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→Pressure coefficient
=== Pressure coefficient ===
The '''pressure coefficient''' at point A (around an aeroplane), by definition, is:
\[ C_p(A) = \frac{p_A-p_{\infty}}{\frac{1}{2}\rho V_{\infty}^2} \]
where:
*\(p_A\) is the static pressure at point A
*\(p_{\infty}\) is the static pressure far away, and
*\(V_{\infty}\) is the flow velocity far away
By far away (known as '''free-stream quantities''') we mean at a sufficient distance away from the aeroplane that effectively the flow is not disturbed by the aeroplane flying through it. Consider a car that passes in front of you at several feet away, you will feel some wind which is the flow disturbed by the presence of the car. However, you do not feel a lot of disturbance even if there are millions of cars driving in the United States.
Note that the velocity is measured in an aeroplane frame of reference so we can treat the problem as flow going around the aeroplane which makes things simpler. If the frame of reference is changed in this way, even the air above the United States can come at you at a velocity \(V\) depending on how fast you fly, so the author is just half joking when the above example is made.
The pressure coefficient is non-dimensional: it is a pressure divided by a pressure so no unit emerge from this algebra. However, if the flying speed is kept constant, i.e. the denominator is kept constant, the pressure coefficient is a representation of \(p_A\) given that the pressure in United States does not depend on the way you fly. If \(C_p\) increases, it means \(p_A\) is higher.
The maximum possible value of \(C_p\) is unity, which corresponds to stagnating the flow. If all the kinetic energy has been transformed into pressure potential, there is nothing else whatsoever we can do to increase the flow pressure further (with the exception of adding some work by mechanical means, which we shall not consider). There is, in theory, no minimum value pf \(C_p\), so long as \(p_A\) is above zero.
=== How to measure pressure ===
