The system of four tanks shown in Figure 1 is part of an industrial process. Tanks...

 

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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

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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