A Physical Introduction to Fluid Mechanics

# A Physical Introduction to Fluid Mechanics

• Problem 1.12: The correct answer is 252,000 N = 56649.6 lbf (the answer in the back comes from using 1 atm instead of 1 bar). Thanks to Sam Ritchie and Nick Frey for pointing this out.
• Problem 1.13: Answer should be 5.20x10^18 kg, not 1.76x10^21 kg.
• Problem 1.20: The right viscosity is 0.104 N.s/m^2, not 0.127 N.s/m^2, so that the fluid corresponds to SAE 10 oil (Won Yoo)
• Problem 1.25: The speed of the submarine should be 20 m/s not 10 m/s (Fengquan Zhong)
• Problem 1.26: the kinematic viscosity of water should be 0.8E-06 m^2/s, not 0.8E-07 m^2/s, so that the Reynolds number is about 1667, and the flow should be laminar (Ellen Longmire)
• Problem 2.2: The answer should be 2.064E4 Pa (Sam Ritchie)
• Problem 2.9(a): The answer is given as 23,091 Pa: it should be 23,091 N (Adrian Clarke)
• Problem 2.14: h=H
• Problem 2.23: Answer should be (\rho w L/\cos \theta)[H+(2L/3)\sin \theta] (Sean Yoo)
• Problem 2.27: h's are lower case in problem text, but capitalized in figure. Also, the problem asks you to "find the resultant hydrodynamic force" but it should ask you to "find the resultant hydrostatic force" (Anthony Chiarelli)
• Problem 2.29: Should say that the fluid is water. Also: for instructors: in next-to-last line of homework solution, there is a factor of 2/sqrt(2) that should be sqrt(2)/2 (although the final numerical answer is as if calculated with the latter, so that answer is correct.
• Problem 3.11: Answer incorrectly given as 39,800 N, but should be 31,800 N.
• Problem 3.23: in the last term (Q/DU1) shouldn't be divided by (Q/4DU1 + 1), but multiplied by it (Lauren L. and Ben)
• Problem 3.26: the x-y plane is horizontal (Ben Essenburg)
• Problem 3.28: The question should ask for U_2 in terms of U_1 (Adrian Clarke). Also, the answer should read \rho h^2(g Delta rho_m/rho -3U_1^2/25) (Ellen Longmire)
• Problem 4.12: The answer is 365 lbf, NOT 795 lbf. (Maya Srinivasan)
• Problem 4.18: The answer in the back of the book is 8.58 ft^3/s, but should be 8.58 ft^3--not per unit time. (Anne Staples)
• Problem 4.19: The flow rate q^dot is measured in m^3/s, not m/s. (Megan McNulty)
• Problem 4.22 (p. 147), the answer key (p. 509) reads off the answers to parts a., b., and c. of the problem, when instead it should read off the answers to parts b., c., and d. (part a. is a question that is answered in words, not mathematical expressions). Also, the answer for part "a." (really part b.) is missing a parenthesis before the H_1 in the denominator of the expression inside the square root, i.e. it should read: A/A_t = sqrt(H_1/(H_1 - y)), not A/A_t = sqrt(H_1/H_1 - y) (which would then make the expression dimensionally inconsistent) (Orion Crisafulli).
• Problem 5.8: Velocity profile as given in problem will lead to a negative force, which is not realistic. That is, velocity profile must display regions of negative velocity to give meaningful drag force (Won Yoo). Answer to second part should read (\rho D W V^2_t)/2g (Ann Staples).
• Problem 5.9 (p. 175), the answer key (p. 510) gives the answer as U_2 in terms of U_1 and U_m, and not U_m in terms of U_1 and U_2, as asked in the text of the problem (Orion Crisafulli).
• Problem 5.12 (p. 175), the answer key (p. 510) has the right answer for rho_1 and rho_2, but the answer for the vector momentum flux needs to be multiplied by "h" (a length) to have the right dimensions (Orion Crisafulli).
• Problem 5.14c: Should be 1 - (U2/U1)^2(1 - (5 delta)/(3H)) (Ellen Longmire)
• Problem 5.24: Solve only for the streamwise-component of the force.
• Problem 5.25: F is the streamwise-component of the force.
• Problem 5.28: The answer is correct for the force exerted by the fluid on the vane (Won Yoo)
• Problem 5.30c: Should be U^2/g = 1.63 m (Ellen Longmire)
• Problem 6.12: Answer should be YES the flow is incompressible (Ellen Longmire)
• Problem 6.15: Answer should be YES the flow is incompressible
• Problem 6.30: Should be v = y^2 (Ellen Longmire)
• Problem 7.4c: Should be p = -2*rho*k^2*A^2*sin^2kx (the solution used the wrong stream function) (Ellen Longmire)
• Problem 7.4 (general): The solution in the manual and the back of the book is for the same streamfunction, but with a plus sign separating the two terms (instead of a minus sign). If you do the solution with the minus sign, parts (a) and (b) have the same answers (yes, satisfies continuity; irrotational), but part (c) has the same answer as 7.5(C) (pressure at the straight wall is -2 rho k^2 A^2 sin^2 kx ) (Anne Staples)
• Problem 7.14b: Answer should be rotational (Ellen Longmire)
• Problem 7.21d: Should be (p -p_\infty)_max = 2.408 Pa; (p -p_\infty)_min = -1.4 Pa (Ellen Longmire)
• Problem 8.12: For the answer in the book, the fluid properties were evaluated at 15C
• Problem 8.21b: Answer should be 0.2
• Problem 9.15: Correct answer for pressure difference is 81,500 Pa, not 77,800 Pa (Won Yoo)
• Problem 9.23: To calculate power, should use effective hydraulic diameter, not actual diameter. If the hydraulic diameter is used throughout instead of the channel height (as it should be) the volume flow rate is 40.0 ft^3/s, and the pressure drop is 0.057 psi. If the hydraulic diameter is used only in computing the Reynolds number, the volume flow rate is 29.6 ft^3/s, and the pressure drop is 0.043 psi. (Won Yoo)
• Problem 9.28: The answer given in the book is for D_1=2 ft, D_2=3 ft. When D_1=3 ft, D_2=4 ft, h_{l1}/h_{l2} = 4.25.
• Problem 9.35: Assume the temperature is 15C.
• Problem 10.2: The note middle C has a frequency of 262 Hz (middle temperament). It is middle A (above middle C) that has a frequency of 440 Hz (David Karp).
• Problem 10.29: The answer should be 1200 N (Sebastien Douville).
• Problem 11.14: It is stated that H_2/H_1 = 4, and yet in the diagram, H_1 is drawn bigger than H_2 (an inconsistency) (Orion Crisafulli).
• Problem 11.31: The depth behind the surge should be 2.04 ft, and the drift velocity is 2.84 ft/s.
• Problem 11.36: Ignore the information that H = Y1/4. An additional part of this question could ask to find the bump height ratio H/Y1 (Rory Loughran).
• Problem 11:38: The answer should read Y4 = 0.883 Y1, not B4 = 0.883 B1 (Nate Lowery, Teddy Wieser)