An Introduction to Fluid Mechanics

School of Civil Engineering, University of Leeds. CIVE1400 FLUID MECHANICS Dr Andrew Sleigh May 2001 Table of Contents 0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

CONTENTS OF THE MODULE

Objectives: Consists of: Specific Elements: Books: Other Teaching Resources. Civil Engineering Fluid Mechanics System of units The SI System of units Example: Units

3

3 3 4 4 5 6 7 7 9

1.

1.1 1.2 1.3 1.4

FLUIDS MECHANICS AND FLUID PROPERTIES

Objectives of this section Fluids Causes of Viscosity in Fluids Properties of Fluids

10

10 10 15 16

2.

2.1 2.2 2.3 2.4

FORCES IN STATIC FLUIDS

Fluids statics Pressure Pressure Measurement By Manometer Forces on Submerged Surfaces in Static Fluids

19

19 20 28 33

CIVE 1400: Fluid Mechanics

Contents and Introduction

1

3.

3.1 3.2 3.3 3.4 3.5 3.6 3.7

FLUID DYNAMICS

Uniform Flow, Steady Flow Flow rate. Continuity The Bernoulli Equation - Work and Energy Applications of the Bernoulli Equation The Momentum Equation Application of the Momentum Equation

44

44 47 49 54 64 75 79

4.

4.1 4.2 4.3 4.4

REAL FLUIDS

Laminar and turbulent flow Pressure loss due to friction in a pipeline. Pressure loss during laminar flow in a pipe Boundary Layers

91

92 96 98 101

5.

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11

DIMENSIONAL ANALYSIS

Dimensions and units Dimensional Homogeneity Results of dimensional analysis Buckingham’s π theorems Choice of repeating variables An example Manipulation of the π groups Common π groups Examples Similarity Models

112

112 113 114 115 115 116 118 118 119 121 122

CIVE 1400: Fluid Mechanics

Contents and Introduction

2

0. Contents of the Module 0.1 Objectives:

• • • The course will introduce fluid mechanics and establish its relevance in civil engineering. Develop the fundamental principles underlying the subject. Demonstrate how these are used for the design of simple hydraulic components.

0.2

Consists of:

• Lectures: 20 Classes presenting the concepts, theory and application. Worked examples will also be given to demonstrate how the theory is applied. You will be asked to do some calculations - so bring a calculator. Assessment: 1 Exam of 2 hours, worth 80% of the module credits. This consists of 6 questions of which you choose 4. 4 Multiple choice question (MCQ) papers, worth 20% of the module credits. Thse will be for 30mins and set during the lectures. The timetable for these MCGs and lectures is shown in the table at the end of this section. Laboratories: 2 x 3 hours These two laboratory sessions examine how well the theoretical analysis of fluid dynamics describes what we observe in practice. During the laboratory you will take measurements and draw various graphs according to the details on the laboratory sheets. These graphs can be compared with those obtained from theoretical analysis. You will be expected to draw conclusions as to the validity of the theory based on the results you have obtained and the experimental procedure. After you have completed the two laboratories you should have obtained a greater understanding as to how the theory relates to practice, what parameters are important in analysis of fluid and where theoretical predictions and experimental measurements may differ. The two laboratories sessions are: 1. Impact of jets on various shaped surfaces - a jet of water is fired at a target and is deflected in various directions. This is an example of the application of the momentum equation. 2. The rectangular weir - the weir is used as a flow measuring device. Its accuracy is investigated. This is an example of how the Bernoulli (energy) equation is applied to analyses fluid flow. [As you know, these laboratory sessions are compulsory course-work. You must attend them. Should you fail to attend either one you will be asked to complete some extra work. This will involve a detailed report and further...