Mathematical Principles in Environmental Engineering

  I need exercise 1-9 to be solved as soon as possible.

Mathematical Principles in
Environmental Engineering

Material Balances
Dr. Mohamad Yassine

drmoyassine@gmail.com

Law of Mass Conservation

In an isolated system, mass is neither created nor
destroyed by chemical reactions or physical
transformations.

Process Boundary

Input Accumulation

Generation Consumption

Inputs – Outputs = Accumulation + Generation – Consumption

General Form:

true for each and every type of material coming in/out of the system. Dr. Mohamad Yassine 2

Material Balance Exercise 1
Chemicals Addition/Dilution System

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Material Balance Exercise 2
Chemical Species in A River System

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Illustrative Example:

Material Balance Exercise 3
Refuse Disposal

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Material Balance Exercise 4
SOx Air Pollution Modeling

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Material Balance Exercise 5
Simple Distillation Column

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Material Balance Exercise 6 & 7
Capacity of Sewers and Manholes

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Exercise 6:
Exercise 7:

Material Balance Exercise 8
Two-Step Distillation Column

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Material Balance Exercise 9
Hydrological Cycle Balance

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Illustrative Example

Material Balance Exercise 10
Plastic Separation Process Design

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Illustrative Example

Material Balance in Reactive Systems
Secondary WWT: The Activated
Sludge System

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Note that there are
reactions (biological,
chemical, or
physical) inside each
tank!

Material Balance in Reactive Systems
Sludge Digestion in WWT

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Note that there are
reactions (biological,
chemical, or
physical) inside each
tank!

Material Balance in Reactive Systems
Material Flow in Solid Waste
Incinerator

Dr. Mohamad Yassine 14

Note that there are
reactions (biological,
chemical, or
physical) inside each
Step!