Applied Engineering Analysis

Chapter 7Application of First-order Differential Equations in Engineering Analysis

Chapter Learning Objectives

• Learn to solve typical first-order ordinary differential equations of both homogeneous and nonhomogeneous types with or without specified conditions.
• Learn the definitions of essential physical quantities in fluid mechanics analyses.
• Learn the Bernoulli 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 noncompressible fluids in large tanks and funnels of different geometries.
• Learn how to find time required to drain liquids from containers of given geometry and dimensions.
• Learn the Fourier law of heat conduction in solids and Newton's cooling law for convective heat transfer in fluids.
• Learn how to derive differential equations to predict times required to heat or cool small solids by surrounding fluids.
• Learn to derive differential equations describing the motion of rigid bodies under the influence of gravitation.

7.1 Introduction

As we have learned in Section 2.5, differential equations are equations that involve “derivatives.” They are used extensively in mathematical modeling of engineering and physical problems.

There are generally two types of differential equations used in engineering analysis:

1. 1. Ordinary differential equations (ODEs): Equations with functions that involve only one variable and “ordinary” derivatives as described in ...