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You are a process control engineer in a water purification plant. In a certain subprocess, water enters a tank through an inlet at a rate of q; and leaves through an outlet at a rate of q.. Liquid flow is maintained such that q; > 9, at any given time. It has been found that the difference between q; and q. is equal to the product of the surface area of the tank bottom A and the rate of change of the liquid column height in the tank h with respect to time. If the variation of h is continuous with respect to time, a. formulate a first-order differential equation to describe the situation. b. It was found that the outlet flow rate depends on the height of the liquid column and is given by q, = 4.429 × 10-³h m³/s. Furthermore, given that A = (0.72) m², q; = 0.003 m /s and that h = 1 m when t = 0 s, solve the differential equation formulated in (a) to find the relationship between the liquid column height h and the time taken t. c. Verify your answer in (b) using another method of solving the differential equation (e.g. Laplace transforms).

You are a process control engineer in a water purification plant. In a certain subprocess, water enters a tank through an inlet at a rate of q; and leaves through an outlet at a rate of q.. Liquid flow is maintained such that q; > 9, at any given time. It has been found that the difference between q; and q. is equal to the product of the surface area of the tank bottom A and the rate of change of the liquid column height in the tank h with respect to time. If the variation of h is continuous with respect to time, a. formulate a first-order differential equation to describe the situation. b. It was found that the outlet flow rate depends on the height of the liquid column and is given by q, = 4.429 × 10-³h m³/s. Furthermore, given that A = (0.72) m², q; = 0.003 m /s and that h = 1 m when t = 0 s, solve the differential equation formulated in (a) to find the relationship between the liquid column height h and the time taken t. c. Verify your answer in (b) using another method of solving the differential equation (e.g. Laplace transforms).

Advanced Engineering Mathematics
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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i need part a, part b and part c

4. You are a process control engineer in a water purification plant. In a certain subprocess, water enters a tank through an inlet at a rate of q; and leaves through an outlet at a rate of q. Liquid flow is maintained such that q; > 9, at any given time. It has been found that the difference between q; and q, is equal to the product of the surface area of the tank bottom A and the rate of change of the liquid column height in the tank h with respect to time. If the variation of h is continuous with respect to time, a. formulate a first-order differential equation to describe the situation. b. It was found that the outlet flow rate depends on the height of the liquid column and is (0.72) m², q; = 0.003 m³ /s and that h = 1 m when t = 0 s, solve the differential equation formulated in (a) to find the relationship between the liquid column height h and the time taken t. given by q, = 4.429 x 10-3h m³/s. Furthermore, given that A = c. Verify your answer in (b) using another method of solving the differential equation (e.g. Laplace transforms).
Transcribed Image Text:4. You are a process control engineer in a water purification plant. In a certain subprocess, water enters a tank through an inlet at a rate of q; and leaves through an outlet at a rate of q. Liquid flow is maintained such that q; > 9, at any given time. It has been found that the difference between q; and q, is equal to the product of the surface area of the tank bottom A and the rate of change of the liquid column height in the tank h with respect to time. If the variation of h is continuous with respect to time, a. formulate a first-order differential equation to describe the situation. b. It was found that the outlet flow rate depends on the height of the liquid column and is (0.72) m², q; = 0.003 m³ /s and that h = 1 m when t = 0 s, solve the differential equation formulated in (a) to find the relationship between the liquid column height h and the time taken t. given by q, = 4.429 x 10-3h m³/s. Furthermore, given that A = c. Verify your answer in (b) using another method of solving the differential equation (e.g. Laplace transforms).
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