Chapter 16, Problem 2SSP

.NET Interactive Solving Sudoku using Grover's Algorithm We will now solve a simple problem using Grover's algorithm, for which we do not necessarily know the solution beforehand. Our problem is a 2x2 binary sudoku, which in our case has two simple rules: •No column may contain the same value twice •No row may contain the same value twice If we assign each square in our sudoku to a variable like so: 1 V V₁ V3 V2 we want our circuit to output a solution to this sudoku. Note that, while this approach of using Grover's algorithm to solve this problem is not practical (you can probably find the solution in your head!), the purpose of this example is to demonstrate the conversion of classical decision problems into oracles for Grover's algorithm. Turning the Problem into a Circuit We want to create an oracle that will help us solve this problem, and we will start by creating a circuit that identifies a correct solution, we simply need to create a classical function on a quantum circuit that…

4) A fixed bed adsorption unit contains rigid (incompressible) silica particles with a diameter of 120 um and porosity of 0.3. The resin bed is 200 cm long and has a diameter of 15 cm. A protein solution is pumped into the column at a rate of 50 L/min, and the mobile phase has a viscosity of 1.2 CP. a) What is the pressure drop for this system (in bar)? b) What would be the pressure drop if the particle diameter were decreased to 30 μm?

You are part of a team constructing a pipeline to transfer shale gas produced at the oceanfloor to the coastline. The temperature of the pipeline is nearly constant at 2 oC. The pipelineis made of smooth stainless steel and is 0.3 m in diameter and 100 m long. The averagevelocity of shale gas is 10 m/s and the inlet temperature is 20 oC ** Useful shale gas properties at 20 oC (Table A-12 for propane gas):(use these values for calculations and validate them later)• Density (ρ) = 18.13 kg/m3• Cp = 1974 J/kg-K• Viscosity (μ) = 8.54*10-6 kg/m-s• Pr = 0.918• k = 0.01836 W/m-Ka) Is the flow laminar or turbulent? Is the flow hydrodynamically and thermally fully developed?(circle your answer below and provide justification. • Laminar vs. Turbulent• Hydrodynamically developing vs. developed• Thermally developing vs. fully developedJustification: b) Calculate convective heat transfer coefficient (h). c) Calculate the exit temperature of the shale gas. d) Are the shale gas properties…

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Water at 20 o C enters the 4 cm-diameter, 14 m-long tube at a rate of 0.8 kg/s. The surfacetemperature of the pipe is maintained at 165 o Cby condensing geothermal stream at the shellside of the heat exchanger. Use water properCesat 85 o C for all calculaCons.(a) Show that the water flow is turbulent and thermally fully developed. (b) EsCmate the heat transfer coefficient for convecCve heat transfer from the pipe to the water. For a fully developed turbulent flow within the smooth pipe, the Nu number can becalculated from the following equaCon:(c) Calculate the exit temperature of the water. (d) Share your opinion on whether the use of water properties at 85°C is appropriate. Yes or No because:

Consider a hot automotive engine, which can beapproximated as a 0.5-m-high, 0.40-m-wide, and 0.8-m-long rectangular block. The bottom surface of the block isat a temperature of 100°C and has an emissivity of 0.95.The ambient air is at 20°C, and the road surface is at25°C. Determine the rate of heat transfer from the bottomsurface of the engine block by convection and radiationas the car travels at a velocity of 80 km/h. Assume theflow to be turbulent over the entire surface because of theconstant agitation of the engine block. a) Calculate convective heat transfer coefficient (h). b) Calculate the total heat transfer rate

3) A pilot-plant Podbielniak centrifugal extractor operating at 11,400 x g (this is G₁) is capable of processing 500 mL/min of filtered fermentation broth and 125 mL/min organic solvent, giving a recovery of 95%. The rotating cylinder inside the extractor has a diameter of 20 cm and is 2.5 cm wide. You need to scale up this extraction by using a larger Podbielniak extractor that has a diameter of 91 cm and width of 91 cm and delivers 2,300 x g (G2). What flow rates (in L/min) should be used in the larger extractor to achieve the same recovery efficiency?

7) You are tasked with separating two proteins by ion exchange chromatography on a 30 cm long column with an inner diameter of 2 cm. The resin has a diameter of 100 μm and a void fraction of 0.3, and your mobile phase flows through the column at a rate of Q = 5 cm³/min. The Van Deemter coefficients A, B, and C have been determined to be 0.0228 cm, 0.0036 cm²/min, and 0.00053 min, respectively, for both proteins. Protein A elutes from the column with an average retention time of 27 min and standard deviation of 0.8 min. Protein B elutes from the column. with an average retention time of 33.8 min and standard deviation of 1.0. a) How many theoretical plates does the column contain? b) What flow rate (Q) will give you the maximum resolution? c) What is the minimum height of a theoretical plate for the system?

1 5) You are asked to design a moving bed adsorption process using two columns (see the figure below). Your feed contains 100 mg/L protein and flows through both columns at 4 m³/h. Fresh resin enters the bottom of both columns (resin does not flow from the bottom column to the top column). The maximum resin flow rate that your pumps can comfortably handle is 120 kg resin/h. Experimental data suggest that the adsorption equilibrium can be modeled as qi=4ci where qi is in g protein/kg resin and c; is in g protein/L broth. (Pay attention with units!) a) What is the lowest concentration of proteins that you could get in the effluent from column 1 (indicated by the *) in mg/L? (Hint: set up a mass balance) 0.25 , * 1 2 b) What should be the flow rate of resin (in kg/h) into the second column (B2) if your overall process needs to remove 99% of the protein?