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Pipe Flow

Gary D. Beckfeld, P.E.


Course Outline

This course presents basic procedures that are used for solving simple pipe flow problems but are also applicable to solutions of more complex cases. These procedures depend on the fluid properties, the type of flow, and the applicable governing equations, energy losses, and the unknown quantities.

Fluid properties reviewed in this course are viscosity and compressibility. Examples of viscosities are given for liquids and gases. The compressibility effect on density change is compared for liquids and gases.

Flow classifications described include uniform, non-uniform, isothermal, adiabatic, steady, unsteady, and laminar and turbulent. Example problems are presented to illustrate solutions of those flows expected to be the most prevalent in engineering problems.

The governing equations of conservation of mass, momentum, and energy are given for compressible, incompressible, isothermal and adiabatic fluid flow. The energy equations include loss terms for pipe fittings and for viscous friction. Isothermal and adiabatic gas laws are given.

Relations are given for viscous friction energy loss friction factors for both laminar and turbulent flows. For turbulent flow the pipe roughness and the Reynolds number are used to evaluate the friction factor from the Colebrook equation. The Mach number is used to check the effect of compressibility.

Finally, several example problems of incompressible flow are presented which illustrate solutions of flow problems for different unknowns. Three basic problems included cover (1) finding viscous friction loss and pumping power (2) finding flow rate and (3) finding pipe diameter. Addition example problems given cover compressible flow, isothermal and adiabatic flow, the thrust forces on pipe fittings, and a case of unsteady flow.

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

Learning Objective

The goal of this course is to teach the following aspects of analysis of fluid flow in pipes:

Intended Audience

The material in this course would be of interest to Mechanical Engineers, Civil Engineers, Chemical Engineers, Agricultural Engineers, and Nuclear Engineers.


Benefit to the Audience

This course would be of benefit to those interested in learning basic procedures in pipe flow analysis and also those wanting to refresh their present understanding of fluid flow in pipes. Benefits to be derived from this course include these: Awareness of the fluid properties of viscosity and compressibility, knowledge of the differences in governing equations for compressible, incompressible, isothermal, and adiabatic flow, use of the Reynolds number to determine laminar or turbulent flow, calculation of energy losses, and different methods of solving the governing equations.


Course Introduction

Pipe flow problems occur in the design of many types of engineering projects. A few of these include refineries (liquid flow), gasoline plants (gas or vapor flow), chemical plants, tank farms, steam plants, cooling towers, domestic water and gas systems, sewers, wells, fire sprinklers, and irrigation systems. The solution to many pipe flow problems in all these cases can be obtained by application of basic procedures.

The basic procedures of pipe flow analysis presented in this course consider the flow to be one-dimensional along the axis of the pipe and average velocities over the pipe cross section are used in obtaining solutions. In some cases solution to the pipe flow governing equations cannot be obtained directly but can be found by a repetitive trial and error process. Where this process is required in the example problems in this course, the problems are simple enough that the answers can be readily obtained by manual calculations.

The pipe flow analysis methods presented here depend on what unknown quantities are to be found, the form of the governing equations, the flow type and the flow properties.

Three basic types of problems have as unknowns (1) the viscous friction loss and/or pumping power, (2) the flow quantity, and (3) the pipe diameter. The equations governing these flow quantities depends on whether the fluid is incompressible or compressible and whether the flow is isothermal (constant temperature) or adiabatic (no heat transfer). Solution to the flow governing equations depends on whether the flow is laminar or turbulent. The Reynolds number which indicates laminar or turbulent flow depends in part on fluid properties of density and viscosity.

Then this study starts with a brief review of the fluid properties of viscosity and the variation of density with compressibility.


Course Content

The course content is in Pipe Flow (PDF File). You need to open or download any of these documents to study this course.


Table of Content

1. Fluid and Flow Classifications
Review of the fluid properties of viscosity and compressibility Comparison of the compressibility of liquids and gases
Review of laminar, turbulent, steady, unsteady, uniform, non-uniform, isothermal, and adiabatic flow

2. Governing Equations
Conservation of mass, momentum, and energy equations
Gas laws, Acoustic velocity, Mach number, Reynolds number
Velocity profiles

3. Energy Losses
Viscous friction energy losses, Darcy-Weisbach equation
Pipe fitting energy losses, pipe roughness ratio, friction factor, Colebrook equation

4. Incompressible Flow Problems
Basic procedures for solving pipe flow problems of friction loss, pump power required, flow rate, pipe diameter

5. Compressible Flow Problems
Adiabatic and isothermal gas flows, thrust forces of pipe fittings
Mach number, compressibility effect

6. Unsteady Flow
Time required to reach steady state conditions in pipe flow


Course Summary

This course has presented basic methods of solving problems of fluid flow in pipes. The compressibility and viscosity properties of liquids and gasses were reviewed. For both compressible and incompressible fluids, and for isothermal and adiabatic gases, the governing equations of continuity, momentum, and energy were presented. Gas laws and relations for acoustic velocity, Mach number, and Reynolds number were also given. Equations for energy loss in pipe flow due to viscous friction and pipe fittings were defined. Relations for friction factors for both laminar and turbulent flow were included. Velocity profiles were shown for laminar and turbulent flow. Example problems were presented for incompressible and compressible and adiabatic and isothermal pipe flow. Different solution methods were shown for finding various flow quantities for viscous turbulent steady uniform flow. Examples of thrust forces on pipe fittings using momentum equations were included. Finally, a problem of unsteady flow was presented.


Quiz

Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.

Take a Quiz

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.