CUP editors and typesetters have shown almost infinite patience and allowed me many proof readings, but after a while, staring at the same words, the experience resembles the occasions when you repeat the same word over and over again—the word becomes meaningless, nonsensical. So errors remain, and I will list these here as I find them, or even better when readers let me know of errors they have found. (Some errata are trivial typoes, but in the unlikely event that the book goes into a second printing, I will have a handy record here.)

• comment: page 11, note that the fractional change in density, ∆ρ/ρ, is the compressibility times the change in pressure. The compressibility of water is about 4.6×10⁻¹⁰ Pa⁻¹ at 20°C (this is small but still about a hundred times larger than in steel); so while the absolute pressure changes by a factor of one hundred, the density increases by only about 0.5% (this is assuming constant temperature so it's only a very rough estimate). This is why we assert here and throughout the book that liquids are effectively incompressible. Complete incompressibility is an artificial construct: solids are as incompressible as liquids, but their bulk modulus is not infinite! I should have made this point in my book. Here is an additional note: pressure as a Lagrange multiplier in an incompressible fluid.
  

• erratum: page 13: "monotonic"?
  

• comment: page 48, it is not self evident that the relations between t_i and n_j are linear; I omitted to mention that fact. The proof, which you will find in a textbook ^† , uses "Cauchy's tetrahedron."
  

• erratum: page 49, footnote 17: before the integral sign should appear the fraction 1/∆τ
  

  comments: It is notable that div applied to a rank-two tensor is ambiguous. If I used the common convention in fluid mechanics that the indices on the Cauchy stress tensor are reversed then the differentiation implied in the divergence is taken with respect to the first, not the second, index. The same applies to the formula in the footnote: the indices j and n would need to be exchanged; albeit in that expression no explicit differentiation is indicated, and the form is valid in any orthogonal coordinate system.
  

  The convention that the first index of the Cauchy stress tensor refers to the direction of the traction vector and the second, the normal to the element of area over which it acts, seems to be most common in solid mechanics. Certainly that's how Professors Eshelby and Bilby taught it. Then the equilibrium condition reads,
  

  σ_ij,j + f_i = 0 which looks elegant. The comma notation is taken from general relativity and according to google's AI it was first used by Einstein and Grossmann in 1913; however I cannot find it in that paper. It's not used in Eddington's book (or rather he just leaves out the comma, or colon for covariant derivative, which is totally confusing). Einstein introduces it in the 1950s appendix to his book, and Dirac has it in his excellent little book, using comma and colon. So I don't know who started it. Mathematicians including William Prager prefer an explicit differential operator, in which case the equilibrium condition in our convention reads,
  ∂_jσ_ij + f_i = 0 which is a little less elegant, since we like our indices which are to be summed to be contiguous. Maybe that's why Prager uses the reverse convention that interchanges the roles of the two indices. This convention seems to be universal in fluid mechanics. There is no right way, but I do deprecate the convention that the sign of the Cauchy stress is reversed in fluid mechanics, which desecration seems to have been perpetrated by Bird, Stewart and Lightfoot.
  

  It was Professor Bilby who first showed me how to get the Navier-Stokes equations from the condition of elastic equilibrium of an isotropic solid. Indeed I found my old undergraduate notes and it appears that he actually did reverse the order of the indices when he made the passage into fluid mechanics. I don't imagine that he intended to confuse the students and maybe he had fused two sets of lecture notes. My choice has been to start with the solid mechanics convention and stick to it!
  

• erratum: page 69, I wrote "The pressure loss is entirely due to friction at the capillary wall…"; I should have written, "… friction at the capillary wall and within the viscous fluid…" In fact, since the fluid sticks to the wall, strictly speaking there is no friction at the wall (but there is a velocity gradient and hence a shear stress).
  

  comment: I sometimes feel that there is a chicken and egg situation behind the Hagen-Poiseuille law. It is the pressure at entry that is the cause of the flow; but the flow rate is actually controlled by the pressure drop, which is itself a consequence of friction. If the fluid were inviscid and there was no stick-to-the-wall then the pressure drop would vanish; although, of course, in the case, say, of a hose pipe the pressure close to the exit will be the pressure at the tap, but this will drop to atmospheric pressure at the exit (the Hagen-Poiseuille law, of course, does not permit end effects).
  

• erratum: page 72: There is mass, m, missing in the formula for angular momentum: L = mr×v
  

• comment: page 78, A student after the lecture (21 Nov 2025) asked two interesting and difficult questions, both concerning equation (4.3.4). First, concerning the second term: the quantity v·da is negative for inflow into the control volume and positive for outflow (because da always, by convention, points in the outward facing direction of the control surface). So why does the second term in (4.3.4) not carry a minus sign? The answer is contained in figure 4.3. When the system has moved relative to the control volume, that little sliver at the lower left is matter than has left the control volume and new matter has entered to replace it; it is that matter which enters (carrying a minus sign in v·da) that no longer belongs to the system so it is subtracted off. Looking to the upper right of the figure, the sliver of matter has exited the control volume, but belongs to the system as it moves on, and hence takes the plus sign of v·da . So the plus sign in (4.3.4) is appropriate because intensive quantity no longer belonging to the system is subtracted and vice versa. This is why, later at equation (4.5.2) we say that the total force is the rate of outflow of momentum, not inflow (at a first glance, I agree that does seem counter intuitive). The second question is even more challenging. Why, if we are concerned with the properties of the system is the first term an integral over the control volume and not over the system? Here is the answer, and I apologise for my shortcomings in explaining this vital construction of the Reynolds theorem (which governs all that follows). To some extent, figure 4.3 is misleading. I have drawn the system as having moved on from time t, to time t+dt. But dt is an infinitesimal. What I really want to do is to let dt go to zero, because I am actually interested in the situation at time t (when the volume containing the system and the control volume coincide). This does not invalidate the argument above leading to the second term in (4.3.4), but it justifies my taking the first integral (as well as the second) over the control volume (or its surface). Hence Reynolds's theorem, while describing the system, is able to use integrals over the control volume. This is most important and I should have made this clearer in my book.
  

• erratum: page 125, figure caption: after (e) the less than sign should be a greater than sign.
  

• erratum: page 178, first sentence in section 6.7: the upper case gothic "B" should be lower case gothic "b" with superscript v.
  

• erratum: page 139, remove comma from first equation.
  

• erratum: page 223, equation (7.7.11) is not Darken's relation. From the equation above (7.7.10) you see that the fraction in (7.7.11) is trivially one. To get Darken's relation you need to use (7.7.6a) for D_A; then you easily find:
  
  D_A / D_A^•
  = 1 +
  d  ln γ_A / d  ln  x_A
  
  This is Darken's thermodynamic relation. The ratio of intrinsic to tracer diffusivity is equal to one if the solution is ideal, Henrian or Raoultian.

^† Ellad B. Tadmore, Ronald E. Miller and Ryan S. Elliott, Continuum Mechanics and Thermodynamics, (Cambridge University Press, 2012)

Last modified: 25 Feb 2026 (Tony Paxton)