/r, but i just can't figure it out.
Your help will be highly appreciated. Thank you in advance.:D

FMDenaro July 22, 2013 04:03

Quote:

Originally Posted by KevinW (Post 441127)
"From basic fluid mechanics it is known that a pressure gradient, ∂p/∂r=rho*V^2/r, is necessary to curve the streamlines; r is the curvature of the streamline and V is the speed. This pressure gradient acts like the centripetal force known from the circular motion of a particle." ------Quoted from a book on wind turbine aerodynamics.
Please do me a favor and explain more in detail the philosophy underlying the equation. I guess it can be derived from F= m*v^2/r, but i just can't figure it out.
Your help will be highly appreciated. Thank you in advance.:D

The Newton law is expressed in fluid mechanics by the momentum equation:

d(rho*v)/dt + Div (rho*vv) = Div T

where T is the stress tensor you can write as -pI + Td. Then you can write the momentum equation in a polar system (r,theta), assume a steady non dissipative motion and so on... You will get the equilibrium equation.


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