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Hello everyone,
I have a concern regarding the conservation of momentum for an incompressible Newtonian fluid with constant viscosity.
Say you have a volume of fluid sliding down an inclined plane with a velocity Vx with the perpendicular axis facing upward in the ydirection. When you try to solve the set of differential equations for NavierStokes in y, you end up with dp/dy=row*g, hence this illustrates the hydrostatic pressure variation. What doesn't make sense is how can a hydrostatic equation for a fluid at rest be applied to a fluid moving? When you derive the hydrostatic balance equation from a simple force balance on an element of fluid you only have 3 forces: Fdown(weight at top surface), Fup(weight at bottom surface), and Fdown(gravity force)... But in our inclined moving fluid system, we should have all the same weight Forces and the ycomponent of Fg AND also an extra Fdown(due to viscous transportation from the flow in the xdirection). Thus by virtue of this force balance, shouldn't the pressure variation in y be shear stress dependant and not simply a hydrostatic consideration?
I attached a diagram of the situation.
Thanks in advance!
I have a concern regarding the conservation of momentum for an incompressible Newtonian fluid with constant viscosity.
Say you have a volume of fluid sliding down an inclined plane with a velocity Vx with the perpendicular axis facing upward in the ydirection. When you try to solve the set of differential equations for NavierStokes in y, you end up with dp/dy=row*g, hence this illustrates the hydrostatic pressure variation. What doesn't make sense is how can a hydrostatic equation for a fluid at rest be applied to a fluid moving? When you derive the hydrostatic balance equation from a simple force balance on an element of fluid you only have 3 forces: Fdown(weight at top surface), Fup(weight at bottom surface), and Fdown(gravity force)... But in our inclined moving fluid system, we should have all the same weight Forces and the ycomponent of Fg AND also an extra Fdown(due to viscous transportation from the flow in the xdirection). Thus by virtue of this force balance, shouldn't the pressure variation in y be shear stress dependant and not simply a hydrostatic consideration?
I attached a diagram of the situation.
Thanks in advance!
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