Species Accumulation and Transport within an Interface Accumulation and transport within an interface can be important for species that reside at phase boundaries, such as gases adsorbed on solids or surfactants at fluid-fluid interfaces. The objective is to derive more general interfacial conservation statements than those in Section 2.2. Consider a species that may be present at an interface or in either of the adjacent bulk phases. Let Cs and Ng be its surface concentration (moles m2) and surface flux (moles m¹s¹), respectively; note the differences in units from the corresponding three-dimensional quantities. The vector Ng is every- where tangent to the surface. (a) For part of an interface corresponding to surface S in Fig. A-2, state the macroscopic (integral) solute conservation equation. Assume that phase A is below S and phase B above it, such that n points toward the latter. Include the possibility of chemical reactions at the interface, trans- port to or from the bulk phases, and interfacial motion. The interface is not necessarily planar. (b) By reducing the integral equation of part (a) to a partial differential equation, show that at where N and C are the species flux and concentration, respectively, in a bulk phase. (Sub- scripts identifying the chemical species have been dropped for simplicity.) This result, which is valid instantaneously and locally, is equivalent to Eq. (5.2-2) of Edwards et al. (1991). How does it compare with what is obtained by applying Eq. (2.2-15) to a chemical species?

2. 35 points A fire truck is sucking water from a river and delivering it through a longhose to a nozzle. The total length of the galvanized iron hose - corrected for valves,fittings, entrance, etc. – is 90 [m]. The energy provided by the fire truck for pumping thewater is 53 [kJ/kg]. What hose diameter is needed for the pump to achieve an average velocity of 30[m/s]?

What are the key differences between Mass Transit and Paratransit?

^^20Given^^20\psi(x,y)=2xy+2x\vee(1.5,0.5)^^20is^^20closest^^20to,^^20m/s\colon A)-1 B) 3 C)-3 D) 0 E) 1

Consider the Navier Stokes and continuity: \text { dvidt }+v \cdot V v=f(1 / \rho) \mathrm{V} P+V \vee^{2} v+1-\mathrm{g} \mathrm{V} \cdot \mathrm{v}=0 in CV; u(x)=3; u(x+dx)=4; v(y)=5; v(y+dy)=4 Which is not true? A) dw/dz may allow d/dz and w terms to be cancelled, or it can be w(z)=w(d+dz) B) must have 3-D flow C) left side of = represents convection D) right side of represents driving force and diffusion E) only valid for constant density and viscosity (Newtonian) fluids

1. 65 points Consider a cylindrical tank of diameter D [m] initially filled with sand andwater. Water is leaving the tank through a small pipe of diameter d [m] as illustratedbelow. How long will it take for the water level to reach the bottom of the tank?(Note: At the time when the water level reaches the bottom of the tank the dischargepipe still contains water.)

A continuous belt passes upward through a chemical bath at velocity Vo and picks up a film of liquid of thickness h, density p, and viscosity u. Gravity tends to make the liquid drain down, but the movement of the belt keeps the fluid from running off completely. Assume that the flow is a well-developed laminar flow with zero pressure gradient, and that the atmosphere produces no shear at the outer surface of the film. Use the shell-balance approach to (1) derive the governing differential equations. (2) State the-boundary conditions for the systems. (3)Determine the velocity profile. Clearly list any-assumptions needed. [DO NOT sketch the velocity profile.]

4- A single-acting air compressor supplies 0.1 m³/s of air measured at, 273 K and 101.3 kN/m²which is compressed to 380 kN/m² from 101.3 kN/m². If the suction temperature is 289 K, the stroke is 0.25 m, and the speed is 4.0 Hz, what is the cylinder diameter? Assuming the cylinder clearance is 4 per cent and compression and re-expansion are isentropic (y = 1.4), what are the theoretical power requirements for the compression?

Multiple questions. Consider a fluidized bed fed with 2 atm air at 25 C; particles have density 910 kg/m3, size 0.23 mm, shape factor 0.81 and Emf = 0.4. Cross section of empty bed is 0.4 m2 and contains 250 kg solids.Find the Remf and velocity Vmf in m/s, and show work on scratch paper. Min fluidization velocity, m/s, closest to: A 0.088954B 0.001258C 0.01184D 0.006654E0.1698

Consider the system with uniform heat generation shown in the figure below the text. \text { qgen }=2 \times 10^{7} \mathrm{~W} / \mathrm{m}^{3} \text { metal thickness }=3 \mathrm{~mm} \mathrm{k}_{\text {fuel }}=60 \mathrm{~W} /(\mathrm{m} \mathrm{K}) \mathrm{k}_{\text {metal }}=18 \mathrm{~W} /(\mathrm{m} \mathrm{K}) \mathrm{h}=10,000 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K} \mathrm{T}_{\text {inf }}=200^{\circ} \mathrm{C} Inner compartment thickness = 2 L where L = 15 mm a. Derive the equation for the temperature distribution T(x) in the fuel compartment. Express your equation in terms of the above variables. (3 points) b. Calculate the maximum and minimum temperatures in the fuel compartment. (2 points) c. Repeat the calculations in part b if the insulation is removed and replaced with the same convection conditions present on the other side. (2 points) d. Write a MATLAB program that plots the temperature profile for the conditions depicted in part b.(9 points) e. Write a MATLAB program that plots the temperature profile for the conditions depicted in part c. (9 points) Note that both MATLAB programs must be m-files containing the necessary coding to generate the plots.You must submit your plots, code and calculations. This assignment must be uploaded to Blackboard by Wednesday morning no later than 10am.