Continuity equation Definition and 88 Threads

Suppose I have two charged particles with charge densities ρ1(r,t) and ρ2 (r,t) with corresponding velocity fields V1(r,t) and V2(r,t). Can I write continuity equation for the combined system? Wouldn't charges moving with different velocities would contribute differently to the current which...

Homework Statement Follow the link to see the question, http://img507.imageshack.us/img507/2246/fluidquestion.png Homework Equations The Attempt at a Solution currently I can't do part a) but from using part a) I can obtain the forces acting on the cone by using the first...

Hello everybody! I am using in my studies this beautiful book by Kippenhahn & Weigert, "Stellar Structure and Evolution", but I have some problems about collapsing polytropes (chapter 19.11)... After defining dimensionless lenght-scale z by: r=a(t)z and a velocity potential \psi...

Why is partial derivative with respect to time used in the continuity equation, \frac{\partial \rho}{\partial t} = - \nabla \vec{j} If this equation is really derived from the equation, \frac{dq}{dt} = - \int\int \vec{j} \cdot d\vec{a} Then should it be a total derivative with...

What does it mean if the continuity equation equals a complex number (rather than zero)? I ask this in the context of the probability current.

Continuity equation is dj+\partial_t\rho_t=0 where j and \rho are a time-dependent 2-form and a time-dependent 3-form on the 3-dimensional space M respectively. (see e.g. A gentle introduction to the foundations of classical electrodynamics (2.5)) If we use differential forms on the...

Hi! I'm trying to implement an implicit scheme for the continuity equation. The scheme is the following: http://img28.imageshack.us/img28/3196/screenshot20111130at003.png With \rho being the density, \alpha is a weighing constant. d is a parameter that relates the grid spacing to the...

Homework Statement Skill Level II Problem Use the Continuity equation to explain how jet engines provide a forward thrust for an airplane. Skill Level Problem III The Contintuity Equation is related to a powerful equation from fluid dynamics called Bernoulli's Equation. Do the research...

Homework Statement Consider the cross section of a sluice gate, which is a device for controlling the flow of water in channels. Determine the force on the gate per unit width of the gate. Hint: think of each line as a surface, with the length given above, and 1 foot of depth in the direction...

Homework Statement A pipe tapers from a diameter of 0.5 m at the inlet to a diameter of 0.25 m at the outlet, and turns by an angle of 45 degrees. The gauge pressure at the inlet and the outlet are 40000 N/m2 and 23000 N/m2, respectively. The pipe carries oil, with a density of 850 kg/m3, at a...

Homework Statement Derive a microscopic version of the continuity equation given \rho(\vec{r},t) = \sum_{i=1}^N \delta(\vec{r}-\vec{q}_i(t)) and \rho is dynamic variablesHomework Equations I wonder if someone can point out the difference (in general) between the macroscopic and microscopic...

Is there such an animal as an energy continuity equation, or one involving Pmu or the stress energy tensor? It suddenly stuck me that if we are to be so inclined by theory as we are by empirical evidence that energy is a conserved quantity, then there should be an equation that describes it in...

Homework Statement I am working on a problem that asks to use the integral form of the continuity equation (for a steady flow) and show that it can equal this (by taking the derivative of it): dr/r + dV/V + dA/A = 0 where V is Velocity and r is the density. Homework Equations What would...

Homework Statement The density in 3-D space of a certain kind of conserved substance is given by \[\rho (x,y,z, t) = At^{-\frac{3}{2}}e^{-\frac{r^2}{4kt}}\] where \mathbf r = x\mathbf i + y\mathbf j +z\mathbf k and r = |\mathbf r|. The corresponding flux vector is given by \mathbf...

Homework Statement I am having problems understanding the differential form of the conservation of mass. Say we have a small box with sides \Delta x_1, \Delta x_2, \Delta x_3. The conservation of mass says that the rate of accumulated mass in a control volume equals the rate of mass going in...

Hi. I have a new one! Prove that if V \left(\stackrel{\rightarrow}{r} , t \right) is complex the continuity equation becomes \frac{\partial}{\partial t}P \left(\stackrel{\rightarrow}{r},t \right)+\nabla \stackrel{\rightarrow}{j} \left(\stackrel{\rightarrow}{r},t \right) = \frac{2}{h} \int...

The Schrodinger equation with the minimal coupling to the Electromagnetic field, in the Coulomb gauge \nabla \cdot A , has a continuity equation \partial_t \rho = \nabla \cdot j where j \propto Re[p^* D p] (D is the covariant gradient D= \nabla + iA . My question is: is there any...

Next question: A garden hose with internal diameter of 13.5 mm lies flat on a sidewalk while water is flowing in it at a speed of 6 m/s. A person happens to step on it at the very edge of the opening of the hose and decreases its internal diameter by a factor of 9 So D (1) = 0.0135m r (1) =...

I'm reading my fluids chapter in my University Physics textbook. We actually didn't go over this in my University Physics I course. :rolleyes: At any rate, I'm looking at the equation of continuity. In explaining it, it says the flow rates through two areas have to be the same because there is...

To solve \frac{\partial\varrho}{\partial t}+\mathrm{div}(\varrho\vec{v})=0

Dear All, I need help on the following issue. Assuming the flow to be potential, I want to compute the potential given the density at all times, that is : From the continuity equation: \partial _t \rho + \nabla \cdot \left( {\rho \nabla \phi } \right) = 0 One can write down an...

Homework Statement A Bose-Einstein condensate can be described by a wave function \psi(x,t) = \sqrt{\rho(x,t)}e^{i\phi(x,t)} Where the functions: \phi(x,t) and \rho(x,t) are real. a) What is the probability density b) Calculate the probability current density as...

Homework Statement Question Details: The question reads: Show that the equation: dA/A + dv/v + dρ/ρ = 0 applies to a one-dimensional steady flow. (Here 'one dimensional' means that both the density ρ and seed v = - v . n (vectors) are constant across any cross-sectional area A...

Homework Statement Given the Hamiltonian H=\vec{\alpha} \cdot \vec{p} c + mc^2 = -i \hbar c \vec{\alpha} \cdot \nabla + mc^2 in which \vec{\alpha} is a constant vector. Derive from the Schrödinger equation and the continuity equation what the current is belonging to the density \rho...

Homework Statement Hi. I have a problem in fluid mechanics that is asking me to derive the conservation of mass equation using an infinitesimal control volume. My problem is I do not know if I should be treating this problem as a fixed element or if the element is a parcel and its...

It is true that \frac{\partial}{\partial x^\beta} T^{0 \beta} = \gamma^2 c \left( \frac{\partial \rho}{\partial t} + \vec{\nabla} \bullet \left[ \rho \vec{v} \right] \right) = 0 but, how do we arrive at this point? What is in T^{ \alpha \beta} and how do we compute it for any...

For the continuity equation (Q= Av, A is cross sectional area, v is velocity), is it independent of the radius of the pipe? If so, why?

So I am trying to derive the continuity equation: \frac{\partial}{\partial x^{\mu}}J^{\mu} = 0 From the Dirac equation: i\gamma^{\mu} \frac{\partial}{\partial x^{\mu}}\Psi - \mu\Psi = 0 And its Hermitian adjoint: i\frac{\partial}{\partial x^{\mu}}\overline{\Psi}\gamma^{\mu} -...

Homework Statement The inside diameters of the larger portions of the horizontal pipe as shown in the image (attached) are 2.50 cm. Water flows to the right at a rate of 1.80*10^4 m^3/s. What is the diameter of the constriction. Homework Equations Continuity equation Rate of Volume...

I have this one as well, using the continuity equation to explain how a jet engine provides a foward thrust for an airplane. I have the equation but can some one explain this to me in laymen's terms. \frac{\partial\rho\left(\vec{r},t\right)}{\partial...

Homework Statement I'm new here and I would like to ask a simple Q: what is the physical meaning of the continuity equation from (electrodynamic 1) I mean it's related to the electromagnatic problems Homework Equations The Attempt at a Solution I know the answer in my language...

Help! I am stuck on the following derivation: Use the conservation of mass to derive the corresponding continuity equation in cylindrical coordinates. Please take a look at my work in the following attachments. Thanks! =)

Hello, I need the derivation of "continuity equation" by the current density equation,in Quantum Mechanics. I really need this derivation quickly,please Thanks

Most of you are probably familiar with the continuity equation, but what does the term "continuity" mean? I mean, what is continuous in the context of the continuity eq.? Just wondering...

Any help would be appreciated - The water flowing through a 1.9 cm (inside diameter) pipe flows out through three 1.3 cm pipes. (a) If the flow rates in the three smaller pipes are 28, 15, and 10 L/min, what is the flow rate in the 1.9 cm pipe? The basic continuity idea is A1v1 = A2v2...

Well we start out with -\frac {d} {dt} \int_{V}^{} \sigma dV = \int_{\Pi}^{} \vec{J} \cdot d\vec{\Pi} Using the Gauss theorem \int_{V}^{} (\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J}) dV = 0 so \frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J} = 0 and written in 4D...

i do not understand how the continuity equation works?

Hi guys. I am solving the axisymmetric free jet of an incompressible fluid. But I have troubles at r=0. Continuty equation can be written in cylindrical coordinates as: 1/r*d(rv)/dr + du/dz=0 v=radial velocity (v=0 at r=0) u=axial velocity. hz=delta(z) hr=delta(r) What happens at...