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lec3_print - Examples of Dynamic Models Srinivas Palanki...

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Unformatted text preview: Examples of Dynamic Models Srinivas Palanki University of South Alabama Srinivas Palanki (USA) Examples of Dynamic Models 1 / 19 Examples Liquid Storage Process A typical liquid storage process is shown in the figure below. q q in Filling Process How does the height change with time ? Srinivas Palanki (USA) Examples of Dynamic Models 2 / 19 Examples Step 1: Problem Statement Given in the previous slide Step 2: Assembly of information Sketch : q q in Filling Process System and Notation q in volumetric flow rate in, m 3 / s q volumetric flow rate out, m 3 / s V volume of liquid in tank, m 3 h height of liquid at time t , m A area of cross section, m 2 liquid density, kg / m 3 C v flow coefficient, m 2 . 5 Srinivas Palanki (USA) Examples of Dynamic Models 3 / 19 Examples Axiomatic Law : Conservation of mass Rate of accumulation of mass = mass flow rate in - mass flow rate out d dt ( V ) = q in - q (1) Rate law and Constitutive Relations : V = Ah q = C v h (2) Assumptions : Density is constant (temperature is constant) No reaction in tank Srinivas Palanki (USA) Examples of Dynamic Models 4 / 19 Examples Step 3: Combine d dt ( Ah ) = q in - C v h (3) Step 4: Boundary Condition At t = 0 , h = h (4) Srinivas Palanki (USA) Examples of Dynamic Models 5 / 19 Examples Step 5: Simplify A dh dt = q in- C v h h (0) = h (5) This can be further simplified to: dh dt = 1 A q in- C v A h h (0) = h (6) If h , A and C v are known, the above equation can be solved to give a relation between the volumetric flow rate into the tank and the height of...
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This note was uploaded on 01/07/2011 for the course CHE 452 taught by Professor Dr.srinivaspalanki during the Spring '10 term at S. Alabama.

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lec3_print - Examples of Dynamic Models Srinivas Palanki...

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