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# Modeling Fluid Systems

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Control Theory, Fluid, Mathematical Modeling

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### Modeling Fluid Systems

1. 1. Modeling Fluid Systems Prachee Sharma 2010B1A3616H
2. 2. High power to weight ratio, accuracy and quick response required Aircraft Control Systems
3. 3. Systems consisting of liquid-filled tanks connected by pipes having orifices, valves, and other flow restricting devices. Industrial Processes
4. 4. Day to Day Uses
5. 5. How Do You Begin?
6. 6. Simplifications! 1) Incompressible 2) Laminar Flow Dynamics- Ordinary Linear D.E.! Turbulent Flow- Non Linear D.E.
7. 7. Basic Fluid Elements Fluid Capacitor Inertor Fluid Resistor
8. 8. Fluid Resistance 
9. 9.  Fluid Capacitance
10. 10.  Fluid Inertance
11. 11. Steps for Problem Solving 1. Identify the basic elements within the system and write the corresponding constitutive relationship (i.e., elemental equation) for each element with respect to a certain equilibrium level (Usually nonzero) 2. Write the applicable interconnection equations, such as pressure or flow balance equations. 3. Assemble the resulting equations to form a system of ordinary differential equations with the same number of unknown variables as the number of equations. 4. Apply Laplace transform if transfer function or further reduction of the equations are required.
12. 12. Relation bet. qo and qi
13. 13. Step-1: Identify the basic elements within the system and write the corresponding elemental equation for each element
14. 14. Step-2: Write the applicable interconnection equations, such as pressure or flow balance equations.
15. 15. Step-3: Write the Differential Equation
16. 16. Step- 4: Laplace Transform
17. 17. Step-1: Identify the basic elements within the system and write the corresponding elemental equation for each element
18. 18. Step-2: Write the applicable interconnection equations, such as pressure or flow balance equations.
19. 19. Step-3: Write the Differential Equation
20. 20. Motivation-Another Fluidic Circuit?  Prosthesis. Re- implantation of the previous separated coronary arteries  Variation of outlet angle affects coronary blood flow  Simulating the blood flow in order to determine velocity and pressure distributions
21. 21. #punintended!