The system of four tanks shown in Figure 1 is part of an industrial process. Tanks...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The system of four tanks shown in Figure 1 is part of an industrial process. Tanks A, B, C, and D have fluid heights of x, y, h, and z (in meters) respectively. Fluid flows into tank A at rate of um'/min. The fluid flows and directions are indicated in Figure 1. For example, the fluid in tank A flows into tank 8 at a rate which is dependent on the height of fluid in the tanks: 6/x- y). Fluid also flows from tank A to tank C at a rate of (F+1)(x-h) and from tank D back to tank A at a rate of (x-z). U=G+10 (F+1)(h) (x-2) 22-y) LD 12y Figure 1 Take Gas the fourth digit and F as the fifth digit of your URN. If your URN is 6835725 then G -5, F-7, and u = (5+10)=15. Write the value of F, G, and u at the top of your solution. A a) Assuming that the system is at a steady state, and the fluid entering each tank is exactly equal to the fluid leaving the tank, () Show that the system of equations for the height of fluid in each tank can be written as (substitute your values of F and u, see above): (6+F)x-6y+z=(1+F)h = z 6x-10y +2z=0 (1+F)x+ 4z -(6+F)h = 0 x-2y +82-4h=0 i) write this system of equations in matrix form b) Using matrix methods, solve for the fluid heights in each tank (x, y, h, z) c) [3] d) Tank 8 and all its connections are now removed (all remaining connections and flow rates between tanks A, C, and D, remain as shown in Figure 1). 121 [20] Discuss the constraints of the physical system shown in Figure 1 that can be used to check if your solution is correct. Check your solution to (b) against these constraints (3) i) Draw a labelled sketch of the new system of tanks and write the corresponding set of equations in matrix form Calculate the determinant of the coefficient matrix in d(). [5] i) [10] ) What does the value you obtained indicate about the solution of the system of equations (do not solve the system of equations)? [21 The system of four tanks shown in Figure 1 is part of an industrial process. Tanks A, B, C, and D have fluid heights of x, y, h, and z (in meters) respectively. Fluid flows into tank A at rate of um'/min. The fluid flows and directions are indicated in Figure 1. For example, the fluid in tank A flows into tank 8 at a rate which is dependent on the height of fluid in the tanks: 6/x- y). Fluid also flows from tank A to tank C at a rate of (F+1)(x-h) and from tank D back to tank A at a rate of (x-z). U=G+10 (F+1)(h) (x-2) 22-y) LD 12y Figure 1 Take Gas the fourth digit and F as the fifth digit of your URN. If your URN is 6835725 then G -5, F-7, and u = (5+10)=15. Write the value of F, G, and u at the top of your solution. A a) Assuming that the system is at a steady state, and the fluid entering each tank is exactly equal to the fluid leaving the tank, () Show that the system of equations for the height of fluid in each tank can be written as (substitute your values of F and u, see above): (6+F)x-6y+z=(1+F)h = z 6x-10y +2z=0 (1+F)x+ 4z -(6+F)h = 0 x-2y +82-4h=0 i) write this system of equations in matrix form b) Using matrix methods, solve for the fluid heights in each tank (x, y, h, z) c) [3] d) Tank 8 and all its connections are now removed (all remaining connections and flow rates between tanks A, C, and D, remain as shown in Figure 1). 121 [20] Discuss the constraints of the physical system shown in Figure 1 that can be used to check if your solution is correct. Check your solution to (b) against these constraints (3) i) Draw a labelled sketch of the new system of tanks and write the corresponding set of equations in matrix form Calculate the determinant of the coefficient matrix in d(). [5] i) [10] ) What does the value you obtained indicate about the solution of the system of equations (do not solve the system of equations)? [21 The system of four tanks shown in Figure 1 is part of an industrial process. Tanks A, B, C, and D have fluid heights of x, y, h, and z (in meters) respectively. Fluid flows into tank A at rate of um'/min. The fluid flows and directions are indicated in Figure 1. For example, the fluid in tank A flows into tank 8 at a rate which is dependent on the height of fluid in the tanks: 6/x- y). Fluid also flows from tank A to tank C at a rate of (F+1)(x-h) and from tank D back to tank A at a rate of (x-z). U=G+10 (F+1)(h) (x-2) 22-y) LD 12y Figure 1 Take Gas the fourth digit and F as the fifth digit of your URN. If your URN is 6835725 then G -5, F-7, and u = (5+10)=15. Write the value of F, G, and u at the top of your solution. A a) Assuming that the system is at a steady state, and the fluid entering each tank is exactly equal to the fluid leaving the tank, () Show that the system of equations for the height of fluid in each tank can be written as (substitute your values of F and u, see above): (6+F)x-6y+z=(1+F)h = z 6x-10y +2z=0 (1+F)x+ 4z -(6+F)h = 0 x-2y +82-4h=0 i) write this system of equations in matrix form b) Using matrix methods, solve for the fluid heights in each tank (x, y, h, z) c) [3] d) Tank 8 and all its connections are now removed (all remaining connections and flow rates between tanks A, C, and D, remain as shown in Figure 1). 121 [20] Discuss the constraints of the physical system shown in Figure 1 that can be used to check if your solution is correct. Check your solution to (b) against these constraints (3) i) Draw a labelled sketch of the new system of tanks and write the corresponding set of equations in matrix form Calculate the determinant of the coefficient matrix in d(). [5] i) [10] ) What does the value you obtained indicate about the solution of the system of equations (do not solve the system of equations)? [21 The system of four tanks shown in Figure 1 is part of an industrial process. Tanks A, B, C, and D have fluid heights of x, y, h, and z (in meters) respectively. Fluid flows into tank A at rate of um'/min. The fluid flows and directions are indicated in Figure 1. For example, the fluid in tank A flows into tank 8 at a rate which is dependent on the height of fluid in the tanks: 6/x- y). Fluid also flows from tank A to tank C at a rate of (F+1)(x-h) and from tank D back to tank A at a rate of (x-z). U=G+10 (F+1)(h) (x-2) 22-y) LD 12y Figure 1 Take Gas the fourth digit and F as the fifth digit of your URN. If your URN is 6835725 then G -5, F-7, and u = (5+10)=15. Write the value of F, G, and u at the top of your solution. A a) Assuming that the system is at a steady state, and the fluid entering each tank is exactly equal to the fluid leaving the tank, () Show that the system of equations for the height of fluid in each tank can be written as (substitute your values of F and u, see above): (6+F)x-6y+z=(1+F)h = z 6x-10y +2z=0 (1+F)x+ 4z -(6+F)h = 0 x-2y +82-4h=0 i) write this system of equations in matrix form b) Using matrix methods, solve for the fluid heights in each tank (x, y, h, z) c) [3] d) Tank 8 and all its connections are now removed (all remaining connections and flow rates between tanks A, C, and D, remain as shown in Figure 1). 121 [20] Discuss the constraints of the physical system shown in Figure 1 that can be used to check if your solution is correct. Check your solution to (b) against these constraints (3) i) Draw a labelled sketch of the new system of tanks and write the corresponding set of equations in matrix form Calculate the determinant of the coefficient matrix in d(). [5] i) [10] ) What does the value you obtained indicate about the solution of the system of equations (do not solve the system of equations)? [21
Expert Answer:
Answer rating: 100% (QA)
Total Equations are 4 8 h 13 x 6 y z 151 0 h 6 x 10 y 2 z 02 13 h 8 x 0 y 4 z 03 4 h x 2 y 8 z 04 Co... View the full answer
Related Book For
Smith and Roberson Business Law
ISBN: 978-0538473637
15th Edition
Authors: Richard A. Mann, Barry S. Roberts
Posted Date:
Students also viewed these mathematics questions
-
Four mutually exclusive events A, B, C and D have probabilities of 0.1, 0.2, 0.3 and 0.4 respectively. What are the probabilities of the following occurring? (a) A and B, (b) A or B, (c) Neither A...
-
In the marginal-productivity theory shown in Figure 1 2-8, let land rather than labor be the varying input. Draw a new figure and explain the theory with this new diagram. What is the residual factor?
-
(a) A beam as shown in Figure 1 is subjected to a point load of P kN at point B and a concentrated moment of M kNm at point E. Flexural rigidity for spans AC and CE are 2EI and EI, respectively....
-
On the cost of goods manufactured schedule, depreciation onfactory equipment... A. is not listed because it is not a product cost. B. is not an inventoriable cost. C. is not listed because it is...
-
The records of Rangler Paper Company provided the selected data given below for the reporting period ended 31 December 20X5. Statement of financial position data Paid cash...
-
Name three entry modes used to input a circuit description into PLD development software
-
Suppose that in the preceding exercise the first measurement is recorded incorrectly as 16.0 instead of 14.5. Show that, even though the mean of the sample increases to \(\bar{x}=14.7\), the null...
-
Vidro Company prepares monthly cash budgets. Relevant data from operating budgets for 2011 are: All sales are on account. Collections are expected to be 60% in the month of sale, 30% in the first...
-
Marco Company shows the following costs for three jobs worked on in April. Job 306 Job 307 Job 308 Balances on March 31 Direct materials used (in March) Direct labor used (in March) Overhead applied...
-
The Community Youth Center (CYC) Corporation failed to pay its annual registration fee in 2000 and was automatically dissolved by the State Corporation Commission. CYC continued to operate as a...
-
Describe how an incentive payment made in one year will affect base pay in the nest year
-
After WorldCom acquired UUNet, it had broadband and networks all over the world and had become a ________________ provider of Internet access and data transmission.
-
A crime fighter might not immediately come to mind when most people think about the role an accountant plays in everyday business. Yet the rapidly growing field of forensic accounting involves...
-
If a company overstates merger reserves at the time of acquiring another company, it can release the surplus reserves into earnings in a later period without decreasing net income at the time of the...
-
WorldCom overstated its sales by holding its books open at the close of a reporting period. True/False
-
When a company overstates reserves at the time of acquisition, in later periods, it can release the ________________ reserves back into earnings.
-
In the universe of investment, risks are usually classified into two types; one is systematic risk and the other unsystematic one. However, a prominent theory says that in the efficient market,...
-
An item of depreciable machinery was acquired on 1 July 2009 for $120,000 by cash It is expected to have a useful life of 10 years and zero salvage value On 1 July 2012, it was decided to revalue the...
-
The City of Richmond, Virginia, adopted a Minority Business Utilization Plan requiring prime contractors awarded city construction contracts to subcontract at least 30 percent of the dollar amount of...
-
On November 1, the Kansas City Post Office Employees Credit Union merged into the Kansas City Telephone Employees Credit Union to form the Communications Credit Union (Credit Union). Systems Design...
-
Six U.S. manufacturers of broad-spectrum antibiotics derived a large percentage of their sales from overseas markets, including India, Iran, the Philippines, Spain, the Republic of Korea, Germany,...
-
A mixture of benzene and monochlorobenzene is to be separated into almost pure products by distillation. Determine an appropriate operating pressure at the top of the tower.
-
The feed to a distillation tower consists of \(14.3 \mathrm{kmol} / \mathrm{hr}\) of methanol, \(105.3 \mathrm{kmol} / \mathrm{hr}\) of toluene, \(136.2 \mathrm{kmol} / \mathrm{hr}\) of ethylbenzene,...
-
In a reboiled absorber, operating as a deethanizer at 400 psia to separate a light hydrocarbon feed, conditions at the bottom tray are: Liquid Phase Molar flow = 1, \(366 \mathrm{lbmol} /...
Study smarter with the SolutionInn App