A point source of strength M is located at the distance of H from an infinite flat wall. What is the force acting on the wall due to the fluid flow from the source?
Solutions are needed for two different approximations:
1) Potential flow with zero fluid viscocity (slip condition at the wall)
2) Stokes flow at very small Reynolds number (no-slip condition at the wall)
See please: https://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-090-introduction-to-fluid-motions-sediment-transport-and-current-generated-sedimentary-structures-fall-2006/course-textbook/ch3.pdf
Best regards
https://www.sciencedirect.com/search?qs=A%20point%20source%20of%20fluid%20is%20located%20near%20a%20solid%20wall&show=25&sortBy=relevance
Dear Dušan Regodić,
Thanks for your reply. I couldn't find tha answer to my question in this chapter. Is it possible to get a pdf of full book?
Dear Mahesh Kumar,
My question is connected with the problem considered in our recent paper (see the ref. below).
Deeper analysis shows that the problem is more complicated than we initially thought.
Article Levitation and Self-Organization of Liquid Microdroplets ove...
https://www.researchgate.net/publication/283122180_On_refinement_of_calculation_dependences_of_the_force_action_of_a_turbulent_gas_jet
Dear Dmitry Zaitsev
Corresponding to your question if the fluid element is some distance away, but not in contact there will act no viscous drag force on the wall and no chemical inter molecular adhesion force will act. However the forces like gravitation, electrical force etc with distance may act.
Dear Krushna Chandra Sahoo,
No gravity, no electrical force, no contact between the source and the wall.
Yes, the viscous drag force acts on the wall in tangential direction and must yield zero outcome (due to the axial symmetry).
However, a force acting on the wall in normal direction may appear because of nonuniform preassure distribution in the fluid.
Dear Dmitry Zaitsev
Viscous drag force is always a contagious force and must not appear. Gravitational force is universal and must appear.
Of course the normal pressure difference force will appear and make the fluid to come in contact with the wall.
Dear Krushna Chandra Sahoo,
For the sake of simplicity, I neglect gravity force.
I need to find only the force acting on the wall due to the fluid flow originating from the point source.
Or, alternatively, I need to find the force acting on the source due to the presence of the wall.
According to the Newton's third law, these two forces must be equal.
Dear Dmitry Zaitsev
Now I think your question is on fluid flow on to the wall from a point source which may be momentum transfer force besides the fluid static pressure force and viscous drag force.
In the approximation of Potential flow with zero fluid viscocity (slip condition at the wall) -- there must be no viscous drag force and no momentum transfer force. However, due to the Bernoulli's principle, the pressure at the wall under the source must be reduced, and thus the wall must attract to the source of fluid.
In the approximation of Stokes flow at very small Reynolds number (no-slip condition at the wall) -- it's not obvious whether the wall will attract to or repell from the source.
Why no momentum transfer force in the case of zero viscosity?
Dear Alexander P Savenoov
momentum transfer force may also occur even in the absence of viscosity, it momentum transfer takes place with a normal component to the wall.
Dear Alexander P. Savencov and Krushna Chandra Sahoo,
In the approximation of Potential flow with zero fluid viscocity (slip condition at the wall) the momentum of each portion of fluid doesn't change. That's why fluid can't transfer any momentum to the wall.
Recall a classical problem of a sphere placed in an uniform potential flow of inviscid fluid. The force acting on the sphere is equal to zero.
Dear Dmitry Zaitsev
In the uniform potential flow of inviscid fluid only static pressure force acts on the immersed sphere from all directions and cancel each other. so net force becomes zero.
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