# What are the Best Fluid Mechanics Books?

**Fluid mechanics** is a vast subject and addresses issues related to the mechanical behavior of fluids. Fluids, in general, can mean both liquids and gasses. Fluid mechanics has a wide range of applications, from mechanical and aerospace engineering to geophysics to biomechanics. It will be hard to find applications which are not influenced by fluid flows, in reality.

This article discusses fluid mechanics books and relevant literature pertaining to different areas of CFD that would be of interest to learners. Starting from basic thermodynamics and dimensional analysis, the article continues to address sources related to incompressible and compressible flows, viscous flows and boundary layers, acoustics, turbomachinery and eventually turbulence.

## Dimensional Analysis and Mathematical Preliminaries

Dimensional analysis is a mathematical technique that is commonly used in fluid mechanics to study the influence of parameters on the influence of the flow. Here dimensional analysis is used to build relationships between several variables.

One of the very common non-dimensional numbers is the **Reynolds number** which quantifies the ratio between inertial and viscous forces prevalent in the flow. For example, when designing large structures in aerospace and aeronautics applications, it is impossible to build real scale models during the design phase. Hence, reduced scale models are used to simulate the same turbulence effects (or Reynolds number flow).

One of the classics is the book titled “Dimensional analysis” by Bridgeman P W. However, the book is quite old and can show inconsistencies with present notation etc. An alternate reference could be the book titled “Similarity and Dimensional Methods in Mechanics” by L. I. Sedov. However, for the more uninitiated, any fluid mechanics book should provide a small overview of dimensional analysis to start with. That would provide a suitable quick read to understand the topic in brevity.

In addition, a basic understanding of vector calculus can go a long way in understanding mechanics easier. Some beginner references include:

- Vectors, Tensors, and the Basic Equations of Fluid Mechanics by R. Aris
- Vector Analysis Schaum’s Outline Series by M. R. Spiegel

## General Fluid Mechanics Books

Once the basics of dimensional analysis and the rationale for non-dimensional numbers have been established, an apt foundation exists to move into the area of general fluid dynamics.

“An Introduction to Fluid Dynamics” by G. K. Batchelor remains one of the classic fluid mechanics books that addresses the theories of fluid mechanics in an elegant manner. Though published in 1960’s, this timeless classic still can hold a reader at sway.

“Physical Fluid Dynamics” by D. J. Tritton provides an excellent treatment of fluid mechanics related issues from the perspective of an engineer. This is a strongly recommended read for mechanical and aerospace engineering who are interested in understanding fluid mechanics.

**Large Eddy Simulation of flow around a cylinder**

For those who are more mathematically inclined, “Fluid Mechanics” by L. D. Landau and E. M. Lifshitz is a perfect treatise on fluid mechanics. The latest reprint also includes a chapter on computational fluid dynamics and introduces simple computational methodologies for simple flows.

Incompressible and inviscid flows or commonly known as potential flows are very commonly used in design processes. Though simple, they provide an excellent estimate regarding the flow parameters. Most often, like in pipe flows, fluid velocity is small enough that there is no change in density. Thus, they can be considered as incompressible in nature. “Incompressible Flow” by R. L. Panton addresses various issues related to primarily incompressible fluids.

Some topics in this topic for a newbie could include: control volume equations, differential equations, eulerian and lagrangian formulations, Reynolds transport theorem, analysis of stress and strain, Newtonian fluid, Navier-Stokes equations, vorticity equation, energy theorems.

## Compressible Fluid Flow

Many of the mechanical and aerospace engineering applications, the fluid speeds are much larger and comparable to the speed of sound. In these applications, the fluid density changes cannot be neglected anymore and thus need to be treated as compressible in nature.

**Density variation in the fluid around an aircraft – simulation performed with SimScale**

“Modern Compressible Flow: With Historical Perspective” by J. D. Anderson has been a well-renowned fluid mechanics book that is followed in most graduate courses in Fluid mechanics. The book is aimed at engineers and professionals and provides a balanced outlook between traditional methods and modern computer techniques. Another commonly used reference book is “Compressible Fluid Dynamics” by P. A. Thompson. Thompson also provides a balanced approach that is most suitable for applied researchers and professionals.

A timeless classic remains in the book “Elements of Gasdynamics” by H. A. Liepmann and A. Roshko. Liepmann and Roshko bring into this book all their expertise of actually having tested even the first airplanes in the wind tunnels of Caltech. Nevertheless, the book requires a good working knowledge of calculus and basic physics.

Some topics in this topic for a newbie could include:

**Quasi 1-D flow:**Shock waves, flows with friction, flows with heat addition, Mollier diagram, the fundamental derivative of gas dynamics, nozzles, subsonic and supersonic flow, choking total pressure, stagnation pressure, static pressure.**1-D unsteady flow:**Riemann invariants, characteristics expansion waves, shock waves, Rayleigh line, shock adiabat or Hugoniot weak shock and strong shock limits, acoustics contact surfaces, shock tubes, detonation, flames**2-D steady flow:**Characteristics, Prandtl-Meyer expansion fan, flow around corners: interior and exterior, formation of shock waves, polar diagrams, Mach waves, Crocco’s theorem, moving sources, acoustic solution

## Viscous Flows and Boundary Layers

All fluids are viscous in nature, i.e. exhibit some frictional behavior. When fluids flow, the neighboring layers of fluids are moving at slightly different velocities and this causes a frictional resistance that is more commonly known as viscosity. The velocity gradient is referred to as strain rate. Some fluids, known as Newtonian fluids, that show a linear dependence between strain rate and viscous force. The constant of proportionality here is often referred to as the coefficient of viscosity. In contrast non-Newtonian fluids, like blood, emulsions etc, demonstrate a more complicated nonlinear behavior.

There are several fluid dynamics books in this regard but three stand out and are commonly used in most universities and professionals

- Viscous Flows by F. Sherman
- Boundary Layer Theory by H. Schlichting
- Viscous Fluid Flow by F. M. White

While the books by F. M. White and H. Schlichting are more up-to-date, the fluid mechanics book by Sherman is slightly harder to find. Nevertheless, all these books are a great read to get an insight into the viscous flows.

Some topics in this topic for a newbie could include: Viscous stress tensor, Navier-Stokes equations, Pipe flow, Couette flow, low Reynold’s number flow, boundary layers, Rayleigh problem, Blasius problem, Karman integral relation, displacement and momentum thickness, Separation, Exact solutions, stagnation point flow, Howarth-Dorodnitsyn transformation and compressible boundary layer.

## Acoustics, Aerodynamics and Rotating Flows

**Fluid flowing in a centrifugal pump – simulation performed with SimScale**

Some other tertiary or specialized topics that need a thorough understanding of fluid flows include acoustics, aerodynamics, and rotating flows. Though each topic caters to a different audience, they are all specialized topics for advanced readers and hence clustered here.

Books that provide an interesting overview of acoustics include

- Acoustics: An Introduction to its Physical Principles and Applications by A. D. Pierce
- Theory of Vortex Sound by M. S. Howe

Aerodynamics in itself is a vast area but some interesting preliminary reads include

- Foundations of Aerodynamics: Bases of Aerodynamic Design by A. M. Kuethe and C. Y. Chow
- Principles of Ideal-Fluid Aerodynamics by K. Karamcheti

Rotating flows are commonly seen in turbomachinery and a starting reference would be “Rotating Fluids in Engineering and Science” by J. P. Vanyo.

## Turbulence

An undisputed book in understanding Turbulence has been the fluid dynamics book on “Turbulent Flows” by Stephen B. Pope. An alternative book for readers who would prefer slightly different notations is the book “Turbulence: An Introduction for Scientists and Engineers” by P. Davidson. Both these books are a treat to read for engineers, scientists, mathematicians and hobbyists alike.

## Thermodynamics and Data Tables

Thermodynamics forms the basis of all mechanics. All mechanics is based upon the foundation of the laws of thermodynamics. As a beginner, it is confusing to see how the two are related. However, one needs to understand that mechanics deals with the motion of bodies and all objects are made of smaller particles that are governed by the laws of thermodynamics.

It would not be wrong to say that mechanics is a derivative of thermodynamics. Some important reference to get started with thermodynamics are

- Thermodynamics, Schaum’s Outline Series by M. M. Abbott and H. A. van Ness
- Equilibrium Thermodynamics by C. J. Adkins

Some important data tables needed for calculations include

- Equations, Tables and Charts for Compressible Flow, NACA 1135
- Thermodynamic Properties in SI by W. C. Reynolds
- The Properties of Gases and Liquids by B. E. Poling, J. M. Prausnitz, and J. P. O’Connell

### Conclusion

So here it is, a list of the best fluid mechanics books to help you understand all areas of fluid dynamics including compressible flows, viscous flows, turbulence, aerodynamics, acoustics, thermodynamics and more. Hope you like it!

**This case study shows a stress analysis of a wheel loader arm performed with the SimScale simulation platform.**