Another Two Questions (fluids And Quantics)

[Raparicio]

Dear Friends,

Two more questions that I could not find the resolution. If anyone knows where is resolved, or could give a little help, I will be so much agreed!

One is about fluids mechanics: imagine one ball, in a fluid composed by much little balls. At much velocity, this big ball could adquire mass from this entorn, and be bigger. What's de velocity of equilibrium that makes that the ball has not acceleration. Imagine that the ball is little at principle, but it creates much big ball derivate of the material arround it. Another example could be a ball of snow running, at much velocity, much bigger...

Another question is about biot-savart law, in fluids mechanics. I don't understand the meaning of the strength... is this the circulation?

And another question is about demonstration of schrödinger equation by the formulae of continuity. I don't know how to do it.

I desire all of you a very good day.

R. Aparicio.

 

[dextercioby]

Dear Friends,

Two more questions that I could not find the resolution. If anyone knows where is resolved, or could give a little help, I will be so much agreed!

One is about fluids mechanics: imagine one ball, in a fluid composed by much little balls. At much velocity, this big ball could adquire mass from this entorn, and be bigger. What's de velocity of equilibrium that makes that the ball has not acceleration. Imagine that the ball is little at principle, but it creates much big ball derivate of the material arround it. Another example could be a ball of snow running, at much velocity, much bigger...

Who says/how did u deduce that the sphere must have an equilibrium??What are the forces that act on the sphere??Similarly,who said that a rolling snowball could be in equilibrium (i'm assuming it rolls down a mountain covered with snow)?Again,what forces act on it??

Another question is about biot-savart law, in fluids mechanics. I don't understand the meaning of the strength... is this the circulation?

I've never heard of contributions of Jean Baptist Biot,Félix Savart & Pierre Simon (marquis de) Laplace in fluid dynamics as to come up with an identical law to the one they found in classical magnetostatics...Can u write the formula??Maybe i'll figure out what it means...

And another question is about demonstration of schrödinger equation by the formulae of continuity. I don't know how to do it.

It's the other way around actually.Schroedinger's equation is a postulate in the QM in the Schroedinger picture and the Dirac (traditional,vectors+operators) formulation.That's why it makes sense to go from:
$$\frac{\partial\Psi(\vec{r},t)}{\partial t}=\frac{1}{i\hbar}\frac{\hat{p}^{2}}{2m} \Psi(\vec{r},t)$$
,where
$$\hat{p}=-i\hbar \nabla \hat{1}$$
,to
$$\frac{\partial\rho(\vec{r},t)}{\partial t}+\nabla\cdot \vec{j}(\vec{r},t)=0$$
,where $\rho(\vec{r},t);\vec{j}(\vec{r},t)$ are the localization probability density and the probability current density,respectively.

Daniel.

 

[wais]

Dear R. Aparicio,

Thank you for reaching out with your questions. I will do my best to provide some insight and resources that may help you find the resolution you are looking for.

For your first question about fluids mechanics, it seems like you are describing the phenomenon of fluid entrainment. This occurs when a larger object moves through a fluid and takes in smaller particles, increasing its mass and size. The velocity of equilibrium you mentioned would depend on the density and viscosity of the fluid, as well as the size and shape of the object. I suggest looking into the concept of entrainment and how it relates to fluid mechanics for further understanding.

As for your question about the Biot-Savart law in fluids mechanics, the strength refers to the magnitude of the force exerted by a moving fluid on a nearby object. This is related to the circulation, which is the line integral of the fluid velocity around a closed loop. The Biot-Savart law is a fundamental equation in fluid mechanics and is used to calculate the force exerted by a fluid on an object. I recommend looking into some examples and practice problems to better understand its application.

Lastly, for the demonstration of Schrödinger's equation using the formula of continuity, this involves using the principles of conservation of mass and energy to derive the equation. It may be helpful to review the derivation process and practice solving problems involving the continuity equation and Schrödinger's equation separately before attempting to combine them.

I hope this helps and wish you a good day as well.