A Physical Introduction to Fluid Mechanics

A Physical Introduction to Fluid Mechanics

Text Updates, Corrections and Additions

Second Printing Updates, Corrections and Additions

  • Page 11: Section 1.3.5, first sentence should finish "slugs/ft^3." The unit lb_m/ft^3 should be added as well since that is the unit used by most engineers (Norbert Bell).
  • Page 11: Section 1.3.5, second paragraph, third sentence: The word "material" should more precisely be stated as "solid or liquid material." That is because it is a common practice to relate the specific gravity of gases to air, not water.  For example, refer to Mark's Standard Handbook for Mechanical Engineers, eighth edition, page 3-35. (Norbert Bell).
  • Page 18: example 1.3: should have 2 times tau*sin(theta/2), leading to a final formula of p_max = (t/r)*tau_y (Josh White).
  • Page 22: Second line from the bottom: \tau_w = \mu (du/dy)_w
  • Page 23: Fig 1.17: The two pictures need to be switched (left one for right one). (Norbert Bell, Peter Joubert)
  • Page 26: last line before Example 1.7: Figure 8.8 rather than 8.7 (Norbert Bell).
  • Page 27: Figure 1.21: The profile on the right should be rounded up some more (Norbert Bell).
  • Page 46: Last parentheses before 2.3.3 should refer to Section 1.3.8, rather than 1.3.7. (Norbert Bell)
  • Page 47: Figure 2.5: The \Delta h dimension should be to the top of the mercury, not the top of the tube. (Norbert Bell)
  • Page 49, Example 2.1: Equation before "That is," has rho_2 and rho_3 inconsistent with Figure 2.4. Either the figure or the equation has to have them reversed. (Norbert Bell)
  • Page 52: Penultimate line in the first paragraph should start with "by itself is going to add to a resultant force." (Norbert Bell)
  • Page 52: Second paragraph parentheses should read: "(this is true for any fluid not near its critical point)" (Norbert Bell)
  • Page 53: First sentence should be expanded: "... acting on the right on the right side of the container, left on the left side of the container." The last two sentences in the first paragraph should also be expanded accordingly. (Norbert Bell)
  • Page 55: Figure 2.12: Force F_H should be in the opposite direction. F designation is missing from the horizontal force in the free-body diagram. The free-body diagram should be designated as "(b)" since it is so referenced in the first sentence of the Solution below. (Norbert Bell)
  • Page 57: In the text at the top of the page the weight of the overhang reads 1/2pghwa but it should be 1/3pghwa (as it is shown two lines down) (Alexis Schulman)
  • Page 58: in the text before section "2.5.1 Horizontal Force", it is noted that the resultant force F can be obtained by taking the square root of the sum of the squares of Fx and Fz, the components of the force in the x and z directions. However, the actual equation for the force has F = sqrt(Fx^2 + Fx^2) instead of F = sqrt(Fx^2 + Fz^2) (Orion K. Crisafulli).
  • Page 58: Midway through Section 2.5.1, after "and": The equation should be "dx = ds cos theta" (not dz=cos theta) (Norbert Bell)
  • Page 62: The last two sentences in the penultimate paragraph: They should read something like "The pressure that the container in the upper case exerts on the base (solid pressure) is  more than the hydrostatic (liquid) pressure on the container bottom. Conversely, the pressure that the container in the lower case exerts on the base is less than the hydrostatic pressure on the container bottom." (Norbert Bell)
  • Page 62: The last paragraph: Suggest adding a sentence at the end: "This is the case where the hydrostatic (liquid) pressure is overwhelmingly higher than the solid pressure on the base of the barrel." (Norbert Bell)
  • Page 63: In Figure 2.18, the formula for the parabolic gate shape should be z = (h/a^2)x^2, not z = (h/a^2)x^2
  • Page 63: Section 2.6.1: The constant a is should be defined/explained as defining the width of the gate. (Norbert Bell)
  • Page 63, Figure 2.18: The equation for the curve should be z = (h/a^2) x^2 . Furthermore, there is a superfluous ds floating between the two parts of the picture. (Norbert Bell)
  • Page 64: Last paragraph, first equation: The second F_x^2 should be F_z^2. (Norbert Bell)
  • Page 65: Section 2.6.2, second sentence should be expanded: "... take moments of horizontal force elements about the y-axis, ...". Similarly, in the second paragraph, the first sentence should be expanded: "Next, we take moments of vertical force elements about the y-axis." (Norbert Bell)
  • Page 92: Line after the equation should start: "where i, j and k are the unit vectors..." (Norbert Bell)
  • Page 96: The second streamline equation should be dy/dz not dy/dx (Mark Short).
  • Page 98: Figure 3.6: (a), (b) and (c) designations are missing. (Norbert Bell)
  • Page 99: Last line before Example 3.1: Delete the parentheses and add "(a) and (c)." at the end. (Norbert Bell)
  • Page 103: The first two equations only hold for a special case of rho_1 = rho_2. (Norbert Bell)
  • Page 103: Above (3.3), Mass in over A_{1} rather than A_{2} (Mark Short).
  • Page 104: Example 3.3, first line: Delete the second "of." (Norbert Bell)
  • Page 104: Figure 3.11: Change "a" to "d" and complete its dimension arrow. (Norbert Bell)
  • Page 108: Near top of the page: ``rate of change of fluid x-mom.." first term on right has a closing parenthesis and V_2 missing in front of cos theta. (Norbert Bell)
  • Page 108: lower half of page: (a) ``rate of change of fluid y-momentum" right hand side should be negative. (b) Next equation should read R_y + p_2A_2sin(\theta)=-\rho_2A_2V_2^2sin(\theta). (c) Next equation should read R_y = -p_2A_2sin(\theta) - \rho_2A_2V_2^2sin(\theta) (Matthew de Jonge)
  • Page 111: Equation 3.6: Delete dl (dee-ell) from the right-hand side denominator. (Norbert Bell)
  • Page 111: Example 3.5, Second paragraph: Suggest augmenting the start of the sentence to read: "In Figure 3.11 and even better in Figure 10.8, we see..." (Norbert Bell)
  • Page 111: Figure 3.16: Change CV1 and CV2 to CV_1 and CV_2. Complete the cylinder dimensional arrow. (Norbert Bell)
  • Page 112: Figure 3.17: Change CV1 and CV2 to CV_1 and CV_2. Capital S (twice) should be lower case. (Norbert Bell)
  • Page 112: Example 3.6, nineth line: Change flow to pressure so that the line will read "mately parallel, so that the pressure is approximately equal to the pressure in the" (Norbert Bell)
  • Page 120: First eqn: Should be -\rho g partial z/partial s dndsdx (Mark Short).
  • Page 121: Above equation 4.4: The derivative should read: \partial z/partial s ds = dz =change in elevation along streamline
  • Page 121: Last line: There is a slash missing in the expression cos beta = delta z/delta n. (Norbert Bell)
  • Page 131: Last paragraph before Section 4.6: The first three sentences ought to start thus: "A liquid can also boil if its velocity is high enough so that the static pressure ...", "The formation of vapor bubbles (vapor cavities), when followed by their collapse, is then called ..." and "Just below the water surface, the dynamic pressure..." Note: A good treatment of cavitation is in Pumps and Systems magazine, June 2002, starting on page 16. (Norbert Bell)
  • Page 134: Last equation: The closing parenthesis is missing in the first term. (Norbert Bell)
  • Page 135: Figure 4.15: Drop the subscript from Area A_1. (Norbert Bell)
  • Page 136: First equation: The left "=" should be replaced by a "+" (Norbert Bell)
  • Page 138: Second equation: The RHS on the second line should read -m\int_1^2 p dv, not m-\int_1^2 p dv.
  • Page 140: Equations 4.23, 4.24, 4.25, 4.26: the V_1 on the RHS should be V_2.
  • Page 141: Example 4.9: The outlet diameter of 2.5 cm never occurs in practice for this flowrate (it is much too small). However, in the following observations, I assume that it will stay. (Norbert Bell)
  • Page 142: First equation: All subscripts in the first three left-hand terms need to be reversed from 1 to 2 and vice versa. Second equation: q-dot needs to be defined. Equation for W_shaft: Switch 101,325 and 405,300. This gives a result of 22,580 watt (in place of 10,420), which then converts to 30.3 HP (in place of 14.0). (Norbert Bell)
  • Page 154: sqrt{2} missing from expression for {\bf v} in figure 5.2 (Mark Short).
  • Page 155: Mass flux should be -0.850 kg/s. x-momentum flux should be 6N (Mark Short).
  • Page 156: "b" multiple missing from volume, mass and momentum expressions (Mark Short).
  • Page 156: {\bf i} missing from momentum flux (Mark Short).
  • Page 169, last equation of Section 5.3: Add closing parenthesis at the end. (Norbert Bell)
  • Page 170: first equation: LHS should read B_{CV} not B_{sys}
  • Page 171: the first equation: The right-hand side terms should also refer to the "system" rather than the "fluid," to be consistent with the left-hand term. (Norbert Bell)
  • Page 171: the two equations for W_viscous: Add the unit vector. (Norbert Bell)
  • Page 172: Example 5.11: In the second equation, add 1/2 to the first right-hand term. In the third equation, add 1/2 to the top right-hand term. (Norbert Bell)
  • Page 172: Example 5.11: In the equation following "Over the outflow area," make the following corrections: In the left-hand term, change the square bracket ([) to a round one. In the top right-hand term, change the upper limit of integration from h_2 to delta_2; remove the square bracket (]); change delta_1 to delta_2; add closing parenthesis before dy. In the middle right-hand term, change the upper limit of integration from h_2 to delta_2. (Norbert Bell)
  • Page 172: Figure 5.13: Move the dimension delta_2 to the exit. (Norbert Bell)
  • Page 173, first equation: Change the upper limit of integration from h_2 to delta_2. (Norbert Bell)
  • Page 190: last equation: g_x should be plain italics, not bold (Norbert Bell).
  • Page 191: the first two equations: Similar to above, g_y and g_z should be plain italics (Norbert Bell).
  • Page 191: the third equation: In the second line, the whole right-hand side should be multiplied by dx dy dz (Norbert Bell).
  • Page 191: the fourth equation: The whole right-hand side should be multiplied by dx dy dz (Norbert Bell).
  • Page 195: Section 6.4: Add an introduction "The derivations in this section are based on the coordinate system in which the negative z-axis is aligned with /b g (gravitational vector)" (Norbert Bell).
  • Page 196: Section 6.5, second paragraph should be introduced: "In this section, we consider that the x-axis is horizontal from left to right, the y-axis is vertical with the positive up, and the z-axis is horizontal into the page. The duct dimension in the z-axis direction is constant" (Norbert Bell).
  • Page 199: equation 6.24: There is a minus sign missing in the left-hand term (Norbert Bell).
  • Page 200: Example 6.6: The tan alpha result should be +2, not -2 (Norbert Bell).
  • Page 201: second to last equation: The lower limit of integration in the left-hand term needs to have the subscript fixed. Add the minus sign to the integrand (Norbert Bell).
  • Page 207: Fig 7.1: "delta y" (in the denominator of the vertical dimension of the new position of point b) should be "delta x" (Norbert Bell).
  • Page 208: last paragraph, second sentence should end: "...and inside this layer the flow is rotational" (instead of irrotational) (Norbert Bell).
  • Page 210, equation (7.6) should read dy/dx = v/u (Johan Tolosa).
  • Page 212, equation (7.11) should read v = -d\phi/dx (Johan Tolosa).
  • Page 215: Section 7.6.2, and Page 220, Section 7.8: Suggest adding "and Sink" to the titles of both (Norbert Bell).
  • Page 221: Fig 7.8: The "O" at the sink should be lower case (Norbert Bell).
  • Page 231: last two equations should read: u_p = V c/ (pi 20c) = V/(20 pi), (because s = 20 c), so that u_p/V = 1/ (20 pi) (Norbert Bell).
  • Page 242, last line: Should refer to Step Vc instead of IVc (Norbert Bell).
  • Page 251: rho V_{0}^{2} missing from grad p term on bottom of page (Mark Short).
  • Page 252, Equation 8.17: Multiply the first right-hand term by 1/2 (Norbert Bell).
  • Page 252, Second equation: The F_0 in the second right-hand term needs to be squared (Norbert Bell).
  • Page 255, Second line after the Weber number definition: Section 8.6 should be 8.7 instead (Norbert Bell).
  • Page 260: Example 8.4: The nuclear explosion similarity variable has rho and E the wrong way around (Mark Short).
  • Page 267: first paragraph of the Section 9.3: The last sentence only applies to turbulent flow (Norbert Bell).
  • Page 268: the second paragraph should start: "For a laminar internal flow, ..." (Norbert Bell).
  • Page 270: Section 9.5, first paragraph should start: "It is possible to find exact solutions to Equation 9.1 for fully developed circular pipe flow, as long as..." (Norbert Bell).
  • Page 272: After 9.3 there is a rho missing (Mark Short).
  • Page 273: Figure 9.4a: u_max should be lower case (Norbert Bell).
  • Page 278: Fourth line of the fourth paragraph: Replace "Section 8.6" with "Section 8.7" (Norbert Bell).
  • Page 281: Equation 9.21: Replace the first plus sign on the right-hand side with a minus sign (Norbert Bell).
  • Page 283: last sentence before Section 9.8.2: The second instance of W_shaft should have a negative sign (Norbert Bell).
  • Page 285: Table 9.3: The column for K is misleading since the K for these fittings depends on the pipe diameter. Suggest leaving the whole column out (Norbert Bell).
  • Page 285: the paragraph after the first equation: Replace "ten times" with "equal to" (Norbert Bell).
  • Page 305: In equation below equation 10.13: LHS should contain U_e^2, not U_e
  • Page 316: Caption for Figure 10.14 belongs to Figure 10.16
  • Page 317: Caption for Figure 10.15 belongs to Figure 10.14
  • Page 318: Caption for Figure 10.16 belongs to Figure 10.15
  • Page 341: In second equation on this page, on RHS, should be -1, not +1.
  • Page 343: V_s should be U_B.
  • Page 347: Vertical axis on Figure 11.16, RHS should be labelled F, not Y.
  • Page 374: Section 12.4.3: It is implicitly assumed that no work is being done on the fluid.
  • Page 375: second paragraph. The first sentence should read: "The isentropic relationships are commonly referred to as stagnation conditions...."
  • Page 379: In Figure 12.8, "i" should be "j"
  • Page 387: Seventh line from the top: should read T_2=(p_2/p_1)(\rho_1/\rho_2)T
  • Page 389: In Figure 12.14(a), "\theta" should be "\beta"
  • Page 390: In equation 12.59, "M" should be "M_1"
  • Page 391: In Figure 12.15, on the horizontal axis, the second 10^\circ should be 20^\circ
  • Page 392: Section 12.8.3 The second sentence should read: "It is also possible to write...."
  • Page 396: In equation 12.69, \nu_2 = \nu_1-(\alpha-\alpha_1) should read \nu_2 = \nu_1+(\alpha-\alpha_1)
  • Appendix A:10, Page 482: the integral form of the momentum equation has a 'rho' in place of a 'p' (Mac Haas).

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