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

In summary, the drag coefficient is a dimensionless number that quantifies the drag or resistance of an object in a fluid flow, while the pressure at the stagnation point refers to the pressure exerted on an object when the fluid flow comes to a complete stop at its surface. Understanding these concepts is crucial in fluid dynamics for predicting how objects behave in various fluid environments, influencing designs in engineering and aerodynamics.
  • #1
happyparticle
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TL;DR Summary
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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  • #2
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.
 

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

What is the drag coefficient in fluid dynamics?

The drag coefficient (Cd) is a dimensionless number that quantifies the drag or resistance of an object in a fluid environment, such as air or water. It is used to compare the drag of different objects regardless of their size. The drag coefficient depends on the shape of the object, the flow conditions, and the Reynolds number.

How is the drag coefficient calculated?

The drag coefficient is calculated using the formula: Cd = (2 * Fd) / (ρ * v^2 * A), where Fd is the drag force, ρ is the fluid density, v is the flow velocity, and A is the reference area (usually the frontal area of the object).

What factors affect the drag coefficient?

Several factors affect the drag coefficient, including the shape and surface roughness of the object, the flow velocity, the fluid's viscosity and density, and the Reynolds number. Streamlined shapes generally have lower drag coefficients, while bluff bodies have higher drag coefficients.

What is the stagnation point in fluid dynamics?

The stagnation point is a point on the surface of an object in a fluid flow where the fluid velocity is zero. At this point, the fluid pressure is at its maximum because the kinetic energy of the fluid is converted into pressure energy. The stagnation point is typically found at the front of the object facing the flow.

How is the pressure at the stagnation point determined?

The pressure at the stagnation point can be determined using Bernoulli's equation. For incompressible flow, the stagnation pressure is given by: P0 = P + 0.5 * ρ * v^2, where P0 is the stagnation pressure, P is the static pressure, ρ is the fluid density, and v is the flow velocity. This equation shows that the stagnation pressure is the sum of the static pressure and the dynamic pressure.

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