Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Chapter 13, Problem 13.25PP
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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?
MacBook Air
a
会
DII
F5
F6
F7
F8
80
F3
F4
0/
20
[8 marksl
8
FO
Chapter 13 Solutions
Applied Fluid Mechanics (7th Edition)
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Ch. 13 - Describe the difference between a simplex...Ch. 13 - Describe the general shape of the plot of pump...Ch. 13 - Describe the general shape of the plot of total...Ch. 13 - To the head-versus-capacity plot of Problem 13.13...Ch. 13 - To what do the affinity laws refer in regard to...Ch. 13 - Fora given centrifugal pump, if the speed of...Ch. 13 - For a given centrifugal pump, if the speed of...Ch. 13 - For a given centrifugal pump, if the speed of...Ch. 13 - For a given size of centrifugal pump casing, if...Ch. 13 - For a given size of centrifugal pump casing, if...Ch. 13 - For a given size of centrifugal pump casing, if...Ch. 13 - Describe each part of this centrifugal pump...Ch. 13 - For the line of pumps shown in Fig.13.22 specify a...Ch. 13 - For the line of pumps shown in Fig. 13.22 ,...Ch. 13 - For the 2x310 centrifugal pump performance curve...Ch. 13 - For the 2310 centrifugal pump performance curve...Ch. 13 - Using the result from Problem 13.26 describe how...Ch. 13 - For the centrifugal pump performance curve shown...Ch. 13 - Prob. 13.29PPCh. 13 - State some advantages of using a variable-speed...Ch. 13 - Describe how the capacity, efficiency, and power...Ch. 13 - If two identical centrifugal pumps are connected...Ch. 13 - Describe the effect of operating two pumps in...Ch. 13 - For each of the following sets of operating...Ch. 13 - For the 112313 centrifugal pump performance curve...Ch. 13 - For the 6817 centrifugal pump performance curve...Ch. 13 - Figure 13.52 shows that a mixed-flow pump is...Ch. 13 - Compute the specific speed for a pump operating at...Ch. 13 - Compute the specific speed for a pump operating at...Ch. 13 - Compute the specific speed for a pump operating at...Ch. 13 - Compute the specific speed for a pump operating at...Ch. 13 - It is desired to operate a pump at 1750 rpm by...Ch. 13 - Define net positive suction head (NPSH).Ch. 13 - Distinguish between NPSH available and NPSH...Ch. 13 - Describe what happens to the vapor pressure of...Ch. 13 - Describe why it is important to consider NPSH when...Ch. 13 - For what point in a pumping system is the NPSH...Ch. 13 - Discuss why it is desirable to elevate the...Ch. 13 - Discuss why it is desirable to use relatively...Ch. 13 - Prob. 13.50PPCh. 13 - If we assume that a given pump requires 7.50 ft of...Ch. 13 - Determine the available NPSH for the pump in...Ch. 13 - Find the available NPSH when a pump draws water at...Ch. 13 - A pump draws benzene at 25 C from a tank whose...Ch. 13 - Determine the available NPSH for the system shown...Ch. 13 - Determine the NPSH available when a pump draws...Ch. 13 - Determine the NPSH available when a pump draws...Ch. 13 - Determine the NPSH available when a pump draws...Ch. 13 - Determine the NPSH available when a pump draws...Ch. 13 - Repeat Problem 13.56 if the pump is 44 in below...Ch. 13 - Repeat Problem 13.59 if the pump is 27 in above...Ch. 13 - Repeat Problem 13.57 if the pump is 1.2 m below...Ch. 13 - Repeat Problem 13.58 if the pump is installed...Ch. 13 - A pump draws propane at F (sgfrom a tank whose...Ch. 13 - A pump draws propane at 45 C (sg =0.48 ) from a...
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- show workingarrow_forwardCFD help Figure 3: Advection equation, solution for three different timesteps. Q1) 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.arrow_forwardanswer pleasearrow_forward
- 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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