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WR Training

The most diverse substances are transported and distributed in piping systems every single day. They include aggressive fluids in the chemical industry, hydrocarbons in petrochemistry or steam for energy transmission.

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The most diverse substances are transported and distributed in piping systems every single day. They include aggressive fluids in the chemical industry, hydrocarbons in petrochemistry or steam for energy transmission.

Chemical engineers who are designing these piping systems and specifying associated equipment like valves, pumps and flow meters probably face more fluid flow problems than any other. Pressure drop calculations help the engineer size pipes and ducts, determine performance requirements for pumps and fans, and specify control valves and flow meters. And although the underlying theory is rather simple, its practical application can be confusing due to the empirical nature of important correlations, multiple methods for expressing parameters, many variable inputs, and alternative units of measurement.

Designed around a series of practical examples which we work through to a solution, this unique training course is an essential guide to understanding the flow of fluids through pipe, valves and fittings. This understanding is a prerequisite for a successful design & flawless operation of your plant and piping system.

The course features 5 major items :

1- An in-depth information on physical properties of fluids (weight density, specific gravity, viscosity, vapor pressure...) and how to calculate them using Flow of Fluids Excel Workbook

2- An in-depth information on compressible and incompressible fluid flow through piping systems, valves, pumps & flow meter devices (Orifice plates, Flow Nozzles & Venturi Meters) and how to calculate them using Flow of Fluids Excel Workbook

3- An iterative method for sizing flow meters and valves

4- An in-depth discussion on cavitation and choking in control valves

5- A flow problem section with 25 concrete examples to help you practice and reinforce your understanding

Many images, equations, graphs, 3D animations and solved flow problems can be found throughout, increasing the value of this course as an educational tool and industrial reference for personnel involved in the fluid handling industries.

So this course is not only of use to practising and professional engineers to whom a knowledge of the behavior of fluids is of crucial importance in cost-effective design and efficient operation of process plants and piping systems but also intended as a study guide for undergraduates in process, chemical, petrochemical & petroleum engineering disciplines.

So with no further ado, check out the free preview videos and the curriculum of the course and we look forward to seeing you in the first section.

Hope to see you there

WR Training

Spread the wings of your knowledge

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Important note about Flow of Fluids Excel Workbook

To accompany this course and help you assess flow of fluids, calculate pressure drops, size pipes, control valves and flow meter devices, WR Training has developed an Excel VBA based engineering tool : Flow of Fluids Excel Workbook.

Flow of Fluids Excel Workbook simulates the operation of small piping systems transporting liquids and industrial gases under a variety of operating conditions.

Flow of Fluids Excel Workbook is based on industry recognized principles and standards from

Flow of Fluids Excel Workbook presents formulas and data for :

1. Physical properties determination for a variety of fluids (specific gravity, viscosity, vapor pressure)

2. Pressure drop and head loss calculations through pipes, fittings and valves

3. Flow calculations for incompressible and compressible fluids through piping systems, fittings, valves and pumps

4. Sizing piping systems for incompressible and compressible fluids

5. Flow resistance coefficients calculations for pipes, fittings and valves

6. Flow calculations for incompressible and compressible fluids through flow meters (Orifice Plates, Nozzles and Venturi meters)

7. Centrifugal pump calculation (Pump head, NPSH, Specific speed, affinity laws)

8. Converting variables and process parameters to a numerous alternative units of measurement

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Flow of Fluids Excel Workbook: Table of content

a. physical properties of fluids

1 properties of water and steam

a. saturation properties with temperature

b. saturation properties with pressure

c. properties given pressure and temperature

d. properties given pressure and enthalpy

2 dynamic viscosity of gases

3 kinematic viscosity

4 weight density of liquids

a. formula 1

b. formula 2

c. formula 3

5 specific gravity of liquids

a. formula 1

b. formula 2

6 specific gravity - deg api

7 specific gravity - deg beaume

8 specific volume

9 weight density of ideal gases

10 weight density of real gases

11 gas compressibility factor

12 specific gravity of gases

13 boiling point pure component

14 vapor pressure : pure component

15 vapor pressure : mixture

b. nature of flow in pipe

1 rate of flow at flowing condition

a. formula 1

b. formula 2

2 rate of flow (gpm)

a. formula 1

b. formula 2

c. formula 3

3 mean velocity of flow in pipe

a. formula 1

b. formula 2

c. formula 3

4 reynolds number

a. formula 1

b. formula 2

c. formula 3

d. formula 4

e. formula 5

f. formula 6

g. formula 7

c. bernoulli's theorem

1 total head or fluid energy

2 loss of static pressure head (hl) due to fluid flow

d. head loss, pressure drop and friction factor through pipe

1 loss of static pressure head

a. formula 1

b. formula 2

c. formula 3

d. formula 4

e. formula 5

f. formula 6

2 pipe pressure drop

a. formula 1

b. formula 2

c. formula 3

d. formula 4

e. formula 5

f. formula 6

g. formula 7

3 pressure drop for laminar flow according to poiseuille's law

4 pressure drop for turbulent flow according to hazen-williams formula

5 friction factor for laminar flow

6 friction factor for turbulent flow

a. colebrook equation

b. serghide equation

c. swamee-jain equation

e. gas calculations

1 perfect gas law

a. determining the number of moles of a perfect gas

b. determining the pressure of a perfect gas

c. determining the temperature of a perfect gas

d. determining the volume of a perfect gas

2 non-ideal gas law

a. determining the number of moles of a non-ideal gas

b. determining the pressure of a non-ideal gas

c. determining the temperature of a non-ideal gas

d. determining the volume of a non-ideal gas

3 standard ◄►actual gas flow

f. compressible flow in straight horizontal pipeline

1 complete isothermal equation

g. gas pipelines : mass flow rate equation

h. horizontal gas pipelines : standard volumetric flow rate equations

1 general standard volumetric flow rate

2 weymouth standard volumetric flow rate equation for sizing horizontal gas pipelines in fully turbulent flow

3 panhandle "a" standard volumetric flow rate equation for sizing horizontal gas pipelines in partially turbulent flow

4 panhandle "b" standard volumetric flow rate equation for sizing horizontal gas pipelines in fully turbulent flow

i. elevated gas pipelines : standard volumetric flow rate equation

j. liquid flow through orifices

k. liquid flow through isa 1932 nozzles

l. liquid flow through long radius nozzles

m. liquid flow through venturi nozzles

n. liquid flow through venturi meters

o. gas flow through orifices

p. gas flow through isa 1932 nozzles

q. gas flow through long radius nozzles

r. gas flow through venturi nozzles

s. gas flow through venturi meters

t. resistance coefficient for pipes, valves and fittings

1 contraction

2 enlargement

3 gate valves

4 globe and angle valves

5 swing check valves

6 lift check valves

7 tilting disc check valves

8 stop check valves

9 foot valves with strainer

10 ball valves

11 butterfly valves

12 diaphragm valves

13 plug valves

14 mitre bends

15 90° pipe bend and flanged or bw 90° elbows

16 multiple 90° pipe bends

17 close pattern return bends

18 standard elbows

19 pipe entrance

20 pipe exit

21 tees and wyes - converging flow

22 tees and wyes - diverging flow

23 orifices, nozzles and venturis

u. head loss and pressure drop through valves and fittings

1 loss of static pressure head

a. formula 1

b. formula 2

c. formula 3

2 pipe pressure drop

a. formula 1

b. formula 2

c. formula 3

v. flow of fluids through valves, fittings and pipe

1 liquid flow through a valve, fittings and pipe

a. formula 1

b. formula 2

c. formula 3

d. formula 4

e. formula 5

f. formula 6

g. formula 7

2 gas flow through a valve; fittings and pipe

a. formula 1

b. formula 2

c. formula 3

3 valve flow coefficient "cv"

a. formula 1

b. formula 2

4 valve resistance coefficient "k"

w. calculations for centrifugal pump

1 pump head

a. head formula

b. pump in suction head

c. pump in suction lift

2 pump discharge pressure

3 net positive suction head required

4 net positive suction head available

5 total dynamic head

6 suction specific speed (nss)

7 specific speed (ns)

x. pump affinity laws

1 impact of speed on flow

2 impact of speed on head

3 impact of speed on bhp

4 impact of impeller diameter on flow

5 impact of impeller diameter on head

6 impact of impeller diameter on bhp

7 pump brake horspower

8 pump efficiency

y. flow of water through schedule 40 steel pipe

1 calculations for pipe other than schedule 40

z. flow of air through schedule 40 steel pipe

1 calculations for pipe other than schedule 40

2 calculations for other set of temperature and pressure

3 from standard to actual volume flow

zz. conversion tables

1 length

2 area

3 volume

4 velocity

5 mass

6 mass flow rate

7 volumetric flow rate

8 force

9 pressure and liquid head

10 energy, work and heat

11 power

12 weight density

13 temperature

14 dynamic viscosity

15 kinematic viscosity

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What's inside

Learning objectives

  • Understand the main physical properties of fluids (viscosity, vapor pressure, specific gravity, weight density...)
  • Understand the theory of flow in pipe : laminar vs turbulent flow
  • Understand and learn how to use the bernoulli theorem for pressure drop, head loss or flow velocity assessment
  • Learn how to calculate the pressure drop "dp" and the head loss "hl" through any piping system
  • Learn how to determine the friction factor "f" of any piping system
  • Learn how to calculate the flow of compressible and incompressible fluids in pipe
  • Learn how to calculate the resistance coefficient "k" of any piping component (pipes, valves, bends, reducers, tees, wyes...)
  • Learn what the flow coefficient "cv" of a control valve means and how to use it in assessing flows and pressure drops
  • Know what a control valve is and its main components
  • Understand the theory of regulating flow with control valves
  • Understand the concepts of cavitation and choking in control valves through graphics and 3d animations
  • Learn how to size and select a control valve when designing and operating any piping system for both gases and liquids
  • Understand the theory of flow measurement using differential pressure meters such as orifice plates, flow nozzles and venturi meters
  • Learn how to calculate the flow of compressible and incompressible fluids through orifice plates, flow nozzles and venturi meters
  • Learn how to size and select a flow meter when designing and operating any piping system for both gases and liquids
  • Show more
  • Show less

Syllabus

ABOUT THE COURSE
Introduction
About Flow Of Fluids Excel Workbook
Before you start this course
Read more
PHYSICAL PROPERTIES OF FLUIDS
Viscosity
Kinematic viscosity
PRACTICE SESSION : Determining viscosity using Flow of Fluids Excel Workbook
Weight density of liquids
PRACTICE SESSION : Weight density of liquids using Flow of Fluids Excel Workbook
Specific volume
Weight density of gases and vapors
PRACTICE SESSION : Weight density of gases using Flow of Fluids Excel Workbook
Specific gravity
PRACTICE SESSION : Specific gravity using Flow of Fluids Excel Workbook
Vapor pressure
PRACTICE SESSION: Determining vapor pressure using Flow of Fluids Excel Workbook
More charts and diagrams - The Chemical Engineer's Reference Folder
NATURE OF FLOW IN PIPE : LAMINAR AND TURBULENT FLOW
Mean velocity of flow
PRACTICE SESSION : Velocity of flow using Flow of Fluids Excel Workbook
Reynolds number (Re)
PRACTICE SESSION : Reynolds number using Flow of Fluids Excel Workbook
BERNOULLI'S THEOREM
Bernoulli's theorem
MEASUREMENT OF PRESSURE
Measurement of pressure
HEAD LOSS AND PRESSURE DROP THROUGH PIPE
Friction factor
Friction factor using the Colebrook equation
Explicit approximations of Colebrook
PRACTICE SESSION: Friction factor using Flow of Fluids Excel Workbook
Hazen-Williams formula for flow of water
PRACTICE SESSION: Hazen-Williams using Flow of Fluids Excel Workbook
Effect of age and use on pipe friction
COMPRESSIBLE FLOW IN PIPE
Definition of a perfect gas
Speed of sound and Mach number
Approaches to compressible flow problems
Application of the Darcy equation to compressible fluids
Complete isothermal equation
Simplified isothermal gas pipeline equation
Other commonly used equations for compressible flow in long pipelines
Comparison of equations for compressible flow in pipelines
Modifications to the isothermal flow equation
Limiting flow of gases and vapors
PRACTICE SESSION: Expansion factor "Y" & ∆P using Flow of Fluids Excel Workbook
FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
Types of valves used in piping systems
Types of fittings used in piping systems
Pressure drop attributed to valves and fittings
Relationship of pressure drop to velocity of flow
Hydraulic resistance
Causes of head loss in valves and fittings
Equivalent length "L/D"
Resistance coefficient "K"
Resistance coef. K for pipelines, valves and fittings in series and in parallel
Flow coefficient "Cv"
Use of flow coefficient "Cv" for piping and components
Flow coefficient Cv for pipelines, valves and fittings in series and in parallel
Laminar flow conditions
Contraction and enlargement
PRACTICE SESSION: Contraction & enlargement using Flow of Fluids Excel Workbook
Valves with reduced seats
PRACTICE SESSION: Valve resistance coef. "K" using Flow of Fluids Excel Workbook
Resistance of bends
PRACTICE SESSION: Resistance of bends using Flow of Fluids Excel Workbook
Hydraulic resistance of Tees and Wyes
Hydraulic resistance of Tees and Wyes : Converging flow
Hydraulic resistance of Tees and Wyes : Diverging flow
PRACTICE SESSION: Resistance of "T" and "Y" using Flow of Fluids Excel Workbook
Discharge of fluids through valves, fittings and pipe
REGULATING FLOW WITH CONTROL VALVES
Valve components
Inherent characteristic curve
Installed characteristic curve
Pressure, Velocity and Energy profiles through a control valve
Cavitation, Choked Flow and Flashing
Sizing and selection
Sizing for INcompressible flow
Sizing for compressible flow
Conversion of Cv to Kv
MEASURING FLOW WITH DIFFERENTIAL PRESSURE METERS
Orifices, Nozzles and Venturi Tubes
Orifice plate
Limits of use of orifice plates
Flow nozzle
Limits of use of flow nozzles
Venturi meter
Limits of use of Venturi meters
LIQUID FLOW THROUGH ORIFICES, NOZZLES AND VENTURI
Differential pressure and pressure loss

Good to know

Know what's good
, what to watch for
, and possible dealbreakers
Develops in-depth understanding of the flow of fluids through pipe, valves and fittings, which is a prerequisite for designing and operating any plant and piping system
Provides practical examples and a Flow of Fluids Excel Workbook to reinforce understanding
Covers all major areas of fluid flow through pipes and valves for practicing and professional engineers
Engages learners with images, equations, graphs, 3D animations and solved flow problems
Intended also as a study guide for undergraduates in process, chemical, petrochemical & petroleum engineering
Instructors are experienced industry professionals (WR Training) specialized in fluid handling

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Flow of fluids through piping systems , valves and pumps with these activities:
Review Basic Fluid Properties and Units
Refresh knowledge of fundamental fluid properties and units, which are essential for understanding flow of fluids concepts.
Browse courses on Fluid Properties
Show steps
  • Review definitions and formulas for density, viscosity, and specific gravity
  • Practice converting between different units of pressure, flow rate, and volume
Practice Dimensional Analysis for Flow Calculations
Refresh dimensional analysis skills to ensure proficiency in assessing flow characteristics and performing calculations.
Browse courses on Dimensional Analysis
Show steps
  • Review the principles of dimensional analysis
  • Practice identifying and expressing relevant parameters in terms of fundamental dimensions
  • Solve flow-related problems using dimensional analysis
Create a Comprehensive Glossary of Flow of Fluids Terms
Compile a glossary of key terms encountered throughout the course, which will serve as a valuable reference for later review.
Show steps
  • Review course materials, including lectures, notes, and readings
  • Identify and define important terms related to flow of fluids
  • Organize the terms in alphabetical order or by topic
Four other activities
Expand to see all activities and additional details
Show all seven activities
Review Concepts of Compressible Flow
Refresh knowledge of compressible flow concepts, which are essential for understanding the behavior of gases in pipelines.
Show steps
  • Review the definition and characteristics of compressible flow
  • Practice calculating Mach number and understanding its significance
  • Solve problems involving isentropic and adiabatic flow of gases
Explore Bernoulli's Equation for Flow Analysis
Follow a guided tutorial to strengthen understanding of Bernoulli's Equation, a fundamental principle in fluid mechanics.
Show steps
  • Review the concepts of pressure, velocity, and elevation head
  • Follow the derivation of Bernoulli's Equation
  • Apply Bernoulli's Equation to simple flow problems
Analyze flow regime in pipe using Reynolds number
Practice determining the flow regime in pipes based on Reynolds number, which is crucial for understanding flow characteristics.
Show steps
  • Gather fluid properties, pipe diameter, and flow rate
  • Calculate the Reynolds number using the provided formula
  • Classify the flow regime as laminar, transitional, or turbulent based on Reynolds number
Explore Different Methods for Sizing and Selecting Control Valves
Follow a guided tutorial to enhance understanding of control valve sizing and selection methods, which are crucial for regulating flow in piping systems.
Show steps
  • Review the function and types of control valves
  • Learn about different valve sizing methods, including Cv and Kv
  • Practice applying sizing equations and selecting appropriate valves for specific flow conditions

Career center

Learners who complete Flow of fluids through piping systems , valves and pumps will develop knowledge and skills that may be useful to these careers:
Chemical Plant Manager
Chemical Plant Managers oversee and direct all activities related to manufacturing operations in a chemical plant. They ensure that the plant operates safely, efficiently, and in compliance with all environmental regulations. Chemical Plant Managers typically need a bachelor's degree in chemical engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and operation of chemical plants.
Petroleum Engineer
Petroleum Engineers design and develop methods for extracting oil and gas from the earth. They also work to improve the efficiency of oil and gas production. Petroleum Engineers typically need a bachelor's degree in petroleum engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and operation of oil and gas production systems.
Process Engineer
Process Engineers design, develop, and improve processes for manufacturing products. They work in a variety of industries, including chemical, pharmaceutical, and food processing. Process Engineers typically need a bachelor's degree in chemical engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and operation of process systems.
Mechanical Engineer
Mechanical Engineers design, develop, and build a wide variety of machines and devices. They work in a variety of industries, including manufacturing, automotive, and aerospace. Mechanical Engineers typically need a bachelor's degree in mechanical engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and operation of mechanical systems.
Civil Engineer
Civil Engineers design, build, and maintain the infrastructure of our society, including roads, bridges, buildings, and water systems. They typically need a bachelor's degree in civil engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and operation of civil engineering systems.
Environmental Engineer
Environmental Engineers design, build, and maintain systems to protect the environment. They work in a variety of industries, including water treatment, air pollution control, and waste management. Environmental Engineers typically need a bachelor's degree in environmental engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and operation of environmental engineering systems.
Nuclear Engineer
Nuclear Engineers design, build, and maintain nuclear power plants. They also work on the development of new nuclear technologies. Nuclear Engineers typically need a bachelor's degree in nuclear engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and operation of nuclear power plants.
Aerospace Engineer
Aerospace Engineers design, build, and test aircraft, spacecraft, and other vehicles that fly. They typically need a bachelor's degree in aerospace engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and operation of aerospace vehicles.
Materials Engineer
Materials Engineers develop and test new materials for use in a variety of applications. They typically need a bachelor's degree in materials science and engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and testing of new materials.
Biomedical Engineer
Biomedical Engineers design and develop medical devices and systems. They typically need a bachelor's degree in biomedical engineering or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the design and development of medical devices and systems.
Chemical Technician
Chemical Technicians conduct experiments and tests in chemical laboratories. They typically need an associate's degree in chemical technology or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the operation of chemical laboratories.
Drafter
Drafters create technical drawings and plans. They typically need an associate's degree in drafting or a related field. A course on flow of fluids through piping systems, valves, and pumps would be extremely helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the creation of technical drawings and plans.
Estimator
Estimators calculate the cost of construction projects. They typically need a bachelor's degree in construction management or a related field. A course on flow of fluids through piping systems, valves, and pumps would be helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the estimation of construction costs.
Inspector
Inspectors ensure that products and services meet quality standards. They typically need an associate's degree in quality control or a related field. A course on flow of fluids through piping systems, valves, and pumps would be helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the inspection of products and services.
Teacher
Teachers instruct students in a variety of subjects. They typically need a bachelor's degree in education or a related field. A course on flow of fluids through piping systems, valves, and pumps would be helpful in preparing for this role. This course would provide a solid understanding of the principles of fluid flow and how to apply them to the teaching of science and engineering.

Reading list

We've selected 12 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Flow of fluids through piping systems , valves and pumps.
Delves specifically into the flow of fluids through valves, fittings, and pipes, providing a practical approach to understanding pressure drop and flow rate calculations. It valuable resource for engineers and professionals working in fluid handling systems.
Focuses exclusively on control valves, their principles of operation, sizing, selection, and maintenance. It provides valuable insights into the application and performance of control valves in fluid handling systems.
This comprehensive manual provides essential guidance on the design, installation, and maintenance of piping systems. It covers various aspects, including pipe materials, selection, sizing, and layout, making it a practical reference for engineers and technicians involved in piping design and operation.
This textbook provides a comprehensive introduction to fluid mechanics, with a focus on engineering applications. It covers topics such as fluid properties, fluid statics, fluid dynamics, and hydraulic machines, making it a valuable resource for students and engineers.
This handbook offers a wide range of engineering calculations and formulas, covering various disciplines including fluid mechanics, heat transfer, and materials science. It provides quick access to essential equations and data, making it a useful reference for engineers and technicians.
This textbook provides a comprehensive introduction to fluid mechanics, covering topics such as fluid properties, fluid statics, fluid dynamics, and hydraulic machines. It valuable resource for students and engineers who are new to the field of fluid mechanics.
This comprehensive book covers the principles and practices of chemical engineering design. It includes sections on fluid flow, heat transfer, mass transfer, and reactor design, providing a broad understanding of the subject.
This handbook offers a vast collection of hydraulic resistance data for various pipe fittings, valves, and components. It serves as a useful reference for engineers and designers involved in fluid flow system design and optimization.
Provides an in-depth examination of incompressible flow, covering topics such as potential flow, boundary layer theory, and computational fluid dynamics. It valuable resource for advanced students and researchers in fluid mechanics.
This textbook provides a concise and accessible introduction to fluid mechanics, covering topics such as fluid properties, fluid statics, fluid dynamics, and hydraulic machines. It valuable resource for students who are new to the field of fluid mechanics.
This textbook offers a comprehensive introduction to compressible fluid dynamics, covering topics such as shock waves, supersonic flow, and nozzle design. It valuable resource for students and engineers interested in the study of compressible flows.
This widely recognized handbook comprehensive resource for chemical engineers, providing data, formulas, and principles across various fields. It includes sections on fluid mechanics, heat transfer, and mass transfer, making it a valuable reference for engineers involved in process design and operation.

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