Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 21, Problem 17P
Develop a user-friendly computer program for the multiple-application version of Simpson's rule based on Fig. 21.13c. Test itby duplicating the computations from Example 21.5.
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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
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…
Chapter 21 Solutions
Numerical Methods for Engineers
Ch. 21 - 21.1 Evaluate the following...Ch. 21 - 21.2 Evaluate the following...Ch. 21 - Evaluate the following integral: 24(1x4x3+2x5)dx...Ch. 21 - Integrate the following function analytically and...Ch. 21 - 21.5 Integrate the following function both...Ch. 21 - Integrate the following function both analytically...Ch. 21 - 21.7 Integrate the following function both...Ch. 21 - 21.8 Integrate the following function both...Ch. 21 - 21.9 Suppose that the upward force of air...Ch. 21 - 21.10 Evaluate the integral of the following...
Ch. 21 - Prob. 11PCh. 21 - 21.12 Determine the mean value of the...Ch. 21 - 21.13 The function can be used to generate the...Ch. 21 - Evaluate the following double integral:...Ch. 21 - Evaluate the following triple integral...Ch. 21 - Develop a user-friendly computer program for the...Ch. 21 - Develop a user-friendly computer program for the...Ch. 21 - Develop a user-friendly computer program for...Ch. 21 - The following data was collected for a...Ch. 21 - 21.20 The outflow concentration from a reactor is...Ch. 21 - 21.21 An 11-m beam is subjected to a load, and the...Ch. 21 - The work produced by a constant temperature,...Ch. 21 - Determine the distance traveled for the following...Ch. 21 - 21.24 The total mass of a variable density rod is...Ch. 21 - 21.25 A transportation engineering study requires...Ch. 21 - Determine the average value for the data in Fig....
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- The 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_forwardFind 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_forward
- Find 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_forwardProblem 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_forward
- Problem 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_forwardProblem 20: Determine the force in members BC, HC, and HG. After the truss is sectioned use a single equation of equilibrium for the calculation of each force. State if the members are in tension or compression. 5 kN 4 kN 4 kN 3 kN 2 kN B D E F 3 m -5 m- -5 m- 5 m 5 m-arrow_forward
- An 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 (19): Given the value of Qp [m³/s], and assuming Reynolds number similitude between the water main and experimental tube, calculate the flow rate in the model tube (Qm) in [lit/s]. = 30.015 m^3/sarrow_forwardProblem 11: The lamp has a weight of 15 lb and is supported by the six cords connected together as shown. Determine the tension in each cord and the angle 0 for equilibrium. Cord BC is horizontal. E 30° B 60° Aarrow_forwardProblem 10: If the bucket weighs 50 lb, determine the tension developed in each of the wires. B $30° 5 E D 130°arrow_forward
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