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Heating Ventilating And Air Conditioning Analysis And Design 6th Edition Faye C. McQuiston, Jerald D. Parker, Jeffrey D. Spitler - Solutions
9–54 The RLC circuit in Figure P9–54 is in the zero state when at t ¼ 0 an exponential source, vS(t) ¼ VAeat V, is suddenly connected to it(a) Find the circuit integrodifferential equation that describes the behavior of the current in the circuit.(b) If R ¼ 100 V, L ¼ 50 mH, C ¼ 10 mF, VA
Repeat problem 9–54 when an exponential source, vS(t) ¼10(1e500t) V, is suddenly connected to the circuit at t ¼ 0.
Find vC(t) for t 0 when the input to the RC circuit shown in Figure P9–56 is vS(t) ¼ VAr(t) V. Assume vC(0) ¼ 0 V. + R w + C=vc(t) vs(t) = Var(t) FIGURE P9-56
Use the initial and final value properties to find the initial and final values of the waveforms corresponding to the transforms below. If either property is not applicable, explain why.(a) F1ðsÞ ¼ 16ðs þ 1Þðs þ 2Þðs þ 3Þ(b) F2ðsÞ ¼ s 100 sðs þ 50Þ
Use the initial and final value properties to find the initial and final values of the waveforms corresponding to the transforms below. If either property is not applicable, explain why.(a) F1ðsÞ ¼ 8s2ðs þ 2Þðs2 þ 12s þ 13Þ(b) F2ðsÞ ¼ s þ 1000 sðs þ 50Þðs þ 100Þ
Use the initial and final value properties to find the initial and final values of the waveforms corresponding to the transforms below. If either property is not applicable, explain why.(a) F1ðsÞ ¼ 400 s ðs þ 10Þ2 þ 202 (b) F2ðsÞ ¼ 30ð3s4 þ 10s2 þ 4Þsðs2 þ 1Þðs2 þ 4Þ
Use the initial and final value properties to find the initial and final values of the waveforms corresponding to the transforms below. If either property is not applicable, explain why.(a) F1ðsÞ ¼ 50sðs2 þ 5s þ 6Þðs þ 2Þðs þ 6Þðs þ 12Þ(b) F2ðsÞ ¼ 25ðs2 þ 10s þ 40Þsðs2
Use the initial and final value properties to find the initial and final values of the waveforms corresponding to the following transforms. If either property is not applicable, explain why.(a) F1ðsÞ ¼ sðs þ 6Þs2 þ 6s þ 9(b) F2ðsÞ ¼ 20ðs2 þ 10s þ 100Þsðs2 þ 20s þ 100Þ
Use the initial and final value properties to find the initial and final values of the waveform corresponding to the following transform. If either property is not applicable, explain why.FðsÞ ¼ 80ðs3 þ 2s2 þ s þ 2Þsðs3 þ 4s2 þ 4s þ 16Þ
The MATLAB function limit can be used to take the limit of a symbolic expression. Use MATLAB and the initial and final value properties to find the initial and final values of the waveforms corresponding to the following transforms. If either property is not applicable, explain why. UseMATLAB again
The Dominant Pole Approximation When a transform F(s) has widely separated poles, then those closest to the j-axis tend to dominate the response because they have less damping. An approximation to the waveform can be obtained by ignoring the contributions of all except the dominant poles.We can
First-Order Circuit Step Response In Chapter 7 we found that the step response of a first-order circuit can be written as f ðtÞ ¼ f ð1Þ þ ½f ð0Þ f ð1Þe1=TC where f(0) is the initial value, f(1) is the final value, and Tc is the time constant. Show that the corresponding transform has
Inverse Transform for Complex Poles In Section 9–4 we learned that complex poles occur in conjugate pairs and that for simple poles the partial fraction expansion of F(s) will contain two terms of the form FðsÞ ¼ . . .k s þ a jbþ k s þ a þ jbþ . . .Show that when the complex conjugate
Solving State Variable Equations With zero input, a series RLC circuit can be described by the following coupled first-order equations in the inductor current iL(t) and capacitor voltage vC(t).dvCðtÞdt¼ 1 CiLðtÞdiLðtÞdt¼ 1 LvCðtÞ R LiLðtÞ(a) Transform these equations into the s
Complex Differentiation Property The complex differentiation property of the Laplace transformation states that If Lff ðtÞg ¼ FðsÞ thenLftf ðtÞg ¼ d ds FðsÞUse this property to find the Laplace transforms of f(t) ¼{tg(t)}u(t) when g(t)¼ eat. Repeat for g(t) ¼sin bt and g(t) ¼cos bt.
Butterworth Poles Steven Butterworth, a British engineer, 1885–1958, discovered a method of designing electric filters. He was quoted saying ‘‘An ideal electrical filter should not only completely reject the unwanted frequencies but should also have uniform sensitivity for the wanted
Solving Differential Equations with MATLAB MATLAB has a built-in function for solving ordinary differential equations called dsolve. We can use this function to quickly explore the solution to a second-order differential equation when the forcing function is a sinusoidal or exponential signal.
Cost-Conscious RLC Circuit Design You are assigned a task to design a series, passive RLC circuit with a characteristic equation of s2 þ 2000s þ 5 106 ¼ 0. To save money, your supervisor wants you to use a previously purchased 150 mH inductor with a 10-V parasitic resistance.The RLC circuit
Intermittent Timing Circuit for Windshield Wipers A car maker needs an RC timing circuit to trigger the windshield wiper relay. The circuit should be driver selectable to trigger at 1, 2, 5, and 10 s 5%. The source circuit is the car voltage of 12 V with a series resistance of 10 V. You must use
Design a series RLC circuit with z ¼ 1 and v0 ¼100 krad/s.(a) What is the form of the natural response of vC(t) for your design?(b) Simulate your circuit in OrCAD.
Design a series RLC circuit with z ¼ 0.1 and v0 ¼50 krad/s.(a) What is the form of the natural response of vC(t) for your design?(b) Simulate your circuit in OrCAD.
Design a parallel RLC circuit whose natural response has the form vLðtÞ ¼ K1e10000t þ K2t e10000t V t 0
In a parallel RLC circuit the inductor current is observed to be iLðtÞ ¼ 20e20 tsinð20tÞ mA t 0 Find vC(t) when vC(0) ¼ 0.5 V.
The zero-input response of a series RLC circuit with R ¼80 V is vCðtÞ ¼ 2e2000tcosð1000tÞ 4e2000tsinð1000tÞ V t 0 If the initial conditions remain the same, what is the zero-input response when R ¼ 40 V?
In a parallel RLC circuit the state variable responses are vC(t) ¼ e100t [5 cos(300t) þ 15 sin(300t)] V t 0 iL(t) ¼ 20 25e100t cos(300t) mA t 0 Find R, L, and C.
In a parallel RLC circuit the zero-input response in the 220-mH inductor is iLðtÞ ¼ 50e6000t 40e3000t mA t 0(a) Find R and C.(b) Find vC(t) for t 0.
In a series RLC circuit the step response across the 1-mF capacitor is vCðtÞ ¼ 15 e200t ½15 cosð1000tÞ þ 3 sinð1000tÞ V t 0(a) Find R and L.(b) Find iL(t) for t 0.
The switch in Figure P7–57 has been in position B for a long time and is moved to position A at t ¼ 0. The circuit parameters are R1 ¼ 500 V, R2 ¼ 500 V, L ¼ 250 mH, C ¼1 mF, and VA ¼ 5V.(a) Find vC(t) and iL(t) for t 0.(b) Is the circuit overdamped, critically damped, or underdamped?(c)
Repeat Problem 7–53 with R1 ¼ 4 kV, R2 ¼ 4 kV.
Use OrCAD to study how the voltage across the circuit in Figure P7–50 changes as the value of the resistor is varied.Use the Parameter function (PARAM) found in the Special Library and do a Transient Analysis for 10 ms. Select Parametric Sweep and then select Global Parameter. Use the same name
Find the i(t) that satisfies the following differential equation and initial conditions:d2iðtÞdt2þ 8 diðtÞdtþ 16iðtÞ ¼ 48uðtÞ; ið0Þ ¼ 0;dið0Þdt¼ 0
Find the v(t) that satisfies the following differential equation and initial conditions:d2vðtÞdt2þ 10 dvðtÞdtþ 125vðtÞ ¼ 250 uðtÞ; vð0Þ ¼ 10V;dvð0Þdt¼ 25 V/s
Find the v(t) that satisfies the following differential equation and initial conditions:d2vðtÞdt2þ 10 dvðtÞdtþ 100vðtÞ ¼ 0; vð0Þ ¼ 5V;dvð0Þdt¼ 0V/s
Find the v(t) that satisfies the following differential equation and initial conditions:d2vðtÞdt2þ 5 dvðtÞdtþ 36vðtÞ ¼ 0; vð0Þ ¼ 0V;dvð0Þdt¼ 20 V/s
The switch in Figure P7–41 has been in positionAfor a long time and is moved to position B at t ¼ 0. Design the firstorder RC interface circuit such that vO(t) ¼ 15e5000t V.
Design a first-order RL circuit that will produce the following current through the inductor: iL(t) ¼ 50 þ100e20000t mA for t 0.
Design a first-order RC circuit using standard parts(see inside rear cover) that will produce the following voltage across the capacitor: vC(t) ¼ 5 10e10000t V.
Design a parallel RL circuit using a dc current source that delivers the following voltage across the resistor for t > 0.vRðtÞ ¼ 100e2000t V t 0
Design a series RC circuit using a dc voltage source that delivers the following voltage across the capacitor for t > 0.vCðtÞ ¼ 100e2000t V t 0
On the circuit of Figure P7–29 the input is vS(t) ¼ 10 e1000t u(t)V. Find the output vC(t) whenR¼ 100 kV, C¼ 0.01 mF, and vC(0) ¼ 0 V.
Use OrCAD to solve Problem 7–25. (Hint: OrCAD switches are located in the EVAL library and are named Sw_tClose and Sw_tOpen, depending on if you want the switch to close or open at a certain time.)
Repeat Problem 7–23 using MATLAB to plot the waveform.
Repeat Problem 7–20 using MATLAB to plot the waveforms
Repeat Problem 7–20 using OrCAD.
Repeat Problem 7–18 for vS(t) ¼ 100e0.02tu(t) V.
Repeat Problem 7–16. However, after the switch is moved to position B at t ¼ 0, the switch is moved back to position A at t ¼ 100 ms. Find vC(t) for t 0.
=+9-11.Estimate the energy requirements for the structure described by the plans and specifications fur-nished by the instructor using a computer program.
=+9-10.Solve Example 9-2 using the shifts of Problem 9-6 for (a) Denver, CO, (b) Washington, DC.and (c) Chicago, IL.
=+9.9.Solve Example 9-2 for (a) Denver, CO. (b) Washington, DC, and (c) Chicago, IL.
=+9-8.Solve Example 9-2 using the shifts of Problem 9-6.
=+9-7.Solve Problem 9-6 for (a) Denver, CO. (b) Washington, DC, and (c) Chicago, IL ...
=+9-6.Consider a building that operates on two shifts, The first shift begins at 10:00 A.M. and ends at midnight, and the second shift includes all the remaining hours, Assume a five-day work week Compute the bin hours in each shift for Oklahoma City, OK. Consider bin temperatures of 62 F and less.
=+9.5.Refer to Problems 9-3 and 9-4. The building has an average internal load of 20,000 Butby[6 kW) due to lights, equipment, and people. Determine the simplified occupied lond profile
=+9-4. Refer to Problem 9-3 and determine the simplified unoccupied load profile assuming a balance point temperature of 60 F (16 C).
=+9-3.istics much like a residence and a design heat load of 120,000 Btu/hr (35 KW). The structure is heated with a natural gas warm-air furnace and is considered energy efficient. Assuming stan-dard design conditions, estimate the yearly heating fuel requirements.
=+A light commercial building. located in Washington, DC, has construction and use character-
=+9-2.energy would be required in kW-hr, assuming a 100 percent efficiency factor? If the electrical energy costs 10 cents per kW-hr and natural gas costs $4.5 per mef, what are the relative heat-ing costs? Assuming a power plant efficiency of 33 percent, compare the total amounts of energy in
=+If electric resistance heat were used to heat the building mentioned in Problem 9-1. how much
=+9-1. Using the degree-day method, estimate the quantity of natural gas required to heat a building located in Denver, CO. Design conditions are 70 F indoor and 12 F outdoor temperatures. The computed heat load is 225,000 Btu/hr. Assume an efficiency factor of 80 percent. The heating value of the
=+8-52.Compute the total hourly cooling loads for the building described by the plans and specifica tions furnished by your instructor, using the RTSM.
=+8-51.For the heat gains specified in Problem 8-18, determine the hourly sensible and latent cooling loads if the zone is the LW zone from Table 8-21.
=+8-50.For the heat gains specified in Problem 8-17, determine the hourly sensible and latent cooling loads if the zone is the MW 1 zone from Table 8-21.
=+8-49.For the heat gains specified in Problem 8-16, determine the hourly sensible and latent cooling loads if the zone is the MW 2 zone from Table 8-21.
=+8-48.For the heat gains specified in Problem 8-15, determine the hourly sensible and latent cooling loads if the zone is the HW zone from Table 8-21.
=+8-47.Compare the results from Problems 8-45 and 8-46. How do the damping and time delay effects of the two zones compare?
=+8-46.A room has an internal heat gain of 2000 W. 50 percent radiative and 50 percent convective.from 8:00 A.M. to 6:00 P.M ., and 200 W with the same radiative-convective split the rest of the day. If the room matches the HW zone from Table 8-21, determine the hourly cooling loads.Plot and
=+8-45.A room has an internal heat gain of 2000 W. 50 percent radiative and 50 percent convective.from 8:00 A.M. to 6:00 P.M ., and 200 W with the same radiative-convective split the rest of the day. If the room matches the MW I zone from Table 8-21, determine the hourly cooling loads.Plot and
=+8-44.For the hourly solar heat gains for the situation in Problem 8-39, determine the hourly cooling loads if the zone matches the MW 2 zone from Table 8-21. Plot and compare the hourly heat gains vs. the hourly cooling loads.
=+8-43.For the hourly solar heat gains for the situation in Problem 8-38, determine the hourly coolmig loads if the zone matches the MW I zone from Table 8-21. Plot and compare the hourly beat gains vs. the hourly cooling loads.
=+8-42.For the conduction heat fluxes determined in Problem 8-36, determine the hourly conduction heat gains if the roof area is 1200 ft2, and determine the hourly cooling loads if the zone matches the HW zone from Table 8-21. Plot and compare the hourly heat gains vs. the hours cooling loads.
=+8-41.For the conduction heat fluxes determined in Problem 8-35, determine the hourly conduction heat gains if the roof area is 1000 ft2, and determine the hourly cooling loads if the ztite matches the HW zone from Table 8-21. Plot and compare the hourly heat gains versus the hourly cooling loads.
=+8-40 For the conduction heat fluxes determined in Problem 8-33, determine the hourly conduction heat gains if the wall area is 800 ft2. and determine the hourly cooling loads if the zone matele the MW 2 zone from Table 8-21. Plot and compare the hourly heat gains vs. the hourly cook-ing loads.
=+8-39. Determine the solar heat gain for an 8 ft wide, 4 ft high, nonoperable triple-pane window with a white vinyl frame, 2.5 in. in width, for 3:00 p.M. on July 21 in Boise. ID. The glazing is Type 29a from Table 7-3. The frame is aluminum-clad wood with insulated spacers.
=+8-38.with a white vinyl frame, 2.5 in. in width, for 3:00 P.M. on July 21 in Albuquerque. NM. The glazing is Type5b from Table 7-3. The frame is aluminum-clad wood with insulated spacers.
=+Determine the solar heat gain for an 8 ft wide, 4 ft high, nonoperable double-paned window
=+8-31, compute the conduction heat flux for each hour of the day. The room air temperature is 74 F. Use periodic response factors.
=+8-36 umn of Table 8-23, compute the conduction heat flux for each hour of the day. The room air temperature is 72 F. Use periodic response factors.If wall 2 from Table 8-16 is exposed to the sol-air temperature profile calculated in Problem 8-37.
=+8-35. If roof 1 from Table 8-17 is exposed to the sol-air temperature profile shown in the last col-umn of Table 8-23, compute the conduction heat flux for hour 12. The room air temperature is 72 F. Use periodic response factors.If roof 2 from Table 8-17 is exposed to the sol-air temperature
=+8-34.If wall 3 from Table 8-16 is exposed to the sol-air temperature profile shown in Table 8-15, compute the conduction heat flux for each hour of the day. The room air temperature is 72 F.Use periodic response factors.
=+8-33.If wall 2 from Table 8-16 is exposed to the sol-air temperature profile shown in Table 8-15, compute the conduction heat flux for hour 15. The room air temperature is 74 F. Use periodic response factors.
=+8-32.Compute the solar irradiation and sol-air temperatures for a flat roof for the conditions of Prob-lem 8-30.
=+8-31. Compute the sol-air temperatures for a south-facing wall in Boise, ID, for each hour of the day on July 21. Assume 0.4 percent outdoor design conditions. The wall has a solar absorptivity of 0.9, a thermal emissivity of 0.9, and an exterior surface conductance of 6.0 Btu/(hr-fr2-F)
=+8-30.Compute the sol-air temperatures for a west-facing wall in Albuquerque, NM, for each hour of the day on July 21. Assume 0.4 percent outdoor design conditions. The wall has a solar absorp-tivity of 0.8, a thermal emissivity of 0.9, and an exterior surface conductance of 4.0 Btu/(hr-ft -- F).
=+8-29.Compute the total hourly cooling loads for the building described by the plans and specifica-tions furnished by your instructor, using the heat balance method.
=+8-28.Example 8-16 uses low-e double-pane windows. If. instead, clear double-pane windows were used, how would the peak cooling load and load profile change? Use either the heat balance method or the radiant time series method, as directed by your instructor.
=+8-27.Compute the hourly cooling loads for Example 8-16, using the heat balance method.
=+8-26.Using the detailed model presented in Section 8-10, estimate the solar radiation absorbed by cach pane of a west-facing double pane window with - in. sheet glass for 3:00 P.M. on July 21 in Billings, MT. You may neglect the solar radiation incident from the inside of the window.
=+8-25.each pane of a west-facing double-pane window with . in. sheet glass for 3:00 P.M. on July 21 in Amarillo, TX. You may neglect the solar radiation incident from the inside of the window.
=+8.24. If the attic air temperature in Problem 8-20 is 29 C, estimate the convective heat flux from each interior surface.Using the detailed model presented in Section 8-10, estimate the solar radiation absorbed by
=+8-23.interior surface.
=+8.22(€ = 0.1), and everything else were to remain the same, how would the radiation flux incident on the attic floor change? Please answer quantitatively.If the attic air temperature in Problem 8-19 is 85 F. estimate the convective heat flux from each
=+8-21. One approach to reducing attic heat transfer is to install a radiant barrier, e.g ., aluminum foil on one or more surfaces. If we were to line the inside of the pitched roof surfaces of Problem 8-19 with aluminum foil (€ = 0.1), and everything else were to remain the same, how would the
=+8-20.The attic space shown in Fig. 8-11 has H = 3 m. W= 12 m. and Z = 18 m, and all interior sur-faces have emissivities of 0.9. For a time when the inside surface temperatures are ", = 43 C.12 = 50 C. f3 = 36 C, t = 38 C, and t = 32 C, estimate the net thermal radiation incident on each surface
=+8-19 The attic space shown in Fig. 8-11 has H = 6 ft, W = 28 ft, and L = 42 ft, and all interior sur-faces have emissivities of 0.9. For a time when the inside surface temperatures are f1 = 122 F.[2= 143 F. +3 = 102 F. r. = 92 F, and ts = 95 F. estimate the net thermal radiation incident on each
=+8-18.A large office complex has a variable occupancy pattern. Forty people arrive at 8:00 A.M. and leave at 4:00 P.M. Twenty people arrive at 10:00 A.M. and leave at 4:00 P.M. Ten people arrive at 1:00 P.M. and leave at 5:00 P.M. Assume seated, light activity, and compute the sensible and latent
=+8-17.A room has 6000 W of vented fluorescent light fixtures on from 6:00 A.M. to 6:00 P.M. The air flows from the lights through a ducted return. Compute the heat gain to the space at 5:00 P.M ., assuming that 20 percent of heat from the lights is convected to the return air.
=+8-16.A space has occupancy of 35 people engaged in sedentary activity from 8:00 A.M. to 5:00 P.M.The average light level is 15 W/m2 of vented fluorescent fixtures with a ceiling plenum return.Office equipment amounts to 7 kW. Estimate the sensible and latent heat gain to the space for a floor
=+8-15.A large office space has an average occupancy of 30 people from 8:00 A.M. to 5:00 P.M. Light-ing is 1.5 W/It2 of recessed, unvented fluorescent fixtures on from 8:00 A.M. to 6:00 P.M. Com-puters, photocopiers, fax machines, etc. create a heat gain of 1 W/ft2. Compute the sensible and latent
=+8-14.On a warm sunny day, the metal surface of the roof of a car can become quite hot. If the root of the car has 330 Btu/(hr-ft3) total solar radiation incident on it, the outdoor air temperature is 95 F. and the windspeed is 7.5 mph, estimate the maximum possible surface temperature Assume the
=+8-13. For the wall described in Problem 8-5, with an outside surface temperature profile given by Table 8-5 and a constant inside surface temperature of 70 F, determine the inside conduction heat flux for each hour.
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