Heating Ventilating and Air Conditioning: Analysis and Design
6th Edition
ISBN: 9780471470151
Author: Faye C. McQuiston, Jeffrey D. Spitler, Jerald D. Parker
Publisher: Wiley, John & Sons, Incorporated
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Chapter 3, Problem 3.28P
Assume that the air in Problem 3-22 is supplied to the space at 53 F (12 C). Compute the volume flow rate of the air required in (a) English units and (b) SI units.
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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 3 Solutions
Heating Ventilating and Air Conditioning: Analysis and Design
Ch. 3 - A space is at a temperature of 75 F (24 C), and...Ch. 3 - Determine the humidity ratio, enthalpy, and...Ch. 3 - Suppose the air of Problem 3-2 is at a pressure...Ch. 3 - What is the enthalpy of moist air at 70 F (20 C)...Ch. 3 - The inside surface temperature of a window in a...Ch. 3 - What is the mass flow rate of dry air flowing at a...Ch. 3 - Determine the dew point of moist air at 80 F (27...Ch. 3 - A room is to be maintained at 72 F (22 C) db. It...Ch. 3 - Air is cooled from 80 F db and 67 F wb until it is...Ch. 3 - Conditions in a room are measured to be 80 F db...
Ch. 3 - The environmental conditions in a room are to be...Ch. 3 - Air enters a cooling coil at the rate of 5000 cfm...Ch. 3 - Air flowing in a duct has dry and wet bulb...Ch. 3 - Air is humidified with the dry bulb temperature...Ch. 3 - Air at 38 C db and 20 C wb is humidified...Ch. 3 - Two thousand cfm (1.0 m3/s) of air at an initial...Ch. 3 - Air at 40 F (5 C) db and 35 F (2 C) wb is mixed...Ch. 3 - Rework Problem 3-25, using Chart 1a, with the...Ch. 3 - The design cooling load for a zone in a building...Ch. 3 - Assume that the air in Problem 3-22 is supplied to...Ch. 3 - The sensible heat loss from a space is 500,000...Ch. 3 - Air enters a refrigeration coil at 90 Fdb and 75...Ch. 3 - A building has a total heating load of 200,000...Ch. 3 - Reconsider Problem 3-36 for an elevation of 5000...Ch. 3 - The system of Problem 3-34 has a supply air fan...Ch. 3 - An evaporative cooling system is to be used to...Ch. 3 - A cooling system is being designed for use at high...Ch. 3 - Consider a space heating system designed as shown...Ch. 3 - A variable-air-volume VAV cooling system is a type...Ch. 3 - Rework Problem 3-43 for an elevation of 5000 feet...Ch. 3 - The design condition for a space is 77 F (25 C) db...Ch. 3 - Rework Problem 3-45 for an elevation of 5000 feet...Ch. 3 - It is necessary to cool and dehumidify air from 80...Ch. 3 - Conditions in one zone of a dual-duct conditioning...Ch. 3 - Rework Problem 3-48 for an elevation of 5000 ft...Ch. 3 - A water coil in Problem 3-48 cools return air to...Ch. 3 - A multizone air handler provides air to several...Ch. 3 - Under normal operating conditions a zone has a...Ch. 3 - An interior zone of a large building is designed...Ch. 3 - Outdoor air is mixed with room return air to...Ch. 3 - Consider an enclosed swimming pool. The pool area...Ch. 3 - One particular zone served by a multizone air...Ch. 3 - A research building requires 100 percent outdoor...Ch. 3 - A space requires cooling in the amount of 120,000...
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- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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