External forces on Stokes flow

In summary, in the limit as Re→0, the material derivative of v is neglected (Dv/Dt = 0), but it is unclear why books always set the effects of gravity to 0. This is because the density is treated as constant, allowing the gravitational force per unit mass to be absorbed into the pressure term without affecting the mathematics. This is also known as the "modified pressure," which is not commonly discussed in available sources of information.
  • #1
Est120
51
3
Homework Statement
find the appropiate Navier-Stokes equation in the low Re number limit
Relevant Equations
Navier Stokes equations
in the limit as Re→0 , we can neglect the material derivate of v ( Dv/Dt =0 ) but why in books they always make the gravity effects equal to 0?
i can't understand and no one really explains this stuff
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  • #2
The density is being treated as constant, so the gravational force per unit mass is [itex]\mathbf{g} = -\nabla\left(-\int\mathbf{g} \cdot d\mathbf{x}\right)[/itex].

You can therefore absorb it into the pressure term. It makes no difference to the mathematics if you work with [itex]p[/itex] or [itex]p' = p - \int\mathbf{g} \cdot d\mathbf{x}[/itex].
 
  • #3
pasmith said:
The density is being treated as constant, so the gravational force per unit mass is [itex]\mathbf{g} = -\nabla\left(-\int\mathbf{g} \cdot d\mathbf{x}\right)[/itex].

You can therefore absorb it into the pressure term. It makes no difference to the mathematics if you work with [itex]p[/itex] or [itex]p' = p - \int\mathbf{g} \cdot d\mathbf{x}[/itex].
yeah, that's the so called "modified pressure" right? i hardly managed to get that but still almost no source of information talks about that...
 

1. What is Stokes flow?

Stokes flow refers to a type of fluid flow that is characterized by low Reynolds numbers, which means that the inertial forces are much smaller than the viscous forces. In this type of flow, the fluid particles move in a smooth, laminar manner.

2. What are external forces on Stokes flow?

External forces on Stokes flow refer to the forces that act on the fluid from outside the system, such as gravity, pressure gradients, and external body forces. These forces can affect the behavior and movement of the fluid particles in Stokes flow.

3. How are external forces calculated in Stokes flow?

The external forces on Stokes flow can be calculated using the Navier-Stokes equations, which are a set of partial differential equations that describe the motion of a viscous fluid. These equations take into account the various external forces acting on the fluid.

4. What is the significance of external forces on Stokes flow?

External forces play a crucial role in determining the behavior of fluids in Stokes flow. They can affect the velocity, pressure, and other properties of the fluid, and can also influence the overall flow pattern. Understanding these forces is important in various applications, such as in the design of microfluidic devices and in the study of biological systems.

5. How do external forces affect the stability of Stokes flow?

The presence of external forces can affect the stability of Stokes flow. For example, gravity can cause a fluid to become unstable and transition from laminar flow to turbulent flow. Pressure gradients can also lead to instabilities in the flow. Understanding these effects is important in predicting and controlling the behavior of fluids in Stokes flow.

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