Notes - Chapter 4.pdf - CIV ENG 2B04 Principles of Environmental Engineering Chapter 4 Material Balances 1 Material Balances The law of conservation of

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Chapter 4 Material Balances CIV ENG 2B04 - Principles of Environmental Engineering 1

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Material Balances The law of conservation of matter: (without nuclear reaction) matter can neither be created nor destroyed. Mass balances/ Material balances: Accumulation = input – output - Control volume (C V ): e.g., reactors, rivers, landfills, tanks, and aquifers. Widely serves as a basis for describing and analyzing many engineering problems. 2
Time as a Factor Accumulation = input – output Mass rate of accumulation = rate of input – rate of output Steady state Mass rate of accumulation = ௗெ ௗ௧ 3

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We will be using this technique to solve many, many problems throughout this term. Mass or volume rate produced Mass or volume rate consumed Mass or Mass or Mass or volume rate = volume volume + Accumulated rate in rate out Material Balances – Single Material 4
Example 5 kg/s 4 kg/s ? 5

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Consider a trunk sewer with a capacity of 10 m 3 /s. The three neighbourhoods currently contributing to the sewer have peak flows of 5 m 3 /s, 2 m 3 /s and 4 m 3 /s. A developer has proposed a new development that would have a peak flow of 0.5 m 3 /s.Should this developer be allowed to proceed without upgrading or twinning the existing trunk sewer? Example 6
Six-step approach 1. Problem identification - Draw a conceptual diagram of the system - Represent all flow using arrows - Draw a dashed line around the control system (C V ) - Decide on your units (e.g., M/T, L 3 /T) 2. Gather available information 3. Make necessary simplification and assumptions 4. Select appropriate theory and relevant equations (Write out the mass balance equation) 5. Solve problem 6. Validate solutions 7

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Solution 8