Introduction to Fluid Mechanics, Sixth Edition

William S. Janna

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000731538
• Edition: 6
• Topic: Technik & Maschinenbau
• Subtopic: Maschinenbau

Introduction to Fluid Mechanics, Sixth Edition, is intended to be used in a first course in Fluid Mechanics, taken by a range of engineering majors. The text begins with dimensions, units, and fluid properties, and continues with derivations of key equations used in the control-volume approach. Step-by-step examples focus on everyday situations, and applications. These include flow with friction through pipes and tubes, flow past various two and three dimensional objects, open channel flow, compressible flow, turbomachinery and experimental methods. Design projects give readers a sense of what they will encounter in industry. A solutions manual and figure slides are available for instructors.

1 Fundamental Concepts

Fluid mechanics is the branch of engineering that deals with the study of fluids—both liquids and gases. Such a study is important because of the prevalence of fluids and our dependence on them. The air we breathe, the liquids we drink, the water transported through pipes, and the blood in our veins are examples of common fluids. Further, fluids in motion are potential sources of energy that can be converted into useful work—for example, by a waterwheel or a windmill. Clearly, fluids are important, and a study of them is essential to the engineer.

After completing this chapter, you should be able to:

• Describe commonly used unit systems;
• Define a fluid;
• Discuss common properties of fluids;
• Establish features that distinguish liquids from gases; and
• Present the concept of a continuum.

1.1 DIMENSIONS AND UNITS

Before we begin the exciting study of fluid mechanics, it is prudent to discuss dimensions and units. In this text, we use two unit systems: the British gravitational system and the international system (SI). Whatever the unit system, dimensions can be considered as either fundamental or derived. In the British system, the fundamental dimensions are length, time, and force. The units for each dimension are given in the following table:

	British Gravitational System
Dimension	Abbreviation	Unit
Length	L	foot (ft)
Time	T	second (s)
Force	F	pound-force (lbf)

Mass is a derived dimension with units of slug and defined in terms of the primary dimensions as

1slug=11bf⋅s2ft

(1.1)

Converting from the unit of mass to the unit of force is readily accomplished because the slug is defined in terms of the lbf (pound-force).

Example 1.1

An individual weighs 150 lbf.

1. a. What is the person’s mass at a location where the acceleration due to gravity is 32.2 ft/s²?
2. b. On the moon, the acceleration due to gravity is one-sixth of that on earth. What is the weight of this person on the moon?

Solution

1. a. Applying Newton’s law, we write

2. F=ma

3. Substituting gives

4. 150lbf=m32.2ft/s2

5. Solving for mass, we obtain

6. m=150lbf32.2ft/s2=4.66lbf⋅s2/ft

7. or

8. m=4.66slug

9. b. The mass is the same on the moon as on the earth. Again we apply Newton’s law,

10. F=ma

11. where m = 4.66 slug and the acceleration due to gravity is

12. a=1632.2ft/s2=5.37ft/s2

13. Substituting, the wei...