Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Textbook Question
Chapter 19, Problem 19.1PP
Determine the velocity of flow and the friction loss as
Expert Solution & Answer
To determine
The velocity of flow
The value of friction loss
Answer to Problem 19.1PP
The velocity of flow, V=570ft/min
The value of friction loss, HL=0.021 in H2O
Explanation of Solution
Given information:
Diameter of the duct, D=18in
Rate of flow, Q=1000 cfm
Length of the duct, L=75 ft
To find out the friction loss, we use the formula
Where,
L= Length of the duct
HL=Friction loss
hL=friction loss of water per 100 ft
friction loss of water per 100 ft is calculated by the chart of friction loss in a duct and it is equal to hL=0.028 in H2O
We compare between any two given values and their intersecting point give the third required value
The velocity of flow is also calculated by the chart of friction loss in a duct and it is equal to
The V=570ft/min
Calculation:
Now we put the known values in equation
HL= 0.021 in H2O
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 19 Solutions
Applied Fluid Mechanics (7th Edition)
Ch. 19 - Determine the velocity of flow and the friction...Ch. 19 - Repeat Problem 19.1 O for duct diameters of 16,...Ch. 19 - Prob. 19.3PPCh. 19 - Determine the velocity of flow and the friction...Ch. 19 - Repeat Problem 19.40 for duct diameters of...Ch. 19 - Prob. 19.6PPCh. 19 - Prob. 19.7PPCh. 19 - '19.8 A branch duct for a heating system measures...Ch. 19 - Prob. 19.9PPCh. 19 - Prob. 19.10PP
Ch. 19 - A branch duct for a heating system measures 75250...Ch. 19 - Prob. 19.12PPCh. 19 - Prob. 19.13PPCh. 19 - Prob. 19.14PPCh. 19 - Repeat Problem 19.14, but use a five-piece elbowCh. 19 - Prob. 19.16PPCh. 19 - Prob. 19.17PPCh. 19 - Prob. 19.18PPCh. 19 - Prob. 19.19PPCh. 19 - Prob. 19.20PPCh. 19 - Compute the pressure drop as 0.20m3/s of air flows...Ch. 19 - Prob. 19.22PPCh. 19 - Compute the pressure drop as 0.85m3/s of air flows...Ch. 19 - A section of duct system consists of 42 ft of...Ch. 19 - A section of duct system consists of 38 ft of...Ch. 19 - The intake duct to a fan consists of intake...Ch. 19 - Forthe conditions shown in figs. 19.719- 19.10 0,...Ch. 19 - Forthe conditions shown in figs. 19.719- 19.10 0,...Ch. 19 - Prob. 19.29PPCh. 19 - Forthe conditions shown in figs. 19.719- 19.10 0,...
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