Mass conservation Definition and 22 Threads

I calculate 4.8x10(^10) particles /kg of sand in the sample. Do you find the same ? Is my solution correct ? How many particles do you find ? Thanks in advance !

Emmy Nöther proved that mathematically, if a certain quantity is conserved, there must be a corresponding symmetry somewhere. Momentum conservation stems from spatial symmetry, charge conservation stems from complex phase symmetry at the quantum level and energy conservation stems from time...

I am not sure what form of mass conservation to use to solve the above problem from An Introduction to Combustion by Stephen Turns. Can anyone explain what form of mass conservation applies to a sphere in this context?

Summary:: Control volume question that has a brine solution entering a tank and mass accumulates over time. Hello, I'm currently struggling with a control volume approach question that has a brine solution entering a tank. I get to a point where I have a first order differential equation. I...

I understand that ##\dot m=\rho Q## and ##{\dot m}_{in}= {\dot m}_{out}## . So one can say that ##\rho Q_1 = \rho Q_2##. But I'm not sure if that equation is correct. I don't know if the density remains constant, or the volume flow rate. And then how I'm also supposed to tie a state equation in...

Ignoring cross-diffusion, diffusive mass fluxes down chemical potential gradients can be described by the equation (I am working from de Groot and Mazur's 1984 text on non-equilibrium thermodynamics): \frac{\partial C_k}{\partial t} = L_{kk}\frac{\partial (\mu_k-\mu_n)}{\partial x} where C_k...

Hi guys, quick simple question. Lets say I have a pipe separated into 3 sectoins (all horizontal), all have the same flow areas. In the first section it is all liquid water. I know the mass flow rate in this. In the second section the water is heated. And I can work out the steam quality...

I've always understood that there's a fnite amount of mass energy in the universe, please correct me if this view is out of date. As a particle accelerates it's mass increases how does this square with not being able to create mass or energy?

Hi guys! This is related to a recent thread but since that thread became cluttered, I figured it would be more coherent to just ask the question here. Say we have a congruence of charged dust particles in some space-time with tangent field ##\xi^a##. The energy-momentum of the charged dust is...

Hi, I'm trying to understand the mass conservation equation for a pulsating sphere which has thickness dr. Please refer to the attached solution. \rho = \rho_{0} (ambient density) + \rho' (small deviation) There are two things I don't follow. First, is that to obtain the mass, the area of...

Homework Statement I will honestly be so grateful if someone can explain this to me. I am studying the Reynolds transport theorem, particularly mass conservation. I have read over my notes and I really do not understand how to calculate the mass flow rate through the control surface if it...

Hello i want to solve \frac{\partial \rho}{\partial t}=\frac{\partial v_1\rho}{\partial x_1}+\frac{\partial v_2\rho}{\partial x_2} for v_1 = -x_2 and v_2=x_1 i obtain equation \frac{\partial \rho}{\partial t}+x_2\frac{\partial\rho}{\partial x_1}-x_1\frac{\partial \rho}{\partial...

Good Morning to all I saw this problem in one of the courses that I am taking this semester. It is very simple, it consists of an open conical tank being filled in the upper part with an stream (which is assumed to be cylindrical) of water (flow Qi through an area Ai). At the bottom of the...

Homework Statement Starting off with a general axisymmetric metric: ds^{2}=g_{tt}dt^{2}+2g_{t\phi }dtd\phi + g_{\phi \phi }d\phi^{2} +g_{rr}dr^2 + g_{\theta \theta }d\theta ^2...\left ( 1 \right ) where the metric components are functions of r and theta only. I have deduced (using...

Homework Statement Starting from a general axisymmetric metric ds^2=g_tt dt^2 + 2g_tφ dtdφ +g_φφ dφ^2 + g_rr dr^2+g_θθ dθ^2 ...(0) where the metric components are functions of the coordinates r and θ only. I've managed to show (via Euler-Lagrange equations) that g_tt dt/dτ + g_tφ...

Dear all, I'm trying to solve the 2d heat equation in a radially symmetric domain, numerically using the Crank-Nicolson method. i.e. \dfrac{\partial u}{\partial t} = D\left( \dfrac{\partial^2u}{\partial r^2}+\dfrac{1}{r}\dfrac{\partial u}{\partial r}\right) Applying the Crank-Nicolson...

Homework Statement integrate [(rs^2)*(rhos)*(us)*(db/dr)=(d/dr)*(r^2)*(rho)*(D)*(db/dr))] rs=radius at surface rhos=density at surface us=velocity at surface r = radius rho = density D= diffusivity b=spalding non-dimensional parameter Homework Equations The Attempt at a...

I realize that to calculate heat being released and contained during nuclear reaction you must understand the difference between its product mass and reactant mass by using *E=mc2.* My Question pertains to the heat being released during a chemical reaction... Is Mass conserved in this chemical...

Part of the mechanics course I'm taking this semester are also fluids, but the material our teacher gave us to this topic is very poor (but unfortunately I haven't found a better source). The problem is that there are many "magic formulas", which come just out of nowhere - without any...

so i got this HW prob, and i don't know exactly where to start, Oil flows steadily in a thin layer down an inclined plane. The velocity profile is u = [(density)(g)(sin theta) / Mu] [(hy - (0.5)y^2] express the mass flow rate per unit width in terms of density, Mu, g, theta, and h...

In the Meson theory of nuclear forces, exchange of pi meson is given by: n\rightarrow n + \pi^{0} p\rightarrow p + \pi^{0} n\rightarrow p + \pi^{-} p\rightarrow n + \pi^{+} Here the charge is conserved. But I don't understand how mass conservation takes place as in some of the cases a...

Hello all, In beta-plus decay, a proton decays into a neutron and emmits a positron. If the neutron weighs more than the proton where did the extra mass come from?