Fluid Mechanics (2nd Edition)
2nd Edition
ISBN: 9780134649290
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 5, Problem 102P
To determine
The required power output of the pump.
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
Chapter 5 Solutions
Fluid Mechanics (2nd Edition)
Ch. 5 - Prob. 1FPCh. 5 - Oil is subjected to a pressure of 300 kPa at A,...Ch. 5 - Prob. 3FPCh. 5 - Water flows through the pipe at 8 m/s. Determine...Ch. 5 - The tank has a square base and is filled with...Ch. 5 - Prob. 6FPCh. 5 - Water flows from the reservoir through the...Ch. 5 - Crude oil flows through the 50-mm-diameter pipe...Ch. 5 - Water at A has a pressure of 400 kPa and a...Ch. 5 - Water from the reservoir flows through the...
Ch. 5 - Prob. 11FPCh. 5 - The jet engine takes in air and fuel having an...Ch. 5 - Determine the required average change in pressure...Ch. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Air at 60°F flows through the horizontal tapered...Ch. 5 - Prob. 5PCh. 5 - The water in an open channel drainage canal flows...Ch. 5 - Water flows out of a faucet at A at 6 m/s....Ch. 5 - Water flows through the 30-mm-diameter pipe at...Ch. 5 - Water flows through the 30-mm-diameter pipe and is...Ch. 5 - Drainage under a canal is provided using a...Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - A fountain is produced by water that flows up the...Ch. 5 - Prob. 14PCh. 5 - Air is drawn into the 200-mm-diameter cylinder...Ch. 5 - The level of mercury in the manometer has the...Ch. 5 - A fountain ejects water through the two nozzles A...Ch. 5 - Prob. 18PCh. 5 - Heavy rain has caused reservoir A to reach a...Ch. 5 - A fire hydrant supplies water under a pressure of...Ch. 5 - Determine the velocity of water through the pipe...Ch. 5 - The sewage siphon regulates the level of water in...Ch. 5 - If the manometer contains mercury, determine the...Ch. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - When the valve at A is opened, the initial...Ch. 5 - Prob. 27PCh. 5 - Prob. 28PCh. 5 - Air is pumped into the top of the tank so that the...Ch. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - A river has an average width of 5 m. Just after...Ch. 5 - A river has an average width of 5 m and flows with...Ch. 5 - Prob. 34PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Water flows through the transition at 0.3 m3/s,...Ch. 5 - If the water in piezometers A and B rises to hA =...Ch. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Water flows through the pipe transition with a...Ch. 5 - Water from a faucet tapers from a diameter of 0.5...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - If the pressure at A is 325 kPa, and the velocity...Ch. 5 - If the pressure at A is 215 kPa, and the velocity...Ch. 5 - Prob. 47PCh. 5 - If the difference in the level of mercury within...Ch. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - If the pressure in the 6-in.-diameter pipe at A is...Ch. 5 - Prob. 53PCh. 5 - Prob. 54PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - The solution is ejected from the 20-mm-diameter...Ch. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Water from the large closed tank is to be drained...Ch. 5 - Prob. 64PCh. 5 - Carbon dioxide at 20°C passes through the...Ch. 5 - Prob. 66PCh. 5 - Prob. 67PCh. 5 - Determine the average velocity and the pressure in...Ch. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71PCh. 5 - Prob. 72PCh. 5 - Water at a pressure of 12 psi and a velocity of 5...Ch. 5 - Prob. 74PCh. 5 - Prob. 75PCh. 5 - The siphon spillway provides an automatic control...Ch. 5 - Prob. 77PCh. 5 - A piezometer and a manometer containing mercury...Ch. 5 - Water is drawn into the pump, such that the...Ch. 5 - Prob. 80PCh. 5 - Prob. 81PCh. 5 - Prob. 82PCh. 5 - Prob. 83PCh. 5 - A pump is used to deliver water from a large...Ch. 5 - A 6-hp pump with a 3-in.-diameter hose is used to...Ch. 5 - The pump is used with a 3-in.-diameter hose to...Ch. 5 - Solve Prob. 5–86 by including frictional head...Ch. 5 - The pump discharges water at B at 0.3 ft3/s. If...Ch. 5 - Prob. 89PCh. 5 - Draw the energy and hydraulic grade lines for the...Ch. 5 - The turbine removes energy from the water in the...Ch. 5 - Prob. 92PCh. 5 - Prob. 93PCh. 5 - Water in the reservoir flows through the...Ch. 5 - Prob. 95PCh. 5 - Determine the power delivered to the turbine if...Ch. 5 - The turbine at C draws a power of 90.5 hp. If the...Ch. 5 - Prob. 98PCh. 5 - Prob. 99PCh. 5 - Prob. 100PCh. 5 - The pump is connected to the 2-in.-diameter hose....Ch. 5 - Prob. 102PCh. 5 - Prob. 103PCh. 5 - Prob. 104PCh. 5 - Prob. 105PCh. 5 - Crude oil is pumped from a test separator at A to...Ch. 5 - Prob. 107PCh. 5 - Prob. 108PCh. 5 - Determine the power that the pump supplies to the...Ch. 5 - The pump delivers water at 120 ft3/min from the...Ch. 5 - Prob. 111PCh. 5 - Prob. 112P
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