Task VI: You are working in the fluid mechanics system engineering department at a firm. You have a task to determine flow rates of different valves that used to fill a tank. The tank is 2000 L that is fed by three valves with different flow rates. The flow rates (in L/min) of the three valves are x, y, and z. The three valves can be used to fill the tank in 3 scenarios. In the first scenario the three valves will fill the tank as follows, valve x will be opened for 10 mins, valve y for 4 mins, and valve z for 40 mins. Second scenario, the valve x opens for 15 mins, valve y for 2 mins, and valve z for 20 mins. Third scenario, valve x opens for 12 mins, valve y for 10 mins, and valve z for 15 mins. 图Y 2000L Tank Knowing that the tank's volume (v=2000L) as a function of three valves' flow rate is given by: x * C + y * D + z * E = 2000 L Where x, y and z represent the 1st, 2nd, and 3rd valve flow rates (L/min), C is the opening time for x valve (min), D is the opening time for y valve (min), E is the opening time for z valve (min). a) For each scenario, write an equation that relates the tank volume to the three valves flow rates. b) Rearrange the equations so that they are in the form Ax=b, where x = |y c) Define the coefficient matrix A and the constant matrix b. d) Use the matrix method to find x. v. and z flow rates. N
Task VI: You are working in the fluid mechanics system engineering department at a firm. You have a task to determine flow rates of different valves that used to fill a tank. The tank is 2000 L that is fed by three valves with different flow rates. The flow rates (in L/min) of the three valves are x, y, and z. The three valves can be used to fill the tank in 3 scenarios. In the first scenario the three valves will fill the tank as follows, valve x will be opened for 10 mins, valve y for 4 mins, and valve z for 40 mins. Second scenario, the valve x opens for 15 mins, valve y for 2 mins, and valve z for 20 mins. Third scenario, valve x opens for 12 mins, valve y for 10 mins, and valve z for 15 mins. 图Y 2000L Tank Knowing that the tank's volume (v=2000L) as a function of three valves' flow rate is given by: x * C + y * D + z * E = 2000 L Where x, y and z represent the 1st, 2nd, and 3rd valve flow rates (L/min), C is the opening time for x valve (min), D is the opening time for y valve (min), E is the opening time for z valve (min). a) For each scenario, write an equation that relates the tank volume to the three valves flow rates. b) Rearrange the equations so that they are in the form Ax=b, where x = |y c) Define the coefficient matrix A and the constant matrix b. d) Use the matrix method to find x. v. and z flow rates. N
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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Transcribed Image Text:Task VI:
You are working in the fluid mechanics system engineering department at a firm. You have a task to
determine flow rates of different valves that used to fill a tank. The tank is 2000 L that is fed by three valves
with different flow rates. The flow rates (in L/min) of the three valves are x, y, and z. The three valves can
be used to fill the tank in 3 scenarios. In the first scenario the three valves will fill the tank as follows, valve
x will be opened for 10 mins, valve y for 4 mins, and valve z for 40 mins. Second scenario, the valve x opens
for 15 mins, valve y for 2 mins, and valve z for 20 mins. Third scenario, valve x opens for 12 mins, valve y
for 10 mins, and valve z for 15 mins.
2000L
Tank
Knowing that the tank's volume (v=2000L) as a function of three valves' flow rate is given by:
x * C + y * D +z * E = 2000 L
Where x, y and z represent the 1st, 2nd, and 3rd valve flow rates (L/min), C is the opening time for
x valve (min), D is the opening time for y valve (min), E is the opening time for z valve (min).
a) For each scenario, write an equation that relates the tank volume to the three valves flow rates.
b) Rearrange the equations so that they are in the form Ax=b, where x = |y
c) Define the coefficient matrix A and the constant matrix b.
d) Use the matrix method to find x, y, and z flow rates.
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