Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Chapter 6, Problem 6.114PP
To determine
Height of water from the fire hydrant.
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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 6 Solutions
Applied Fluid Mechanics (7th Edition)
Ch. 6 - Convert a volume flow rate of 3.0 gal/min to...Ch. 6 - Convert 459 gal/min to rrP/s.Ch. 6 - Convert 3720 gal/min to mJ/sCh. 6 - Convert 34.3 gal/min to mJ/sCh. 6 - Convert a volume flow rate of 125 L/min to m3/s.Ch. 6 - Convert 4500 L/min to m5/s.Ch. 6 - Convert 15 000 L/minto m3/s.Ch. 6 - Convert 459 gal/min to L/mninCh. 6 - Convert 3720 gal/min to L/minCh. 6 - Convert 23.5cm2/stom3/s.
Ch. 6 - '6.11 Convert 0.296cm5/stom3/s.Ch. 6 - Convert 0.105 cm3/s to L/minCh. 6 - Convert 3.53103m3/s to L/min.Ch. 6 - Convert 5.26106m3stoL/min.Ch. 6 - Prob. 6.15PPCh. 6 - Convert 20 gal/min to ft'/s.Ch. 6 - Convert 2500 gal/min to ft5/s.Ch. 6 - Convert 2.50 gal/min to ft3/s.Ch. 6 - Convert 125 ft3/s to gal/minCh. 6 - Convert 0.060 ft3/s to gal/min.Ch. 6 - Convert 0.03 ft5/s to gal/minCh. 6 - Convert ft5/s sto gal/minCh. 6 - Table 6.21 lists the range of typical volume flow...Ch. 6 - Table 6.2 lists the range of typical volume flow...Ch. 6 - A certain deep-well pump for a residence is rated...Ch. 6 - A small pump delivers 0.85 gal/h of liquid...Ch. 6 - A small metering pump delivers 11.4 gal of a water...Ch. 6 - A small metering pump delivers 19.5 mL/min of...Ch. 6 - Water at 10 C is flowing at 0.075 m3/s Calculate...Ch. 6 - Oil for a hydraulic system (sg =0.90 ) is flowing...Ch. 6 - A liquid refrigerant (sg = 1.08) is flowing at a...Ch. 6 - After the refrigerant from Problem 6.31 flashes...Ch. 6 - A fan delivers 640ft3/min (CFM) of air. If the...Ch. 6 - A large blower for a furnace delivers 47000ft3/min...Ch. 6 - A furnace requires 1200 Ib/h of air for efficient...Ch. 6 - If a pump removes 1.65 gal/min of water from a...Ch. 6 - Calculate the diameter of a pipe that would carry...Ch. 6 - If the velocity of a liquid is 1.65 ft/s in a...Ch. 6 - When 2000 L/min of water flows through a circular...Ch. 6 - Water flows at 1.20 m/s in a circular section with...Ch. 6 - Figure 6.16 shows a fabricated assembly made from...Ch. 6 - A standard Schedule 40 steel pipe is to be...Ch. 6 - If water at 180 F is flowing with a velocity of...Ch. 6 - A standard steel tube, 1.5 25-mm OD 3 1,5-mm wall...Ch. 6 - The recommended velocity of flow in the discharge...Ch. 6 - Repeat Problem 6.45, except specify suitable sizes...Ch. 6 - Table 6.2 shows the typical volume flow rate for...Ch. 6 - Repeat Problem 6.47 but use Schedule 80 DM pipeCh. 6 - Compute the resulting velocity of flow if 400...Ch. 6 - Repeat Problem 6.49 for a DN 50 Schedule 30 pipe.Ch. 6 - Compute the resulting velocity of flow if 400...Ch. 6 - Repeat Problem 6.51 for a 4-in Schedule 30 pipe.Ch. 6 - From the list of standard hydraulic steel tubing...Ch. 6 - A standard 6-in Schedule 40 steel pipe is carrying...Ch. 6 - For Problems 6.55-6.57, use Fig. 6.3 O to specify...Ch. 6 - For Problems 6.55-6.57, use Fig. 6.3 to specify...Ch. 6 - For Problems 6.55-6.57, use Fig. 6.3 O to specify...Ch. 6 - A venturi meter is a device that uses a...Ch. 6 - A flow nozzle, shown in Fig. 6.18 is used to...Ch. 6 - Gasoline (sg = 0.67) is flowing at 0.11 m3/s in...Ch. 6 - Water at 10 C is flowing from point A to point B...Ch. 6 - Calculate the volume flow rate of water at 5 C...Ch. 6 - Calculate the pressure required in the larger...Ch. 6 - Kerosene with a specific weight of 50.0 lb/ft3 is...Ch. 6 - For the system shown in Fig. 6.23 ; calculate (a)...Ch. 6 - For the system shown in Fig. 6.24ss, calculate (a)...Ch. 6 - For the tank shown in Fig. 6.25lO, calculate the...Ch. 6 - Calculate the pressure of the air in the sealed...Ch. 6 - For the siphon in Fig. 6.26, calculate (a) the...Ch. 6 - For the siphon in Fig. 6.26 , calculate the...Ch. 6 - For the siphon in Fig. 6.26 , assume that the...Ch. 6 - For the siphon shown in Fig. 6.27, calculate (a)...Ch. 6 - For the special fabricated reducer shown in Fig....Ch. 6 - In the fabricated enlargement shown in Fig. 6.29,...Ch. 6 - Figure 6.30 shows a manometer being used to...Ch. 6 - For the venturi meter shown in Fig. 6.30,...Ch. 6 - Oil with a specific weight of 8.64 kN/m3 flows...Ch. 6 - The venturi meter shown in Fig. 6.32 iP carries...Ch. 6 - Oil with a specific gravity of 0.90 is flowing...Ch. 6 - Oil with a specific gravity of 0.90 is flowing...Ch. 6 - Gasoline (sg = 0.67) is flowing at 4.0 ft3/s in...Ch. 6 - Oil with a specific weight of 55.0lb/ft3 flows...Ch. 6 - Draw a plot of elevation head, pressure head,...Ch. 6 - Prob. 6.84PPCh. 6 - Figure 6.36 shows a system in which water flows...Ch. 6 - Figure 6.37 shows a venturi meter with a U-tube...Ch. 6 - For the tank shown in Fig. 6.38, compute the...Ch. 6 - What depth of fluid above the outlet nozzle is...Ch. 6 - Derive Torricelli's theorem for the velocity of...Ch. 6 - Solve Problem 6.88 using the direct application of...Ch. 6 - To what height will the jet of fluid rise for the...Ch. 6 - To what height will the jet of water rise for the...Ch. 6 - What pressure is required above the water in Fig....Ch. 6 - What pressure is required above the water in Fig....Ch. 6 - Compute the time required to empty the tank shown...Ch. 6 - Compute the time required to empty the tank shown...Ch. 6 - Compute the time required to empty the tank shown...Ch. 6 - Compute the time required to empty the tank shown...Ch. 6 - Compute the time required to reduce the depth in...Ch. 6 - Compute the time required to reduce the depth in...Ch. 6 - Compute the time required to reduce the depth in...Ch. 6 - Compute the time required to reduce the depth in...Ch. 6 - Prob. 6.103PPCh. 6 - Repeat Problem 6.101 if the tank is sealed and a...Ch. 6 - Repeat Problem 6.96 if the tank is sealed and a...Ch. 6 - Repeat Problem 6.100 if the tank is sealed and a...Ch. 6 - A village currently carries water by hand from a...Ch. 6 - A "spa tub" is to be designed to replace bath tubs...Ch. 6 - A simple soft drink system relies on pressurized...Ch. 6 - A concept team for a toy company is considering a...Ch. 6 - 6.111 Bernoulli's principle applies to Venturi...Ch. 6 - Prob. 6.112PPCh. 6 - You are to develop a mixing valve for use in a...Ch. 6 - Prob. 6.114PPCh. 6 - You would like to empty the in-ground pool in the...Ch. 6 - Prob. 6.116PPCh. 6 - Create a spreadsheet for computing the values of...Ch. 6 - Prob. 2APCh. 6 - Prob. 3APCh. 6 - Create a spreadsheet for computing, using Eq....Ch. 6 - Prob. 5APCh. 6 - Create a spreadsheet for computing the velocity of...
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