Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 8, Problem 8.6P
An incompressible plane flow has the velocity potential
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Problem (17): water flowing in an open channel of a rectangular cross-section with width (b) transitions from a
mild slope to a steep slope (i.e., from subcritical to supercritical flow) with normal water depths of (y₁) and
(y2), respectively.
Given the values of y₁ [m], y₂ [m], and b [m], calculate the discharge in the channel (Q) in [Lit/s].
Givens:
y1 = 4.112 m
y2 =
0.387 m
b = 0.942 m
Answers:
( 1 ) 1880.186 lit/s
( 2 ) 4042.945 lit/s
( 3 ) 2553.11 lit/s
( 4 ) 3130.448 lit/s
Problem (14): A pump is being used to lift water from an underground
tank through a pipe of diameter (d) at discharge (Q). The total head
loss until the pump entrance can be calculated as (h₁ = K[V²/2g]), h
where (V) is the flow velocity in the pipe. The elevation difference
between the pump and tank surface is (h).
Given the values of h [cm], d [cm], and K [-], calculate the maximum
discharge Q [Lit/s] beyond which cavitation would take place at the
pump entrance. Assume Turbulent flow conditions.
Givens:
h = 120.31 cm
d = 14.455 cm
K = 8.976
Q
Answers:
(1) 94.917 lit/s
(2) 49.048 lit/s
( 3 ) 80.722 lit/s
68.588 lit/s
4
Chapter 8 Solutions
Fluid Mechanics
Ch. 8 - Prob. 8.1PCh. 8 - The steady plane flow in Fig. P8.2 has the polar...Ch. 8 - P8.3 Using cartesian coordinates, show that each...Ch. 8 - P8.4 Is the function 1/r a legitimate velocity...Ch. 8 - Prob. 8.5PCh. 8 - An incompressible plane flow has the velocity...Ch. 8 - Prob. 8.7PCh. 8 - For the velocity distribution u=By,=+Bx , evaluate...Ch. 8 - Prob. 8.9PCh. 8 - Prob. 8.10P
Ch. 8 - Prob. 8.11PCh. 8 - Prob. 8.12PCh. 8 - P8.13 Starting at the stagnation point in Fig....Ch. 8 - P8.14 A tornado may be modeled as the circulating...Ch. 8 - Hurricane Sandy, which hit the New Jersey coast on...Ch. 8 - Prob. 8.16PCh. 8 - P8.17 Find the position (x, y) on the upper...Ch. 8 - Prob. 8.18PCh. 8 - Prob. 8.19PCh. 8 - Plot the streamlines of the flow due to a line...Ch. 8 - P8.21 At point A in Fig. P8.21 is a clockwise line...Ch. 8 - P8.22 Consider inviscid stagnation flow, (see...Ch. 8 - P8.23 Sources of strength m = 10 m2/s are placed...Ch. 8 - P8.24 Line sources of equal strength m = Ua, where...Ch. 8 - Prob. 8.25PCh. 8 - Prob. 8.26PCh. 8 - Prob. 8.27PCh. 8 - Sources of equal strength m are placed at the four...Ch. 8 - Prob. 8.29PCh. 8 - Prob. 8.30PCh. 8 - A Rankine half-body is formed as shown in Fig....Ch. 8 - Prob. 8.32PCh. 8 - P8.33 Sketch the streamlines, especially the body...Ch. 8 - Prob. 8.34PCh. 8 - Prob. 8.35PCh. 8 - Prob. 8.36PCh. 8 - Prob. 8.37PCh. 8 - Consider potential flow of a uniform stream in the...Ch. 8 - A large Rankine oval, with a = 1 m and h = 1 m, is...Ch. 8 - Prob. 8.40PCh. 8 - Prob. 8.41PCh. 8 - Prob. 8.42PCh. 8 - P8.43 Water at 20°C flows past a 1-rn-diameter...Ch. 8 - Prob. 8.44PCh. 8 - Prob. 8.45PCh. 8 - P8.46 A cylinder is formed by bolting two...Ch. 8 - Prob. 8.47PCh. 8 - Prob. 8.48PCh. 8 - Prob. 8.49PCh. 8 - It is desired to simulate flow past a...Ch. 8 - Prob. 8.51PCh. 8 -
P8.52 The Flettner rotor sailboat in Fig. E8.3...Ch. 8 - P8.52 The Flettner rotor sailboat in Fig. E8.3 has...Ch. 8 - Prob. 8.54PCh. 8 - Prob. 8.55PCh. 8 - Prob. 8.56PCh. 8 - Prob. 8.57PCh. 8 - Prob. 8.58PCh. 8 - Prob. 8.59PCh. 8 - Prob. 8.60PCh. 8 - Prob. 8.61PCh. 8 - Prob. 8.62PCh. 8 - The superposition in Prob. P8.62 leads to...Ch. 8 - Consider the polar-coordinate stream function...Ch. 8 - Prob. 8.65PCh. 8 - Prob. 8.66PCh. 8 - Prob. 8.67PCh. 8 - Prob. 8.68PCh. 8 - Prob. 8.69PCh. 8 - Prob. 8.70PCh. 8 - Prob. 8.71PCh. 8 - Prob. 8.72PCh. 8 - Prob. 8.73PCh. 8 - Prob. 8.74PCh. 8 - Prob. 8.75PCh. 8 - Prob. 8.76PCh. 8 - Prob. 8.77PCh. 8 - Prob. 8.78PCh. 8 - Prob. 8.79PCh. 8 - Prob. 8.80PCh. 8 - Prob. 8.81PCh. 8 - Prob. 8.82PCh. 8 - Prob. 8.83PCh. 8 - Prob. 8.84PCh. 8 - Prob. 8.85PCh. 8 - Prob. 8.86PCh. 8 - Prob. 8.87PCh. 8 - Prob. 8.88PCh. 8 - Prob. 8.89PCh. 8 - NASA is developing a swing-wing airplane called...Ch. 8 - Prob. 8.91PCh. 8 - Prob. 8.92PCh. 8 - Prob. 8.93PCh. 8 - Prob. 8.94PCh. 8 - Prob. 8.95PCh. 8 - Prob. 8.96PCh. 8 - Prob. 8.97PCh. 8 - Prob. 8.98PCh. 8 - Prob. 8.99PCh. 8 - Prob. 8.100PCh. 8 - Prob. 8.101PCh. 8 - Prob. 8.102PCh. 8 - Prob. 8.103PCh. 8 - Prob. 8.104PCh. 8 - Prob. 8.105PCh. 8 - Prob. 8.106PCh. 8 - Prob. 8.107PCh. 8 - P8.108 Consider two-dimensional potential flow...Ch. 8 - Prob. 8.109PCh. 8 - Prob. 8.110PCh. 8 - Prob. 8.111PCh. 8 - Prob. 8.112PCh. 8 - Prob. 8.113PCh. 8 - Prob. 8.114PCh. 8 - Prob. 8.115PCh. 8 - Prob. 8.1WPCh. 8 - Prob. 8.2WPCh. 8 - Prob. 8.3WPCh. 8 - Prob. 8.4WPCh. 8 - Prob. 8.5WPCh. 8 - Prob. 8.6WPCh. 8 - Prob. 8.7WPCh. 8 - Prob. 8.1CPCh. 8 - Prob. 8.2CPCh. 8 - Prob. 8.3CPCh. 8 - Prob. 8.4CPCh. 8 - Prob. 8.5CPCh. 8 - Prob. 8.6CPCh. 8 - Prob. 8.7CPCh. 8 - Prob. 8.1DPCh. 8 - Prob. 8.2DPCh. 8 - Prob. 8.3DP
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- Problem (13): A pump is being used to lift water from the bottom tank to the top tank in a galvanized iron pipe at a discharge (Q). The length and diameter of the pipe section from the bottom tank to the pump are (L₁) and (d₁), respectively. The length and diameter of the pipe section from the pump to the top tank are (L2) and (d2), respectively. Given the values of Q [L/s], L₁ [m], d₁ [m], L₂ [m], d₂ [m], calculate total head loss due to friction (i.e., major loss) in the pipe (hmajor-loss) in [cm]. Givens: L₁,d₁ Pump L₂,d2 오 0.533 lit/s L1 = 6920.729 m d1 = 1.065 m L2 = 70.946 m d2 0.072 m Answers: (1) 3.069 cm (2) 3.914 cm ( 3 ) 2.519 cm ( 4 ) 1.855 cm TABLE 8.1 Equivalent Roughness for New Pipes Pipe Riveted steel Concrete Wood stave Cast iron Galvanized iron Equivalent Roughness, & Feet Millimeters 0.003-0.03 0.9-9.0 0.001-0.01 0.3-3.0 0.0006-0.003 0.18-0.9 0.00085 0.26 0.0005 0.15 0.045 0.000005 0.0015 0.0 (smooth) 0.0 (smooth) Commercial steel or wrought iron 0.00015 Drawn…arrow_forwardThe flow rate is 12.275 Liters/s and the diameter is 6.266 cm.arrow_forwardAn experimental setup is being built to study the flow in a large water main (i.e., a large pipe). The water main is expected to convey a discharge (Qp). The experimental tube will be built at a length scale of 1/20 of the actual water main. After building the experimental setup, the pressure drop per unit length in the model tube (APm/Lm) is measured. Problem (20): Given the value of APm/Lm [kPa/m], and assuming pressure coefficient similitude, calculate the drop in the pressure per unit length of the water main (APP/Lp) in [Pa/m]. Givens: AP M/L m = 590.637 kPa/m meen Answers: ( 1 ) 59.369 Pa/m ( 2 ) 73.83 Pa/m (3) 95.443 Pa/m ( 4 ) 44.444 Pa/m *******arrow_forward
- Find the reaction force in y if Ain = 0.169 m^2, Aout = 0.143 m^2, p_in = 0.552 atm, Q = 0.367 m^3/s, α = 31.72 degrees. The pipe is flat on the ground so do not factor in weight of the pipe and fluid.arrow_forwardFind the reaction force in x if Ain = 0.301 m^2, Aout = 0.177 m^2, p_in = 1.338 atm, Q = 0.669 m^3/s, and α = 37.183 degreesarrow_forwardProblem 5: Three-Force Equilibrium A structural connection at point O is in equilibrium under the action of three forces. • • . Member A applies a force of 9 kN vertically upward along the y-axis. Member B applies an unknown force F at the angle shown. Member C applies an unknown force T along its length at an angle shown. Determine the magnitudes of forces F and T required for equilibrium, assuming 0 = 90° y 9 kN Aarrow_forward
- Problem 19: Determine the force in members HG, HE, and DE of the truss, and state if the members are in tension or compression. 4 ft K J I H G B C D E F -3 ft -3 ft 3 ft 3 ft 3 ft- 1500 lb 1500 lb 1500 lb 1500 lb 1500 lbarrow_forwardProblem 14: Determine the reactions at the pin A, and the tension in cord. Neglect the thickness of the beam. F1=26kN F2 13 12 80° -2m 3marrow_forwardProblem 22: Determine the force in members GF, FC, and CD of the bridge truss and state if the members are in tension or compression. F 15 ft B D -40 ft 40 ft -40 ft 40 ft- 5 k 10 k 15 k 30 ft Earrow_forward
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Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License