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Chapter 7 First-order Differential Equations

Chapter 7 Application of First-order Differential Equations in Engineering Analysis( Chapter 7 First order DEs) Tai-Ran Hsu*Based on the book of Applied Engineering Analysis , by Tai-Ran Hsu, published byJohn Wiley & Sons, 2018 Applied Engineering Analysis- slides for class teaching* Chapter Learning Objectives Learn to solve typical first order ordinary Differential Equations of both homogeneous and non homogeneous types with or without specified conditions. Learn the definitions of essential physical quantities in fluid mechanics analyses. Learn the Bernoulli s equation relating the driving pressure and the velocities of fluids in motion. Learn to use the Bernoulli s equation to derive Differential Equations describing the flow of non compressible fluids in large tanks and funnels of given geometry. Learn to find time required to drain liquids from containers of given geometry and dimensions.

How differential equations are derived? They are derived from the three fundamental laws of physics of which most engineering analyses involve. These laws are: (1) The law of conservation of mass, (2) The law of conservation of energy, and (3) The law of conservation of momentum.

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