Starting from the species mass balance derive the reaction-diffusion equation where D is diffusivity.
Identify all variables and state all assumptions
I have used DAB instead of D(ALPHA)(BETA),please apologise and replace.I have clearly mentioned the assumption and derived the above equation.
Starting from the species mass balance derive the reaction-diffusion equation where D is diffusivity. Identify all...
3) Starting at the heat diffusion equation, derive the final expression to identify the temperature profile through a 1-D, steady state, plane wall with uniform generation with one adiabatic surface (equation C.22). Using Table 3.3 & C.1, C.2, and C.3 in the appendix as well as appendix A of your textbook, answer the following questions:
B2 (a) Derive the Klein-Gordon equation (in S.I. units) starting from the energy-momentum relationship, E2 -mc4+kc2 using the quantum mechanical relations [3 Marks] (b) Write this in natural units [2 Marks] (c) Using the expression for the Laplacian in the radially symmetric case 8(3) r2 a show that the solution of the Klein-Gordon equation in the static case is (re-/R where R 1/m. You may wish to use the substitution [8 Marks] (d) Using the Heisenberg Uncertainty Principle, show that...
(6 pts) Perform a simple mass balance on the completely mixed reactor below to identify the recycled sludge concentration, X, as a function of the recycle ratio, R, and the mixed liquor concentration, x. Draw the system control boundary across which your mass balance is performed. a. b, Set-up your mass balance equation. Make sure to clearly identify inflows, outflows, rates of growth/consumption, etc., within your system; Identify ALL assumptions; c. d. e. Solve your mass balance equation for the...
Steady-state Diffusion with Chemical Reaction. One of the most studied bioarticificial organ systems is the encapsulation of islets of Langerhans cells to produce insulin in diabetic patients. They consist of islets encapsulated in a spherical gel bead. The spheres are kept at 310K, are 150 microns in diameter, and the islets consume oxygen at a rate of 25.9 mu M/s. The diffusivity of oxygen into the system is 1.67 Times 10-5 cm2/sec. The average partial pressure of oxygen at the...
Problem 4 - Steady-state Diffusion with Chemical Reaction. (20 pts) One of the most studied bioarticificial organ systems is the encapsulation of islets of Langerhans cells to produce insulin in diabetic patients. They consist of islets encapsulated in a spherical gel bead. The spheres are kept at 310K, are 150 microns in diameter, and the islets consume oxygen at a rate of 25.9 UM/s. The diffusivity of oxygen into the system is 1.67 x 10-9 cm/sec. The average partial pressure...
Starting from equation (6), derive the equation for the experimental uncertainty in wavelength due to the uncertainties in d and θ. Refer to page xx of the introduction of the lab manual for information on handling the sine function. Do not use calculus. If the ruling spacing is known and the angular position of a spectral line in a known order is measured, the wavelength of the light forming that spectral line can be calculated: dsin Obright 2=- m If...
Diffusion Mechanisms - Nonsteady State Diffusion - Copy Learning Goal: To learn how the diffusion rate changes in dynamic conditions where the diffusion profile changes with time, and how in some cases it can be modeled easily In steady stadision, the concentration Cis a function only of position (not of time). When usion is nonsteady Cis a function of position and time, Oix Nonsteady state diffusion in one direction can be modeled using Fick's Second Law -D where is the...
5. A particle of mass m slides without friction and starting from rest down a block of mass M in which the surface is shaped into a quadrant of a circle of radius R. The block also slides without friction on a table top. Choose two suitable generalized coordinates a) Using the Lagrange-multiplier formalism, find the equations of motion of the mass and the block and the reaction force of the block on the mass (ie. the constraint force b)...
4. Use the Biot-Savart law to derive Equation 1. Show all your work. Use additional paper if needed. 5 Show that for 2 Helmholtz coils with N loops, and z=a/2, Equation 2 can be derived from Equation 1. Show all your work. Use additional paper if needed. Floure 4 Connections for em Experiment Theory A charged particle moving through a magnetic field experiences a force. In this experiment, the velocity of the accelerated electrons is perpendicular to the magnetic field,...
could you please solve a and b? Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...