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Inertial Force in Fluid Mechanics
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[QUOTE="Arjan82, post: 6396499, member: 177647"] I have a little bit of trouble interpreting your question, but here is a shot. Navier stokes states indeed that the mass times acceleration of a fluid parcel is equal to the gradient of the (static) pressure, the viscous forces and the body forces. This is very accurate indeed. Whether you choose to solve these Navier-Stokes equation in a inertial or non-intertial frame of reference is a choice which is unrelated, both is possible in principle. Either choice can be solved accurately in principle. But the Navier-Stokes equations look different if you describe them in a non-inertial reference frame, for which case you indeed need to add these fictitious forces due the acceleration of the reference frame. These fictitious forces are however unrelated to the real forces that affect the motion of the parcel. Does this answer your question? The inertial force is a fictitious force equal and opposite to the force applied to a fluid parcel to change its velocity. The dynamic pressure is just the kinetic energy per unit volume. I don't see how the inertial force can be 'due to' a dynamic pressure; a flow parcel only reacts to a static pressure gradient (or a viscous or body force...). So, in short, I'm struggling with the question a bit. Yes, if you have a dense fluid moving at a high constant speed, there are no inertial forces. But that's not the point of the Reynolds number. This number gives the ratio of the inertial forces to the viscous forces to characterize a flow. A high Reynolds number means that inertial forces are more important in the dynamics of the flow than viscous ones if you were to perturb the flow (there should be an asterisk attached to this remark). This would mean that you can neglect viscous forces and describe the problem with potential flow theory (more asterisks to be attached here). This would mean your problem is easier to solve, you don't need to solve the full Navier-Stokes equations. On the other side, for Reynolds numbers much lower than one, the inertial forces are not important anymore and you can just use the Stokes equations to solve your problem. In this case the ##\rho V^2## term is just a measure of the inertial forces to be expected. [/QUOTE]
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Inertial Force in Fluid Mechanics
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