# A question on Fluid Dynamics

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 July 22, 2013, 02:12 A question on Fluid Dynamics #1 New Member   Join Date: Jul 2013 Posts: 25 Rep Power: 5 "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.

July 22, 2013, 04:03
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by KevinW "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.
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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