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In Problem 6.31, find the rate of discharge if the frictional head loss in the pipe is 3.2 v 2 /g where v is the flow velocity in the pipe. Data From Problem 6.31 Referring to the figure, assume the... Benzene flows steadily and continuously at 100F through a 3000-ft horizontal pipe with a constant diameter of 4 in. The pressure drop across the pipe under these conditions is 300 lb f /ft 2 .... You have been asked to calculate the density of an in-compressible Newtonian fluid in steady flow that is flowing continuously at 250F along a 2500-ft pipe with a constant diameter of 4 in. and a... Apply the law of conservation of mass to an element in a polar coordinate system and obtain the continuity equation for a steady, two-dimensional, in-compressible flow. Using the NavierStokes equations and the continuity equation, obtain an expression for the velocity profile between two flat, parallel plates. Continuity equation, v0 The solar radiation incident on a steel plate 2 ft square is 400 Btu/h. The plate is 1.4 in. thick and lying horizontally on an insulating surface, its upper surface being exposed to air at 90F. If... The Fourier field equation in cylindrical coordinates is a. What form does this equation reduce to for the case of steady-state, radial heat transfer? b. Given the boundary conditions T = T i at r =... Dimensional analysis has shown the following parameters to be significant for forced convection: Evaluate each of these parameters at 340 K, for air, water, benzene, mercury, and glycerin. The... A plane surface 25 cm wide has its temperature maintained at 80C. Atmospheric air at 25C flows parallel to the surface with a velocity of 2.8 m/s. Using the results of boundary layer analysis,... For the case of a turbulent boundary layer on a flat plate, the velocity profile has been shown to follow closely the form Assuming a temperature profile of the same formthat is, and assuming that... Determine the required time for the rubber balls described in Problem 20.8 to reach the condition such that the center temperature is 320 K. What will be the surface temperature when the center... Air at 203 kPa and 290 K flows in a long rectangular duct with dimensions 10 cm by 20 cm. A 2.5-m length of this duct is maintained at 395 K, and the average exit air temperature from this section is... Consider the exchanger in Problem 22.9. After 4 years of operation, the outlet of the oil reaches 28C instead of 30C with all other conditions remaining the same. Determine the fouling resistance on... Two parallel black rectangular surfaces, whose back sides are insulated, are oriented parallel to each other with a spacing of 5 m. They measure 5 m by 10 m. The surroundings are black at 0 K. The... In a gas-phase diffusion mass-transfer process, the steady-state flux of species A in a binary mixture of A and B is 5.0 10 5 kgmole A/m 2 s, and the flux of B is 0 (zero). At a particular point in... A cylindrical graphite rod (pure solid carbon, density 2.25 g/cm 3 ) of length 25 cm and initial diameter of 2.0 cm is inserted into a flowing air stream at 1100 K and 2.0 atm total system pressure.... Many bio catalytic reactions are carried out with living cells as the bio catalyst. In some processes, the cells are immobilized within an agarose gel. However, living cells uniformly distributed... In the distillation of a benzene/toluene mixture, a vapor richer in the more volatile component benzene is produced from the benzene/toluene liquid solution. Benzene is transferred from the liquid to... In the fabrication of a p-type semiconductor, elemental boron is diffused a small distance into a solid crystalline silicon wafer. The boron concentration within the solid silicon deter mines... An engineer at a pulp mill is considering the feasibility of removing chlorine gas (C1 2 , solute A) from an air steam using water, which will be reused for a pulp bleaching operation. The process... Consider the waste treatment process shown in the figure below. In this process, wastewater containing a dissolved TCE concentration of 50 gmole/m 3 enters a clarifier, which is essentially a... A starship is circling a distant planet of radius R. The astronauts find that the free-fall acceleration at their altitude is half the value at the planets surface. How far above the surface are they... Water flows from the pipe shown in FIGURE P14.60 with a speed of 4.0 m/s.a. What is the water pressure as it exits into the air?b. What is the height h of the standing column of water? Open 5.0 cm? h... A 1.0 kg block is attached to a spring with spring constant 16 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 40 cm/s. What... In a science museum, a 110 kg brass pendulum bob swings at the end of a 15.0-m-long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5 m to the side and releasing it.... A gas with initial state variables p 1 , V 1 , and T 1 is cooled in an isochoric process until p 2 = 1/3 p 1 . What are (a) V 2 (b) T 2 ? 0.0050 mol of gas undergoes the process 1?? 2 ?? 3 shown in Figure P16.38.? What are (a) Temperature T 1 , (b) Pressure p 2 , (c) Volume V 3 ? p (atm) P2 - T = 2926 K 3 T3 = 2438 K 1 0+ V (cm) V3... One cylinder in the diesel engine of a truck has an initial volume of 600 cm 3 . Air is admitted to the cylinder at 30C and a pressure of 1.0 atm. The piston rod then does 400 J of work to rapidly... FIGURE P21.46 shows a Carnot heat engine driving a Carnot refrigerator. a. Determine Q 2 , Q 3 , and Q 4 . b. Is Q 3 greater than, less than, or equal to Q 1 ? c. Do these two devices, when operated... A negatively charged electroscope has separated leaves. a. Suppose you bring a negatively charged rod close to the top of the electroscope, but not touching. How will the leaves respond? Use both... You sometimes create a spark when you touch a doorknob after shuffling your feet on a carpet. Why? The air always has a few free electrons that have been kicked out of atoms by cosmic rays. If an... A ring of radius R has total charge Q. a. At what distance along the z-axis is the electric field strength a maximum? b. What is the electric field strength at this point? What is the net electric flux through the torus (i.e., doughnut shape) of FIGURE EX24.20? +) -1 nC (inside) +100 nC FIGURE EX24.20 A capacitor with plates separated by distance d is charged to a potential difference V C . All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a... What potential difference is needed to accelerate a He + ion (charge +e, mass 4 u) from rest to a speed of 2.0 10 6 m/s? What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.36? Give your answer (a) In component form. (b) As a magnitude and angle measured cw or... Draw a circuit diagram for the circuit of FIGURE EX28.1. 75 0 T00n FIGURE EX28.1 A refrigerator has a 1000 W compressor, but the compressor runs only 20% of the time. If electricity costs $0.10/kWh, what is the monthly (30 day) cost of running the refrigerator? Bulbs A, B, and C in FIGURE Q28.10 are identical, and all are glowing. a. Rank in order, from most to least, the brightnesses of the three bulbs. Explain.b. Suppose a wire is connected between points... For the circuit shown in FIGURE P28.59, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading. 20 24 VE 80 120 12 FIGURE P28.59 FIGURE EX29.37 is a cross section through three long wires with linear mass density 50 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are... An LC circuit has a 10 mH inductor. The current has its maximum value of 0.60 A at t = 0 s. A short time later the capacitor reaches its maximum potential difference of 60 V. What is the value of the... A small, 2.0-mm-diameter circular loop with R = 0.020 is at the center of a large 100-mm-diameter circular loop. Both loops lie in the same plane. The current in the outer loop changes from +1.0 A... FIGURE P30.59 shows a U-shaped conducting rail that is oriented vertically in a horizontal magnetic field. The rail has no electric resistance and does not move. A slide wire with mass m and... FIGURE P33.49 shows the interference pattern on a screen 1.0 m behind an 800 line/mm diffraction grating. What is the wavelength (in nm) of the light? Intensity x (cm) 89.7 cm 89.7 cm FIGURE P33.49... A Michelson interferometer uses red light with a wavelength of 656.45 nm from a hydrogen discharge lamp. How many brightdark-bright fringe shifts are observed if mirror M 2 is moved exactly 1 cm? In a single-slit experiment, the slit width is 200 times the wavelength of the light. What is the width (in mm) of the central maximum on a screen 2.0 m behind the slit? Light of wavelength 550 nm illuminates a double slit, and the interference pattern is observed on a screen. At the position of the m = 2 bright fringe, how much farther is it to the more distant slit... The current lags the emf by 30 in a series RLC circuit with 0 = 10 V and R = 50 . What is the peak current through the circuit? A high-pass filter consists of a 1.59 F capacitor in series with a 100 resistor. The circuit is driven by an AC source with a peak voltage of 5.00 V. a. What is the crossover frequency fc? b. What... Find the focal length of the glass lens in FIGURE EX34.27. 40 cm 40 cm FIGURE EX34.27 An object is 12 cm in front of a concave mirror with a focal length of 20 cm. Use ray tracing to locate the image. Is the image upright or inverted? A fortune tellers crystal ball (actually just glass) is 10 cm in diameter. Her secret ring is placed 6.0 cm from the edge of the ball. a. An image of the ring appears on the opposite side of the... The two sides of a V-shaped water trough are hinged to each other at the bottom where they meet, as shown in Fig. P11??25, making an angle of 45? with the ground from both sides. Each side is 0.75 m... Water enters a hydraulic turbine through a 30-cmdiameter pipe at a rate of 0.6 m 3 /s and exits through a 25-cmdiameter pipe. The pressure drop in the turbine is measured by a mercury manometer to be... What is the speed, as a fraction of c, of a particle whose momentum is mc? Often aerobatic fermentations give off CO 2 gas because the respiring cells produce CO 2 as glucose nutrient is converted to chemical energy. The conditions used to set k L a for O 2 transfer in the... Advertisement signs are commonly carried by taxicabs for additional income, but they also increase the fuel cost. Consider a sign that consists of a 0.30-m-high, 0.9-m-wide, and 0.9-m-long... A hot surface at 100°C is to be cooled by attaching 3-cm-long, 0.25-cm-diameter aluminum pin fins (k = 237 W/m·K) to it, with a center-to-center distance of 0.6 cm. The temperature of the... A plane wall with surface temperature of 350°C is attached with straight rectangular fins (k = 235 W/m·K). The fins are exposed to an ambient air condition of 25°C and the convection... A 5-mm-diameter spherical ball at 50°C is covered by a 1-mm-thick plastic insulation (k = 0.13 W/m·K). The ball is exposed to a medium at 15°C, with a combined convection and radiation... Hot water at an average temperature of 70C is flowing through a 15-m section of a cast iron pipe (k = 52 W/mK) whose inner and outer diameters are 4 cm and 4.6 cm, respectively. The outer surface of... A 2.2-mm-diameter and 10-m-long electric wire is tightly wrapped with a 1-mm-thick plastic cover whose thermal conductivity is k = 0.15 W/m·K. Electrical measurements indicate that a current... Superheated steam at an average temperature 200C is transported through a steel pipe (k = 50 W/mK, D o = 8.0 cm, D i = 6.0 cm, and L = 20.0 m). The pipe is insulated with a 4-cm thick layer of gypsum... Solar radiation is incident on the glass cover of a solar collector at a rate of 700 W/m 2 . The glass transmits 88 percent of the incident radiation and has an emissivity of 0.90. The entire hot... Consider a refrigeration truck traveling at 70 mi/h at a location where the air is at 1 atm and 80°F. The refrigerated compartment of the truck can be considered to be a 9-ft-wide, 8-ft-high, and... The heavyweight boxing champion of the world punches a sheet of paper in midair, bringing it from rest up to a speed of 25.0 m/s in 0.050 s. The mass of the paper is 0.003 kg. Show that the force of... An appliance that uses 1000W of power is connected by 12 gauge (diameter 2.053mm) copper wire to a120V (RMS) AC outlet. Estimate the power lost permeter, dP lost /dL, (in W/m) as resistive heating in... Take the divergence of both sides of eq. Use Coulombs law on the left and current conservation on right to show that the equation is consistent. V - 3D . at Roughly 70% of the 5 10 14 m 2 of Earths surface is covered by oceans. How much energy would it take to melt enough of the ice in Greenland and Antarctica to raise sea levels 1 meter? Suppose that... Everyday experience indicates that it is much easier to compress gases than liquids. This property is measured by the isothermal compressibility, =1/V V/p| T , the fractional change in a substances... Find the frequency of the lowest vibrational mode of a diatomic molecule in terms of the parameters of the Morse potential, eq. Vstone () = De (1-e -r)* -1 -a(r-re Look up the standard enthalpies of formation and the entropies of solid ice and liquid water and verify that ice may spontaneously melt at NTP (20 C, 1 atm). Consider a Carnot engine cycle operating between a maximum temperature of T 3 = T 4 = 400 F and a minimum temperature of T 1 = T 2 = 60 F. Assume that the lowest pressure attained is p 1 = 1 atm,... Mirrors are used to concentrate sunlight and heat a molten salt mixture to 500K. A heat engine is then used to convert the thermal energy to useful mechanical form. Compare a Carnot engine to a... Suppose two engines, one SI, the other CI, have the same temperature range, T 1 = 300K and T 3 = 1800K. Suppose the SI engine, modeled as an ideal Otto cycle, has a compression ratio of 10:1, while... An industrial freezer is designed to use ammonia (NH 3 )as a working fluid. The freezer is designed so that ammonia flowing through tubes inside the freezer at p vaporizes at T = 40 C, drawing heat... Consider a volume of 100 L of water, initially in liquid form at temperature T i , to which U = 25 MJ of energy is added from an external reservoir at temperature T r through a thermal resistance, so... A steam turbine can be modeled as an is entropic expansion. The incoming steam is super heated at an initial temperature T + and pressure p + . After expansion, the exhausted steam is at temperature... A uranium enrichment facility produces nuclear reactor fuel enriched to 4% 235 U to fuel the reactor whose power to fuel consumption ratio is described by eq. (19.15) For each tonne of natural... Show that a charged particle moving in the plane perpendicular to a constant magnetic field (eq. (19.29) moves in a circle with Br = mv/q. What is the radius of the circle for an electron with energy... The flux of cosmic ray muons at sea level is about one per square centimeter per minute. Given their mass stopping power of2 MeV cm 2 /gm, and their weighting factor , w = 1 estimate an average... The relativistic transformation law that relates the coordinates seen by an observer (2) moving at velocity v relative to an observer (1) is x 2 = (cosh ?)x 1 ?(sinh ?)ct 1 , ct 2 = (cosh ?)ct 1 ?... Estimate the rate of thermal radiation from a household hot-water radiator with a surface area of 1 m 2 and a temperature of 80. Show that the insolation averaged over the year and over the entire Earth is 341 W/m 2 . Use the data given in the wind rose Figure 28.19 To make a crude estimate of the average ?v? and root mean cube v? wind speed at Klamath Lake, Oregon. From these, estimate the Weibull parameters for... Estimate the energy extracted from 1 km 3 of granite if cooled from 300 C to 200 C. Assume that a power plant runs between the (time-varying) temperature T g of the granite and an ambient... A car moves along a straight line so that its position (distance from some starting point) varies with time as described by the graph shown here. a. Does the car ever go backward? Explain. b. Is the... The engine of a car is part of the car and cannot push directly on the car in order to accelerate it. What external force acting on the car is responsible for the acceleration of the car on a level... A 6-kg block being pushed across a table by a force P has an acceleration of 3.0 m/s 2 . a. What is the net force acting upon the block? b. If the magnitude of P is 20 N, what is the magnitude of the... A 4-kg sled sliding freely on an icy surface experiences a 2-N frictional force exerted by the ice and an air-resistive force of 0.5 N. a. What is the net force acting on the sled? b. What is the... A rough measure of the enthalpy of combustion of a hydrocarbon can be obtained by assuming that all CC bonds contribute the same energy to the combustion process when broken, and that the same is... Show that an n-layer atmosphere of the type described in Example 34.2 gives a surface temperature? = ( Vn + 1) 255 K Is 4 Earths albedo is currently estimated to be a 0.30.By what percentage would a have to increase to offset the estimated increase in forcing eq. (34.36) due to doubling of CO 2 since pre-industrial... Reproduce the results in Example 36.4 using eq. (36.25) rather than by the direct calculation of available work that was used in the example. you can use the Sackur?Tetrode formula (8.65) for the... Consider using the McIntosh salt mine described in Example 37.2 for adiabatic storage. Compute the energy stored if a volume of air initially at p 0 = 1 atm is compressed to p H = 75 atm, and compare... According to Figure 37.7, the energy density of hydrogen compressed to 700 atm is approximately 5.6 MJ/L.Assuming hydrogen behaves as an ideal gas throughout,estimate the energy density of hydrogen... The initial temperature of 150 g of ice is -20C. The specific heat capacity of ice is 0.5 cal/gC and waters is 1 cal/gC. The latent heat of fusion of water is 80 cal/g. a. How much heat is required... If you increase the speed of a wave on a Slinky by increasing the tension but keep the same frequency of back-and forth motion, does the wavelength increase or decrease? Explain. An organ pipe closed at one end and open at the other has a length of 0.5 m. a. What is the longest possible wavelength for the interfering sound waves that can form a standing wave in this pipe? b....
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