Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Chapter 10, Problem 71P
The absolute velocities and directions of the jets entering and leaving the blade system are as shown. Calculate the power transferred from the jet to the blade system and the blade angles required.
P10.71
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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 10 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 10 - The geometry of a centrifugal water pump is r1 =...Ch. 10 - Find the resulting -groups when (a) D, , and Q or...Ch. 10 - Consider the centrifugal pump impeller dimensions...Ch. 10 - Dimensions of a centrifugal pump impeller areCh. 10 - Dimensions of a centrifugal pump impeller areCh. 10 - The blade is one of a series. Calculate the force...Ch. 10 - This blade is one of a series. What force is...Ch. 10 - A centrifugal water pump, with 15-cm-diameter...Ch. 10 - A centrifugal water pump designed to operate at...Ch. 10 - A series of blades, such as in Example 10.13,...
Ch. 10 - In passing through this blade system, the absolute...Ch. 10 - A centrifugal pump runs at 1750 rpm while pumping...Ch. 10 - A centrifugal water pump designed to operate at...Ch. 10 - Kerosene is pumped by a centrifugal pump. When the...Ch. 10 - In the water pump of Problem 10.8, the pump casing...Ch. 10 - Use data from Appendix C to choose points from the...Ch. 10 - Data from tests of a water suction pump operated...Ch. 10 - A centrifugal pump impeller having r1 = 50 mm, r2...Ch. 10 - A centrifugal pump impeller having dimensions and...Ch. 10 - An axial-flow fan operates in sea-level air at...Ch. 10 - Data measured during tests of a centrifugal pump...Ch. 10 - A small centrifugal pump, when tested at N = 2875...Ch. 10 - If the impeller of Problem 10.20 rotates between...Ch. 10 - At the outlet of a pump impeller of diameter 0.6 m...Ch. 10 - Typical performance curves for a centrifugal pump,...Ch. 10 - A pump with D = 500 mm delivers Q = 0.725 m3/s of...Ch. 10 - At its best efficiency point ( = 0.87), a...Ch. 10 - Using the performance curves in Appendix C, select...Ch. 10 - A pumping system must be specified for a lift...Ch. 10 - A centrifugal water pump operates at 1750 rpm; the...Ch. 10 - A set of eight 30-kW motor-pump units is used to...Ch. 10 - A blower has a rotor with 12-in. outside diameter...Ch. 10 - A centrifugal water pump has an impeller with an...Ch. 10 - Appendix C contains area bound curves for pump...Ch. 10 - Use data from Appendix C to verify the similarity...Ch. 10 - A centrifugal water pump has an impeller with...Ch. 10 - Catalog data for a centrifugal water pump at...Ch. 10 - A 1/3 scale model of a centrifugal water pump...Ch. 10 - Sometimes the variation of water viscosity with...Ch. 10 - A large deep fryer at a snack-food plant contains...Ch. 10 - Data from tests of a pump, with a...Ch. 10 - A four-stage boiler feed pump has suction and...Ch. 10 - A centrifugal pump operating at N = 2265 rpm lifts...Ch. 10 - A centrifugal pump is installed in a piping system...Ch. 10 - Part of the water supply for the South Rim of...Ch. 10 - Consider the flow system shown in Problem 8.94....Ch. 10 - Afire nozzle is supplied through 300 ft of...Ch. 10 - Performance data for a centrifugal fan of 3-ft...Ch. 10 - The performance data of Problem 10.57 are for a...Ch. 10 - Experimental test data for an aircraft engine fuel...Ch. 10 - Preliminary calculations for a hydroelectric power...Ch. 10 - Conditions at the inlet to the nozzle of a Pelton...Ch. 10 - A Francis turbine is to operate under a head of 46...Ch. 10 - A Kaplan (propeller with variable-pitch blades)...Ch. 10 - Francis turbine Units 19, 20, and 21, installed at...Ch. 10 - Measured data for performance of the reaction...Ch. 10 - For a flow rate of 12 L/s and turbine speed of 65...Ch. 10 - The velocity of the water jet driving this impulse...Ch. 10 - An impulse turbine is to develop 15 MW from a...Ch. 10 - An impulse turbine under a net head of 33 ft was...Ch. 10 - The absolute velocities and directions of the jets...Ch. 10 - A fanboat in the Florida Everglades is powered by...Ch. 10 - A jet-propelled aircraft traveling at 225 m/s...Ch. 10 - When an air jet of 1-in.-diameter strikes a series...Ch. 10 - The volume flow rate through the propeller of an...Ch. 10 - A typical American multi blade farm windmill has D...Ch. 10 - An airplane flies at 200 km/h through still air of...Ch. 10 - This ducted propeller unit drives a ship through...Ch. 10 - A model of an American multi blade farm windmill...Ch. 10 - A large Darrieus vertical axis wind turbine was...Ch. 10 - Show that this ducted propeller system when moving...Ch. 10 - This ducted propeller unit (now operating as a...Ch. 10 - What is the maximum power that can be expected...Ch. 10 - If an ideal windmill is operating at best...Ch. 10 - A prototype air compressor with a compression...Ch. 10 - Prob. 89PCh. 10 - We have seen many examples in Chapter 7 of...
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