I Fluid dynamics: drag coefficient and pressure at the stagnation point.

AI Thread Summary
The drag coefficient (c_d) is defined as the drag force divided by the product of the pressure at the stagnation point and the area perpendicular to the flow. To determine the pressure at the stagnation point, Bernoulli's equation is applied for an incompressible fluid, assuming both ends are at the same level and the object's boundary velocity is zero. The equation simplifies to show that if the pressure far from the object is considered zero, it accurately reflects the pressure at the stagnation point used in the drag coefficient calculation. This assumption is based on the concept that at the stagnation point, dynamic pressure is converted entirely into static pressure. Understanding this relationship helps clarify how c_d quantifies the kinetic energy loss due to friction and turbulence in the airstream.
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Pressure at the stagnation point of an incompressible fluid.
Hi,
In my textbook the author say that the drag coefficient is the drag force divided by the pressure at the stagnation point time the area perpendicular to the stream.
##c_d = \frac{2F_d}{\rho v^2 A}##

To get the pressure at the stagnation point I'm using Bernoulli for an incompressible fluid. If both ends are at the same level and knowing that the velocity at the boundary of an object (a sphere for example) is null. Bernoulli equation is now:

##\frac{u^2}{2} + \frac{P}{\rho} = \frac{P'}{\rho}## Where P' is the pressure at the stagnation point.
If the pressure far from the object is 0. We get exactly the pressure at the stagnation point used in the drag coefficient.

If this above is correct why exactly the pressure far from the object is 0?
 
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Cd represents the percent of the kinetic energy of the airstream that is wasted in friction and turbulence.
At the stagnation point, the whole dynamic pressure becomes static pressure.
 
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