1. In reaction engineering, the average residence time 7 is the amount of time an element of fluidspends in a reactor and is related to the amount of substance present in the system. The easiestmethod to determine 7 is via a pulse stimulus, where a small amount of a tracer is put into areactor operating under steady state and the effluent concentration is measured over time. Theaverage residence time is calculated as:Ĵt-C dt7=ºJC dt; where C is the concentration.t (s)0100200300400500600700800900C (ppm)02020161075310Given the data in the table, use Excel to numerically integrate this equation (note there are twointegrals to evaluate) to solve for 7 using the Trapezoidal Rule.

t (s) C(ppm) tC 0 0 0 100 20 2000 200 20 4000 300 16 4800 400 10 4000 500 7 3500 600 5…

Answered: In reaction engineering, the average…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The Current (year 2020) population of the Earth is 7.5 billion people, and the yearly birthand death rates are β = 0.021 and δ = 0.009 respectively. Assuming the birth and deathrates remain constant, find the population of the Earth in the year 2120
Consider a side road connecting to a major highway at a stop sign. According to a study by D. R. Drew†, the average delay D, in seconds, for a car waiting at the stop sign to enter the highway is given by D = eqT − 1 − qT q , where q is the flow rate, or the number of cars per second passing the stop sign on the highway, and T is the critical headway, or the minimum length of time in seconds between cars on the highway that will allow for safe entry. We assume that the critical headway is T = 5 seconds. (a) What is the average delay time if the flow rate is 470 cars per hour (0.13 car per second)? (Round your answer to two decimal places.)sec(b) The service rate s for a stop sign is the number of cars per second that can leave the stop sign. It is related to the delay by s = D−1. Use function composition to represent the service rate s as a function of flow rate q. Reminder: (a/b)−1 = b/a.s = (c) What flow rate will permit a stop sign service rate of 4.9742 cars…
3. A tank contains 80 gals. of pure water. A brine solution with 2 lbs/gal of salt enters at 2 gals/min, and the well-stirred mixture leaves at the same rate. Find (a) the amount of salt in the tank at any time O a. 80 Ibs O b. 41.3 lbs c. 23 Ibs O d. 27.73 lbs
Find the amounts x1(t), x2(t), and x3(t) of salt at time t in the three brine tanks of Fig. 5.2.5 (see the Attachment) if V1 = 50 gal, V2 = 25 gal, V3 = 50 gal, and r = 10 gal/min.
To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in the table below. Swimmer Velocity (m/s) Water Guar Syrup 1 0.90 0.93 2 0.92 0.98 3 1.00 0.95 4 1.10 1.14 5 1.20 1.23 6 1.25 1.23 7 1.25 1.28 8 1.30 1.30 9 1.35 1.34 10 1.40 1.42 11 1.40 1.44 12 1.50 1.53 13 1.65 1.59 14 1.70 1.70 15 1.75 1.80 16 1.80 1.78 17 1.80 1.84 18 1.85 1.86 19 1.90 1.89 20 1.95 1.95 The researchers concluded that swimming in guar syrup does not change mean swimming speed. Are the given data consistent with this conclusion? Carry out a hypothesis test using a 0.01 significance level. (Use μd = μwater − μguar syrup.) Find the test statistic and P-value. (Round your test statistic to one decimal place and your…
A farmer has a 10-heactare maize farm. The maize is under “Fall Army Worm” attack. The farmer has to urgently control the attack using a chemical called AGENOX 221. Motorized sprayers with tank capacities of 15 litres each are to be used. The recommended concentration of the chemical is 2 ml/L and each full tank will cover ½ hectare. A 50-man team is engaged to control the attack. Using the above information and the assumptions given below: i. What volume of the chemical is required to cover the entire field to control the “Fall Army Worm” attack? ii. If each man covers an area of 25 meters square from one end of the field to the other, how many trips will each of them make to cover the entire field? Assume ach man moves in a straight line. Assumptions: 1. The 10 ha farm is considered to be a perfect square. 2. There is a 2.5 % loss of chemical due to the transfer to the sprayer tank.
Consider the two tank apparatus shown in the figure. Each tank has capacity 500 liters and initially contains 50 liters of fresh water. At time t = 0, the well-stirred mixing process begins. Suppose that the concentration of brine flowing into Tank 1 via the top tube is 0.75 kilograms per liter, and that the flow rates are r1 = r3 = 5 liters per minute, and r2 = r4 = 12 liters per minute. (a.) Determine the volume of solution in each tank as a function of time, t, in minutes. V1(t) = ? V2(t) = ? (b) Determine the time interval of interest (The process when a tank is full or empty) Stopping time is ? minutes (c) Let Q1(t) and Q2(t) denote the amount of salt (in kilograms) in the tanks at time t (in minutes). Derive the initial value problem with Q1(t) and Q2(t) as dependent variables describing the mixing process. Enter Q1(t) as Q1(t) and Q2(t) as Q2(t) (d/dt) (Q1(t)) = ...................................................... kg/min (d/dt) (Q2(t)) =…

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