EBK APPLIED FLUID MECHANICS
7th Edition
ISBN: 8220100668340
Author: UNTENER
Publisher: PEARSON
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Chapter 3, Problem 3.34PP
If milk has a specific gravity of
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Consider the bar, shown in Figure 1 that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.10-3 m², and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
x=0.0
x=2.0
2.0m
10 kN
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x))
-) +1(x) = 0.
d.x
dx
What are the accompanying boundary conditions for this bar?
b) Using the mesh in Figure 2, form the basis functions associated with element 2 and write the FEM
approximation over the element.
1
2
3
1
2
1m
1m
Figure 2: Mesh of 2 elements. Elements are numbered with underlines.
c) The general form of the element stiffness matrix system, with nodes indexed by i and j, is,
AE
Uj
N;(x)l(x)dx
– Ng(0)f(0)
¥ [4]}]{{}}={{{}\(\\+} + {N(2)f(2) = N (0)5() },
(1)
0, respectively.
L
=
(2)
where f(2) and f(0) denote the boundary forces at positions x 2 and x
Evaluate…
answer please
amination)
Question 1
Consider the bar, shown in Figure 1, that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.103 m2, and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
10 kN
X
x=0.0
x=2.0
2.0m
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x)) + 1(x) = 0.
dx
dx
What are the accompanying boundary conditions for this bar?
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DII
F5
F6
F7
F8
80
F3
F4
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20
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Chapter 3 Solutions
EBK APPLIED FLUID MECHANICS
Ch. 3 - Write the expression for computing the pressure in...Ch. 3 - Define absolute pressureCh. 3 - Define gage pressureCh. 3 - Define atmospheric pressureCh. 3 - Write the expression relating gage pressure,...Ch. 3 - State whether statements 3.6-3.10 are (or can be)...Ch. 3 - State whether statements 3.6-3.10 are (or can be)...Ch. 3 - State whether statements 3.6-3.10 are (or can be)...Ch. 3 - State whether statements 3.6-3.10 are (or can be)...Ch. 3 - State whether statements 3.6-3.10 are (or can be)...
Ch. 3 - State whether statements 3.6-3.10 are (or can be)...Ch. 3 - State whether statements 3.6-3.10 are (or can be)...Ch. 3 - State whether statements 3.6-3.10 are (or can be)...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - Problems 3.14-3.33 require that you convert the...Ch. 3 - If milk has a specific gravity of 1.08, what is...Ch. 3 - The pressure in an unknown fluid at a depth of 4.0...Ch. 3 - The pressure at the bottom of a tank of propyl...Ch. 3 - When you dive to a depth of 12.50 ft in seawater,...Ch. 3 - A water storage tank is on the roof of a factory...Ch. 3 - An open tank contains ethylene glycol at 25C....Ch. 3 - For the tank of ethylene glycol described in...Ch. 3 - Figure 3.19 shows a diagram of the hydraulic...Ch. 3 - Figure 3.20 shows a clothes washing machine The...Ch. 3 - An airplane is flying at 10.6km altitude. In its...Ch. 3 - For the tank shown in Fig. 3.21, determine the...Ch. 3 - For the tank shown in Fig. 3.21, determine the...Ch. 3 - For the tank shown in Fig. 3.21. determine the...Ch. 3 - For the tank shown in Fig. 3.21 determine the...Ch. 3 - For the tank in Fig. 3.22, compute the depth of...Ch. 3 - For the tank in Fig. 3.22, compute the depth of...Ch. 3 - Figure 3.22 represents an oil storage drum that is...Ch. 3 - A storage tank for sulfuric acid is 1.5m in...Ch. 3 - A storage drum for crude oil ( sg=0.89 ) is 32 ft...Ch. 3 - The greatest known depth in the ocean is...Ch. 3 - Figure 3.23 shows a closed tank that contains...Ch. 3 - Figure 3.24 shows a closed container holding water...Ch. 3 - Determine the pressure at the bottom of the tank...Ch. 3 - Describe a simple J-tube manometerCh. 3 - Describe a differential U-tube manometer.Ch. 3 - Describe a well-type manometer.Ch. 3 - Describe an inclined well-type manometer.Ch. 3 - Describe a compound manometer.Ch. 3 - Water is in the pipe shown in Fig. 3.26Calculate...Ch. 3 - For the differential manometer shown in Fig. 3.27,...Ch. 3 - For the manometer shown in Fig. 3.28, calculate...Ch. 3 - For the manometer shown in Fig. 3.29, calculate...Ch. 3 - For the manometer shown in Fig. 3.30, calculate...Ch. 3 - For the compound manometer shown in Fig.3.31,...Ch. 3 - For the compound differential manometer in...Ch. 3 - Figure 3.33 shows a manometer being used to...Ch. 3 - For the well-type manometer in Fig. 3.34,...Ch. 3 - Figure 3.35 shows an inclined well-type manometer...Ch. 3 - a. Determine the gage pressure at point A in Fig....Ch. 3 - What is the function of a barometer?Ch. 3 - Describe the construction of a barometer.Ch. 3 - Why is mercury a convenient fluid to use in a...Ch. 3 - If water were to be used instead of mercury in a...Ch. 3 - What is the barometric pressure reading in inches...Ch. 3 - What is the barometric pressure reading in...Ch. 3 - Why must a barometric pressure reading be...Ch. 3 - By how much would the barometric pressure reading...Ch. 3 - Denver, Colorado, is called the "Mile-High City"...Ch. 3 - The barometric pressure is reported to be 28.6 in...Ch. 3 - A barometer indicates the atmospheric pressure to...Ch. 3 - What would be the reading of a barometer in inches...Ch. 3 - Prob. 3.85PPCh. 3 - The pressure in a heating duct is measured to be...Ch. 3 - The pressure in a ventilation duct at the inlet to...Ch. 3 - The pressure in an air conditioning duct is...Ch. 3 - The pressure in a compressed natural gas line is...Ch. 3 - The pressure in a vacuum chamber is 68.2 kPa....Ch. 3 - The pressure in a vacuum chamber is 12.6 psig....Ch. 3 - Prob. 3.92PPCh. 3 - Prob. 3.93PPCh. 3 - A passive solar water heater is to be installed on...Ch. 3 - The elevated tank similar to the one shown in Fig....Ch. 3 - Prob. 3.96PPCh. 3 - A concrete form used to pour a basement wall is to...Ch. 3 - An environmental instrumentation package is to be...Ch. 3 - Prob. 3.99PPCh. 3 - Prob. 3.100PPCh. 3 - A meteorologist reports a "high pressure system"...Ch. 3 - What is the pressure, in psig, at the bottom of a...Ch. 3 - If air has a constant specific weight of...
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- Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0 0.8- 0.6 0.4- 0.2 0.0 00 -0.2 -0.4 -0.6- 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps.arrow_forwardQuestion 2 Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0 0.8- 0.6- 0.4- 0.2- 0.0- -0.2- -0.4- -0.6 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep. b) Consider explicit schemes with central and upwind discretisations. Explain how each of these candidate discretisations could produce the behaviour shown in Figure 3. c) Determine the CFL number that was used in the simulation for each of the candidate schemes for all possible updates. Assume that the timestep and mesh-width used are constant. Read the data to two digits of accuracy from Figure 4 shown at the end of the question, which is an enlarged version of Figure 3. Demonstrate your method and input data for one calculation, but then use a…arrow_forwardanswer pleasearrow_forward
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