Principles Of Embedded Networked Systems Design 1st Edition Gregory J. Pottie ,William J. Kaiser - Solutions

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average temperature of the copper tube is 100°F.5.5 Solve Problem 5.4 again assuming that the thermal resistance of the copper tube is negligible. Compare the two answers and comment on the validity of this assumption.
5.6 Because of extreme pressures for a particular application, a 10-ft long pipe within a heat exchanger is made of 2-nom sch 160 pipe (kpipe = 70 Btu/h·ft·°F).The convective heat transfer coefficients inside and outside of the pipe have been determined to be hi = 1248 Btu/h·ft2·°F and ho =
5.7 A copper coil heat exchanger is inserted in a 4-in. (ID) stovepipe to capture some of the energy normally rejected to the atmosphere from a wood-burning stove for preheating domestic hot water. The copper coil is made of 6 ft of½-std type K tubing. Cold water flows at a rate of 5 gpm through
5.8 A specialized tube designed to enhance heat transfer between a condensing refrigerant and water is shown in Figure P5.8. The inner tube is 3 8-std type L copper and the outer tube is 2-std type L copper. Rectangular straight fins made of copper (k = 400 W/m K) with a thickness of 2 mm are
5.9 A heat exchanger is being used to cool 48,000 lbm/h of oil from 150°F to 102°F by using 32,000 lbm/h of water at an inlet temperature of 70°F. The overall heat transfer coefficient is determined to be 136 Btu/h·ft²·°F. The average heat capacities of the oil and water can be taken as 0.5
5.10 A counterflow DPHX is being used to cool hot oil from 320°F to 285°F using cold water. The water, which flows through the inner tube, enters the heat exchanger at 70°F and leaves at 175°F. The inner tube is ¾-std type L copper.The overall heat transfer coefficient based on the outside
5.11 A flow of cold water enters a parallel-flow heat exchanger at 20°C and leaves at 100°C. The cold water is being heated by a hot water flow that enters the heat exchanger at 160°C and leaves at 120°C. The overall heat transfer coefficient for this heat exchanger is 325 W/m2 K. The heat
5.12 A counterflow heat exchanger is being used to cool a flow of hot water using a cold 20% ethylene glycol solution. The hot water enters at 80°F with a volumetric flow rate of 400 gpm. The ethylene glycol solution enters the heat exchanger at −10°F and leaves at 15°F. The ethylene glycol
5.13 Solve Problem 5.12 for a parallel-flow heat exchanger.
5.14 Solve Problem 5.12 for a STHX with 1-shell pass and 2-tube passes.
5.15 Solve Problem 5.12 for a CFHX where both fluids are unmixed.
5.16 A parallel-flow heat exchanger is utilizing a cold 20% magnesium chloride solution to cool a flow of hexane. The hexane enters the heat exchanger at 30°C and the magnesium chloride solution enters at −20°C. The volumetric flow rates of the hexane and magnesium chloride solution are 25 and
5.17 Solve Problem 5.16 for a counterflow heat exchanger.
5.18 Solve Problem 5.16 for a STHX with 1-shell pass and 2-tube passes.
5.19 Solve Problem 5.16 for a CFHX with both fluids unmixed.
5.20 Liquid heptane enters a counterflow heat exchanger at 45°F. The heptane is heated using a flow of hot water entering the heat exchanger at 150°F. The volumetric flow rates of the heptane and water are 280 and 200 gpm, respectively.The UA product of the heat exchanger is found to be 25,675
5.21 Solve Problem 5.20 for a parallel-flow heat exchanger.
5.22 Solve Problem 5.20 for a STHX with 1-shell pass and 2-tube passes.
5.23 Solve Problem 5.20 for a CFHX where the heptane flow is mixed and the water flow is unmixed.
5.24 A counterflow heat exchanger is being used to heat a flow of liquid toluene.The toluene enters the heat exchanger at 5°C with a volumetric flow rate of 18 L/s. Hot water is being used to heat the toluene. The water enters the heat exchanger at 70°C and at a volumetric flow rate of 13 L/s.
5.25 Solve Problem 5.24 for a parallel-flow heat exchanger.
5.26 Solve Problem 5.24 for a STHX with 2-shell passes and 4-tube passes.
5.27 Solve Problem 5.24 for a CFHX where the water flow is mixed and the toluene flow is unmixed.
5.28 The series of heat exchangers shown in Figure P5.28 has the purpose of raising a liquid’s temperature so a desired chemical reaction can take place in the reactor.The specific heat of the liquid can be assumed constant at an average value of 3.2 kJ/kg·K. The liquid flow rate is 1.5 kg/s.
5.29 A gas turbine cycle utilizes a counterflow regenerative heat exchanger as shown in Figure P5.29. Air enters the compressor at atmospheric conditions, 1 atm and 70°F, with a mass flow rate of 15,000 lbm/h. The exhaust pressure of the compressor is 7 atm. The compressor is operating with an
5.30 Water is being heated in a STHX by condensing steam. The water is flowing in the tubes at a rate of 0.8 kg/s. The water enters the heat exchanger at 15°C and leaves at 58°C. The steam condenses on the shell side of the heat exchanger at a condensing pressure of 110 kPa. Determine the
5.31 The evaporator of a vapor compression refrigeration cycle utilizing R-123 as the refrigerant is being used to chill water. The evaporator is a STHX with the water flowing through the tubes. The water enters the heat exchanger at a temperature of 54°F and leaves at 44°F. The evaporating
5.32 The outer pipe in a DPHX is 4-nom sch 40 commercial steel. The inner tube is 3-std type K copper. The fluid inside the inner tube is flowing at a volumetric rate of 60 gpm and the fluid in the annulus flows at 40 gpm. For this heat exchanger determinea. Hydraulic diameter of the annulus (ft)b.
5.33 A DPHX is made of a 6-nom sch 80 outer pipe and a 4-nom sch 40 inner pipe.The fluid in the annular space is liquid water that has a volumetric flow rate of 20 L/s and an average temperature of 40°C. The fluid in the inner tube is a 40% ethylene glycol solution at an average temperature of
5.34 A DPHX is made of a 6-nom sch 40 commercial steel outer pipe and a 5-nom sch 40S stainless steel inner pipe. The fluid in the annular space is cyclohexane that has a volumetric flow rate of 120 gpm and an average temperature of 60°F.The fluid in the inner tube is water at an average
5.35 A DPHX is made of type M copper tubing. The heat exchanger is a 3 × 1 design(3-std outside tube with a 1-std inside tube). Toluene flows through the inner tube with a volumetric flow rate of 0.5 L/s and an average temperature of 30°C. Water flows in the annulus at a rate of 3 L/s with an
5.36 A 3 × 1¼ type M copper tube double-pipe counterflow heat exchanger is used to cool a flow of liquid toluene. The heat exchanger consists of three 10-ft-long DPHX hairpinned together. The toluene enters the annulus of the heat exchanger at a flow rate of 25,000 lbm/h and a temperature of
5.37 Solve Problem 5.36 for a double-pipe parallel-flow heat exchanger.
5.38 A 2 × ¾ DPHX is made from sch 40S stainless steel. Acetone enters the heat exchanger at 80°F with a volumetric flow rate of 12 gpm. The other fluid, ethanol, enters the heat exchanger with 10°F with a flow rate of 45 gpm. The required heat exchanger duty (heat transfer rate between the two
5.39 A STHX has 2-tube passes inside of a 29 in. shell. The tubes are 1-in. 15 BWG tubes on a 1¼-in. square pitch, and the heat exchanger contains the maximum amount of tubes allowable. Water at an average temperature of 80°F is flowing through the tubes. The total flow rate of the water is
5.40 The condenser of a steam power plant is a shell and tube design with cooling water flowing through the tubes. The condenser has 4-tube passes inside a 39-in. shell. The tubes are 1½-in. 12 BWG tubes on a 1⅞-in. triangular pitch.The cooling water enters the heat exchanger at a flow rate of
5.41 The tubes in a STHX are 12 ft long. The liquid in the tubes is cyclohexane at an average temperature of 110°F. The flow rate of the cyclohexane entering the heat exchanger is 120,000 lbm/h. The heat exchanger tubes are 1-in. 14 BWG tubes on a 1¼-in. triangular pitch. The shell diameter is 12
5.42 The evaporator of a refrigeration cycle is a shell and tube design being used to chill water. The water flows in the tubes while the refrigerant boils in the shell. The water enters the heat exchanger at a flow rate of 50 L/s. The average temperature of the water through the heat exchanger is
5.43 A STHX has a single shell and 4-tube passes. The shell diameter is 25 in. The shell contains 10 baffles with a spacing of 0.36 m. Water flows through the shell with a flow rate of 70 kg/s and an average temperature of 85°C. The tubes are 1¼-in. 13 BWG tubes on a 1 9 16-in. square pitch.
5.44 A 20% magnesium chloride solution is flowing at a rate of 240,000 lbm/h through the shell side of a STHX. The average temperature of the magnesium chloride is 25°F. The shell has a diameter of 17¼ in. and there is 1-tube pass.The shell contains 12 baffles with a spacing of 10 in. The tubes
5.45 Normal heptane is flowing in the shell of a STHX at a rate of 400,000 lbm/h and an average temperature of 130°F. The shell has a diameter of 27 in. and a length of 16 ft. The tubes in the heat exchanger are ¾-in. 15 BWG tubes on a 1-in. triangular pitch. The purpose of this problem is to
5.46 At a certain point in the processing of crude oil, it must be heated. The heating occurs in a 1-4 (1-shell pass, 4-tube pass) STHX. The oil is flowing at a rate of 110,000 lbm/h and it enters the heat exchanger at 80°F. The heating will be accomplished with hot water entering the heat
5.47 Design a STHX that will heat liquid octane from 70°F to 110°F using a 20% propylene glycol solution available at 165°F. The flow rate of both fluids is the same, at 110,000 lbm/h. The fouling factors for both fluids can be considered equal at 0.002 h·ft2·°F/Btu. Specify the following
5.48 A 1-1/U counterflow PFHX has 37 active plates. The plates are made from titanium and stamped with a 30° chevron pattern. Each plate has a length of 32 in. and a width of 17 in. The plate thickness is 0.09 in. and the separation distance is 0.2 in. The hot fluid, hard water, flows at 120,000
5.49 In a distillery, a PFHX with a 1-1/U counterflow plate arrangement is being used to cool down a flow of pure ethanol using cold water. The plates are stamped with a 30° chevron pattern. The plate width is 248 mm and the active heat transfer area of each plate is 0.2 m2. The plates are
5.51 Hot air is used to heat cold water from 35°C to 95°C in a finned-tube heat exchanger. The water flows in the tubes at a flow rate of 2.5 kg/s. The air, at 1 atm, enters the heat exchanger at 205°C and leaves at 97°C. The overall heat transfer coefficient for the heat exchanger is 185 W/m2
5.52 Solve Problem 5.51 for the case where the tubes are not finned, resulting in an overall heat transfer coefficient of 170 W/m2 K.
5.53 To increase the thermal efficiency of a gas turbine cycle, the combustion air is often preheated using the hot gases exhausting the turbine. Consider the case where this is being accomplished using a cross-flow (unmixed–unmixed) heat exchanger, as shown in Figure P5.53. Hot combustion gases
6.1 Develop an empirical equation that represents the pump head (ft) as a function of capacity (gpm) for a Bell & Gossett Series 80-SC 2 × 2 × 7 pump with a 6½in. impeller operating at 1750 rpm. The equation should be valid from 40 to 110 gpm. Develop a deviation plot to validate the accuracy of
6.2 Develop an empirical equation for the power draw (W) of the refrigeration compressor as a function of the saturated evaporating and condensing temperatures(°F) described by the 9-point performance data shown in Figure 6.8.
6.3 Develop and solve a simulation to determine the operating point (head [ft]and capacity [gpm]) of the pump and pipe system shown in Figure P6.3. All fittings are regular and the globe valve is wide opened.
6.4 Using the simulation developed in Problem 6.3, develop a plot that shows the operating point (head [ft] and capacity [gpm]) as a function of the rotational speed of the 6½ in. impeller over the range 1500 ≤ rpm ≤ 2500 in 50-rpm increments.Plot the pump head as a function of capacity using
6.5 A centrifugal pump and a gear pump are operating in series in a closed loop to deliver a 20% ethylene glycol solution at an average temperature of 10°C through a long pipe system. In the capacity range up to 2 m3/s, the pump performance equations expressed in terms of pressure increase as a
6.7 One way to liquefy a gas is to flash it through a valve. However, this requires that the inlet conditions to the valve be at a state where an expansion will cause the gas to flash into saturated liquid and saturated vapor. Consider a situation where helium gas is at 10 bar and the desired
6.8 Use the simulation developed in Problem 6.7 to determine how the inlet helium flow rate at state 1 influences the liquid helium production rate and the turbine output power. Plot the following parameters as a function of the inlet helium mass flow rate at state 1 for the range 3.4 ≤ m 1 ≤
6.9 Process steam boilers often incorporate a continuous blowdown scheme to eliminate impurities that can accumulate over time. One possible way to accomplish this is shown in Figure P6.9A. In this system, the boiler is operating at 300 psia. Saturated vapor steam leaves the boiler as the
6.10 Investigate the effect of the separator pressure on the operating parameters of the boiler blowdown system described in Figure P6.9B. For this evaluation, vary the separator pressure from 20 to 100 psia and plot the following curves:a. The annual energy cost savings as a function of the
6.11 A retrofit HVAC project includes installing rectangular air ducts in braced floor joists. The dimensions of the joist and bracing are shown in Figure P6.11.Using the Method of Lagrange Multipliers, determine the optimal values of h and w that maximize the cross-sectional area of the duct.
6.12 A flow rate of 32,000 cfm of gas at a temperature 120°F and a pressure 25 psia is to be compressed to 2500 psia. Under these conditions, the gas behaves according to the ideal gas law. The choice of compressor type is influenced by the fact that centrifugal compressors can handle high-volume
6.13 A cascade refrigeration cycle is shown in Figure P6.13. The purpose of a refrigeration cycle of this type is to achieve very low-temperature refrigeration while saving energy costs. Energy costs are reduced because the work required for the two-stage cascade system is lower than the
6.14 Two heat exchangers in a circulating water loop transfer heat from a fluid condensing at 175°F to a boiling fluid at 68°F, as shown in Figure P6.14. The overall heat transfer coefficients of the evaporator and condenser are UE =5.3 Btu/h·ft2·°F and UC = 7 Btu/h·ft2·°F, respectively.
The Rayleigh distribution Let z be Rayleigh-distributed with pdf:fðzÞ ¼z2 ez2=22; z > 0:Find the mean and the variance of z.
The binary symmetric channel Consider the binary symmetric channel (BSC), which is shown in Figure 2.10.This is a binary channel in which the input symbols are complemented with probability p. The probability associated with each input–output pair is also shown in the figure. For example, the
The binary entropy function Let X ¼1 with probability p;0 with probability 1 p:Plot H(X) as a function of p. Prove the maximum occurs when the likelihoods of the two outcomes are equal. Input 1-p 1-p Figure 2.10 The binary symmetric channel. Output 0
The Max quantizer Let X N(0, 2) (i.e., X takes on a normal distribution) and let the distortion measure be the squared error. Consider a one-bit Max quantizer for this Gaussian source. One bit is used to represent the RV X. If the RV is greater than or equal to 0, the value is represented by the
The binomial distribution Compute the mean and standard deviation of the binomial distribution shown in Example 2.1.
Comparison of Gaussian and binomial distributions To demonstrate the similarity between the binomial and the Gaussian distributions, consider a binomial distribution with n¼150 and p¼0.5. First, plot the pdfs of both distributions with the same variance. Also plot the absolute values of the
The lognormal distribution Let X Nð; 2Þ and Y¼10X/10. Therefore Y is lognormal-distributed. Compute the mean and the variance of this lognormal distribution.Hints: This problem can be solved using moment generating functions. The moment generating function of x is defined by
The cumulative density function(cdf)In addition to the pdf, another function that is also commonly used is the probability distribution function. It is also called the cumulative distribution function (cdf). It is defined as FðxÞ ¼ PðX xÞ ð15x51Þ:Its relationship with the pdf is fðxÞ
Fourier transform for angular frequency In Section 2.2, the Fourier transform is defined in terms of frequencyf. To avoid confusion here, it is denoted as Xf ( f ). The Fourier transform is often defined in terms of radians per second, i.e., the angular frequency !X!ð!Þ ¼Z11
The name game There are four persons. They write their names on individual slips of paper and deposit the slips in a common box. Each of the four draws at random a slip from the box in sequence. If a person draws a slip with his name on it, he duplicates all slips remaining in the box and deposits
Some handy transforms Compute the Fourier transform of the following signals from first principles:(a) rect t 2T1 1 jtj5T1 0 jtj > T1;(b) ðtÞ;(c) eatuðtÞ; Refag > 0:
Some more challenging transforms Compute the Fourier transform of each of the following signals, using the results in Problem 2.11 and the properties described in this chapter:(a) cosð2pf0tÞ;(b) periodic square wave xðtÞ ¼1; jtj5T1 0; T15jtj5T0 2 and xðt þ T0Þ ¼ xðtÞ:8
Filtered noise(a) Suppose white Gaussian noise with a psd of N0/2 passes through a linear filter with response h1(t)¼eatu(t),Re{a}>0. Determine the psd and autocorrelation function of the output process y1(t).(b) y1(t) passes through another linear filter with response h2ðtÞ ¼ ðt T0Þ þ1
Uniform quantizer The uniform quantizer of eight bins shown in Figure 2.4 is used to quantize two kinds of input. Compute the mean square error (MSE) for each of the following inputs:(a) A random process with uniform distribution between –4 and 4.(b) 4sin(2pf0t). It is assumed the sampler has no
The Rice distribution In wireless communications, the amplitude of the received signal is often modeled by the Rice distribution:fðzÞ ¼z2 eðz2þs2Þ=22 I0 zs2 ; z > 0;where s2¼m1 2þm2 2. The value of s depends on the line of sight signal path. If this path is present and the path gain is
A/D and D/A conversion In this problem, A/D and D/A conversion are practiced and two simulations are compared. Consider the steps in Figure 2.11.The quantizer is the three-bit uniform quantizer shown in Figure 2.4. The reproducer is a D/A converter. It converts the binary labels into analog values
Dipole antenna pattern The gain pattern of the short dipole is 1.5cos2, where is the angle in the x–z or y–z plane. Plot the gain pattern in the x–y vs. z plane, as in Figure 3.1. Find the half-power bandwidth.
Noise figure The noise figure, denoted by F, is defined as F ¼measured noise power out of device at room temperature power out of device if device were noiseless:Explain why the output noise power described in Example
is NFG. Suppose the receiver consists of a cascade of three devices. Derive the composite noise figure.
Shadowing Suppose the average propagation loss at a distance of 1kmfrom a transmitter is 80 dB.The average propagation loss is inversely proportional to the square of the distance.The shadowing effect is modeled as lognormal shadowingwith ¼8 dB. Compute the probability that the propagation loss
Coverage area The coverage area U() is defined as the percentage of useful service area (i.e., the percentage of area where the received signal is equal to or greater than ), given a known likelihood of coverage at the cell boundary (boundary coverage, i.e., the fraction of the time the received
Satellite link budget Suppose a satellite receiver consists of a low-noise amplifier with G¼200 and F¼1.5, with subsequent stages having the noise figure 30. The satellite is ingeostationary orbit (r¼40 000 km), the carrier frequency is 7.5GHz, the bandwidth W is 5kHz, Gt¼200, Gr¼100, and the
Frequency coherence For a WSS process, prove thatHðf1; f2;tÞ ¼Z11hð;tÞej2pfd Hðf;tÞ:
Doppler spectrum Consider a mobile unit with an antenna characterized by again G(). If the distribution of the power of the reflected signal is p(), then within a differential angle d, the normalized received power is G()p()d. This power is equal to the differential variation of the received
Sonar Consider two submarines under water. Submarine A transmits an acoustic signal to determine the speed of submarine B in the direction towards A. The frequency of the transmit signal is 100 Hz. The frequency of the received signal after being reflected from submarine B is 101 Hz. The speed of
Geological layers Consider Example 3.12. The distances to the detectors are x1¼100m and x2¼200 m. The propagation times to node 1 and node 2 are 0.6675 s and 0.67 s respectively. Compute the values of d and .
Image location Consider two glass lenses A and B with unknown radii of curvature. Nevertheless, the two lenses are known to have the same curvature on one side. When lens A is tested and rays propagate from the side of identical curvature at a distance of20cm, the image is at a distance of 40 cm.
Near-ground radio propagation In free space, the electric field received by a receiver antenna which is separated from a radiating transmitter antenna by a distance d is Eðd; tÞ ¼E0d0 dcos !c t d c :The received power is given by the Friis free-space equation PrðdÞ ¼PtGtGrl2ð4pÞ2d2:In
Accelerometer system design and system scale estimate Consider the design of an accelerometer that is intended to meet specific acceleration sensitivity goals over a specified bandwidth given a position sensor sensitivity.The designer may adjust mass, spring constant, proof mass value, and
Feedback controlled accelerometer design(a) If force feedback is used to supply a rebalance force equivalent to 1 g of acceleration applied to the proof mass for the accelerometer above, what rebalance force is required to satisfy the mass requirements for each Q value above?(b) If electrostatic
High sensitivity accelerometer design An accelerometer is being selected for seismic applications. The ENS designer wishes to estimate the minimum mass and size that this device can attain while meeting the goal of acceleration values of 109 g=ffiffiffiffiffiffiffi Hz p:(a) This accelerometer
Signal-dependent temperature coefficients A silicon pressure microsensor system employs a piezoresistive strain sensor for diaphragm deflection having a responsivity to displacement of ¼1V/mm (at T¼300 K). Further, this displacement is related to pressure with a pressuredependent deflection of
Design for elimination of temperature cross-talk in a pressure sensor A pressure sensor has a non-linear temperature coefficient of its responsivity such that a variation in package temperature contributes to the output signal. In an ENS application, it is desired to measure pressure with a stated
Fourier series The Fourier series coefficients of a periodic signal x(t) with period T0 are defined by ak ¼1 T0 ZT0 xðtÞejk!0tdt;where !0¼2p /T0 and x(t) can be obtained from ak:xðtÞ ¼Xþ1 k¼1 ake jk!0t:(a) Compute the Fourier series of sin!0t.(b) Compute the Fourier series of the
Binary hypothesis test and SNR Consider the binary choice in Gaussian noise, as shown in Example 5.2. With the threshold of k/2, the SNR is also maximized at the decision point. Since the possible signal values are known, maximization of the SNR means that the hypothesized noise variance is
Binary hypothesis testing and mutual information Consider the binary choice in Gaussian noise, as shown in Example 5.2. When k ¼1 and the variance of the Gaussian distribution is 1, show numerically that the mutual information is maximized when ¼ 0.5.
MAP and the LRT Show that the MAP decision rule is equivalent to the likelihood ratio test.
Binary decisions with unequal a priori probabilities For the binary choice in Gaussian noise in Example 5.2, compute the threshold when the probabilities of H0 and H1 are 1/3 and 2/3 respectively.
MAP vs. ML To examine the difference between MAP and ML detection, we consider the binary choice in Gaussian noise of Example 5.2. The probabilities of H0 and H1 are 1/4 and 3/4 respectively and k¼1. Compute the difference between the thresholds for MAP and ML detection as a function of noise

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Principles Of Embedded Networked Systems Design 1st Edition Gregory J. Pottie ,William J. Kaiser - Solutions

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