Questions and Answers of Principles Of Embedded Networked Systems Design

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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,
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
Thresholds with costs Compute the threshold in Example 5.5 analytically.
Noise under orthogonal decomposition One property of the white noise n(t) is that the autocorrelation function E[n(t)n(tþ)] is equal to (N0/2()). When this noise is expanded as a set of
Cross-products for ML detection The ML decision is to choose the signal space point closest to the received vector of decision variables. This requires the calculation of the Euclidean distance. The
Frequency shift keying (FSK)In an FSK scheme, transmitted signals are orthogonal to each other. For binary FSK (BFSK), the two equally likely signals are s1ðtÞ ¼ffiffiffiffi Ep
Correlation vs. matched filter receiver In Section 5.2, it is shown that the correlation filter for signal x(t) can be replaced by a matched filter with impulse response x(T t). Show that the
Matched filter and SNR Prove that the matched filter maximizes the output SNR and compute the maximum output SNR as a function of the energy of the signal s(t) and N0.
Vector and integral forms of likelihood function Show that the likelihood function lðkÞ ¼ N 2lnðpN0Þ 2 N0 XN i¼1ðxi skiÞ2 can be written in the form lkðxÞ ¼2 N0 Z T 0xðtÞskðtÞdt 1
Likelihood function for non-coherent detection Show that the likelihood functionk ¼ eEk N0 I0 2ffiffiffiffiffiffi Ek pN0 jLkj ;which is discussed in Section 5.2 for non-coherent detection, can
On–off signaling Explain the reason why l0 is equal to 0 in Example 5.6.
Detection of two sinusoids Consider the problem of detecting two signals s1 (t) ¼ A1 sin (2p fctþ) and s2 (t) ¼ A2 sin (2p fctþ) over the interval (0,T), perturbed by AWGN with psd N0/2. The a
Decision threshold for on–off signaling Show that in Example 5.6 the threshold is approximately E/4 at high SNR.
MR combining In MR combining, the received signals xk from each of the N sensors with channel coefficient kejk are cophased to provide coherent voltage addition and are individually weighted to
MR combining with unequal SNRs Derive the weights forMRcombining when the noise variances are not equal and compute the resulting SNR.
Coverage area with cooperation In Example 5.12(d) it is shown that with the cooperation of two nodes, the coverage area per sensor is doubled. If the channel and the requirements are the same,
Mean square estimation Let X be a real-valued RV with a pdf of fX(x). Find an estimate ^x such that the mean square error of x by ^x is minimized when no observation is available. 10 d Ok d 2 3
Fitting functions to observations Consider RVs X and Y. Find a function g(.) of the observed X such that g(x)minimizes Y in the minimal mean square sense. (Note, you will need the results from
Orthogonality and MMSE filters In Section 5.3, it is shown that the input u is orthogonal to the estimation error e.Show that for the MMSE filter e and y are also orthogonal.
Three-tap equalizer In Example 5.16, an equalizer with two taps is considered. Now assume that three taps are available. Compute the tap coefficients and the overall response of the channel and the
Beamforming for interference suppression Assume M sensors are deployed to implement beamforming, as depicted in Figure 5.24. The distance from the reference sensor to the ith sensor is denoted by di.
LMS algorithm Show that the gradient G0 in the LMS algorithm is equal to E e0u0.
Cramer–Rao bound Let X be the sample mean from n independent Gaussian RVs X1 ,X2 , . . . , Xn with distribution N(, 2). Assume 2 is known. First, derive the Cramer–Rao bound. Then, show that
ML estimates of the mean and variance of Gaussian random variables Consider n independent random samples from N(, 2). Let ¼(, ). That is,1¼and 2¼. Find the ML estimates of and .
Spectral density of non-zero mean sequences In Section 6.1 the baseband-equivalent psd is given for a zero mean sequence.Derive the baseband-equivalent psd of linearly modulated signals if the mean

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