Concerning a pressure coefficient

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The pressure coefficient, C_p, is defined as C_p = 1 - (V/V_{inf})^2, where V represents velocity. In a steady velocity field, the equation applies to the magnitude of velocity, calculated as the speed √(v_x^2 + v_y^2), rather than individual coordinates. The discussion raises the question of whether separate pressure coefficients can be defined for the x and y directions. To determine the maximum and minimum values of C_p, the overall speed should be used rather than directional components. The pressure coefficient is typically treated as a scalar quantity derived from the total velocity magnitude.
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On wikipedia it says that the pressure coefficient can be written as

C_p = 1 - (V/V_{inf})^2

where V is the velocity.

So if I have given a steady velocity field, V = (v_x,v_y), does the equation for C_p hold for both coordinates or only the speed \sqrt{v_x^2+v_y^2} ?

I'm supposed to determine the largest and lowest value for C_p and I don´t know which formula to use.
 
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Basically I'm asking if there is such a thing as a pressure coefficient in the x-direction and a pressure coefficient in the y direction?
 

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