Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977237
Author: BEER
Publisher: MCG
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Chapter 14.2, Problem 14.52P
For the game of billiards of Prob. 14.51, it is now assumed that
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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 14 Solutions
Vector Mechanics For Engineers
Ch. 14.1 - A 30-g bullet is fired with a horizontal velocity...Ch. 14.1 - Two identical 1350-kg automobiles A and B are at...Ch. 14.1 - Prob. 14.3PCh. 14.1 - Prob. 14.4PCh. 14.1 - Two swimmers A and B, of weight 190 lb and 125 lb,...Ch. 14.1 - A 180-lb man and a 120-lb woman stand side by side...Ch. 14.1 - A 40-Mg boxcar A is moving in a railroad...Ch. 14.1 - Two identical cars A and B are at rest on a...Ch. 14.1 - A 20-kg base satellite deploys three...Ch. 14.1 - For the satellite system of Prob. 14.9. assuming...
Ch. 14.1 - A system consists of three identical 19.32-lb...Ch. 14.1 - A system consists of three identical 19.32-lb...Ch. 14.1 - A system consists of three particles A, B, and C....Ch. 14.1 - For the system of particles of Prob. 14.13,...Ch. 14.1 - A 13-kg projectile is passing through the origin O...Ch. 14.1 - A 300-kg space vehicle traveling with a velocity...Ch. 14.1 - A 2-kg model rocket is launched vertically and...Ch. 14.1 - An 18-kg cannonball and a 12-kg cannonball are...Ch. 14.1 - Prob. 14.19PCh. 14.1 - Prob. 14.20PCh. 14.1 - An expert archer demonstrates his ability by...Ch. 14.1 - Two spheres, each of mass m, can slide freely on a...Ch. 14.1 - Prob. 14.23PCh. 14.1 - A 6-kg shell moving with a velocity...Ch. 14.1 - A 6-kg shell moving with a velocity...Ch. 14.1 - In a scattering experiment, an alpha particle A is...Ch. 14.1 - Derive the relation Ho=rmv+HG between the angular...Ch. 14.1 - Show that Eq. (14.23) may be derived directly from...Ch. 14.1 - Consider the frame of reference Ax'y'z' in...Ch. 14.1 - Show that the relation MA=HA where HA is defined...Ch. 14.2 - Determine the energy lost due to friction and the...Ch. 14.2 - Prob. 14.32PCh. 14.2 - In Prob. 14.6. determine the work done by the...Ch. 14.2 - Determine the energy lost as a result of the...Ch. 14.2 - Two automobiles A and B, of mass mA and mB,...Ch. 14.2 - It is assumed that each of the two automobiles...Ch. 14.2 - Solve Sample Prob. 14.5, assuming that cart A is...Ch. 14.2 - Ball B is suspended from a cord of length l...Ch. 14.2 - A 15-lb block B starts from rest and slides on the...Ch. 14.2 - A 40-lb block B is suspended from a 6-ft cord...Ch. 14.2 - In a game of pool, ball A is moving with a...Ch. 14.2 - In a game of pool, ball A is moving with a...Ch. 14.2 - Three spheres, each with a mass of m, can slide...Ch. 14.2 - In a game of pool, ball A is moving with the...Ch. 14.2 - The 2-kg sub-satellite B has an initial velocity...Ch. 14.2 - A 900-lb space vehicle traveling with a velocity...Ch. 14.2 - Four small disks A, B, C, and D can slide freely...Ch. 14.2 - In the scattering experiment of Prob. 14.26, it is...Ch. 14.2 - Prob. 14.49PCh. 14.2 - Three small spheres A, B, C, each of mass m, are...Ch. 14.2 - In a game of billiards, ball A is given an initial...Ch. 14.2 - For the game of billiards of Prob. 14.51, it is...Ch. 14.2 - Two small disks A and B of mass 3 kg and 1.5 kg,...Ch. 14.2 - Two small disks A and B of mass 2 kg and 1 kg,...Ch. 14.2 - Prob. 14.55PCh. 14.2 - Prob. 14.56PCh. 14.3 - A stream of water with a density of =1000kg/m3 is...Ch. 14.3 - A jet ski is placed in a channel and is tethered...Ch. 14.3 - Tree limbs and branches are being fed at A at the...Ch. 14.3 - The nozzle shown discharges water at the rate of...Ch. 14.3 - A rotary power plow is used to remove snow from a...Ch. 14.3 - A hose discharges water at a rate of 8 m3/min with...Ch. 14.3 - Sand falls from three hoppers onto a conveyor belt...Ch. 14.3 - The stream of water shown flows at a rate of 550...Ch. 14.3 - The nozzle shown discharges water at the rate of...Ch. 14.3 - A stream of water flowing at a rate of 1.2 m/min...Ch. 14.3 - A stream of water flowing at a rate of 1.2 m3/min...Ch. 14.3 - Prob. 14.68PCh. 14.3 - The total drag due to air friction on a jet...Ch. 14.3 - Prob. 14.70PCh. 14.3 - In order to shorten the distance required for...Ch. 14.3 - The helicopter shown can produce a maximum...Ch. 14.3 - Prior to takeoff, the pilot of a 3000-kg...Ch. 14.3 - The jet engine shown scoops in air at A at a rate...Ch. 14.3 - A jet airliner is cruising at a speed of 900 km/h...Ch. 14.3 - A 16-Mg jet airplane maintains a constant speed of...Ch. 14.3 - The propeller of a small airplane has a...Ch. 14.3 - The wind turbine generator shown has an...Ch. 14.3 - A wind turbine generator system having a diameter...Ch. 14.3 - While cruising in level flight at a speed of 570...Ch. 14.3 - In a Pelton-wheel turbine, a stream of water is...Ch. 14.3 - A circular reentrant orifice (also called Borda’s...Ch. 14.3 - A railroad car with length L and mass mg when...Ch. 14.3 - The depth of water flowing in a rectangular...Ch. 14.3 - Determine the rate of flow in the channel of Prob....Ch. 14.3 - A chain of length I and mass m lies in a pile on...Ch. 14.3 - Solve Prob. 14.86, assuming that the chain is...Ch. 14.3 - The ends of a chain lie in piles at A and C. When...Ch. 14.3 - A toy car is propelled by water that squirts from...Ch. 14.3 - A toy car is propelled by water that squirts from...Ch. 14.3 - The main propulsion system of a new space...Ch. 14.3 - The main propulsion system of a new space...Ch. 14.3 - A rocket sled bums fuel at the constant rate of...Ch. 14.3 - A space vehicle describing a circular orbit about...Ch. 14.3 - A 540-kg spacecraft is mounted on top of a rocket...Ch. 14.3 - The rocket used to launch the 540-kg spacecraft of...Ch. 14.3 - The weight of a spacecraft, including fuel, is...Ch. 14.3 - The rocket engines of a spacecraft are fired to...Ch. 14.3 - Determine the distance traveled by the spacecraft...Ch. 14.3 - A rocket weighs 2600 lb. including 2200 lb of...Ch. 14.3 - Determine the altitude reached by the spacecraft...Ch. 14.3 - For the spacecraft and the two-stage launching...Ch. 14.3 - In a jet airplane, the kinetic energy imparted to...Ch. 14.3 - In a rocket, the kinetic energy imparted to the...Ch. 14 - Three identical cars are being unloaded from an...Ch. 14 - A 50-kg mother and her 26-kg son are sledding down...Ch. 14 - An 80-Mg railroad engine A coasting at 6.5 km/h...Ch. 14 - In a game of pool, ball A is moving with a...Ch. 14 - Mass C, which has a mass of 4 kg, is suspended...Ch. 14 - A 15-lb block B is at rest and a spring of...Ch. 14 - A 6000-kg dump truck has a 1500-kg stone block...Ch. 14 - For the ceiling-mounted fan shown, determine the...Ch. 14 - An airplane with a weight W and a total wing span...Ch. 14 - The final component of a conveyor system receives...Ch. 14 - A garden sprinkler has four rotating arms, each of...Ch. 14 - A chain of length I and mass m falls through a...
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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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