Concerning a pressure coefficient

[naggy]

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.

 

[naggy]

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?

 

[astrokreng]

I would say that the equation for C_p holds for both coordinates, as it is a function of velocity and not specific to any particular direction. However, the equation does require the magnitude of the velocity, so you would need to use the speed, \sqrt{v_x^2+v_y^2}, rather than the individual components of velocity.

To determine the largest and lowest values for C_p, you can use the given equation and plug in the maximum and minimum values for the velocity components. This will give you a range of values for C_p. Additionally, you can also plot the equation as a function of velocity and visually determine the maximum and minimum values.