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The velocities in a circular duct of 20-in. diameter were measured as follows: Find (a) the average velocity; (b) the flow rate in cubic feet per second. Velocity Distance from Velocity Distance from... A stationary jet engine is shown. Air with a density of 0.0805 lb/ft 3 enters as shown. The inlet and outlet cross sectional areas are both 10.8 ft 2 . The mass of fuel consumed is 2% of the mass of... a. Determine the magnitude of the x and y components of the force exerted on the fixed blade shown by a 3-ft 3 /s jet of water flowing at 25 fps. b. If the blade is moving to the right at 15 fps,... The pump in the boat shown pumps 6 ft 3 /s of water through a submerged water passage, which has an area of 0.25 ft 2 at the bow of the boat and 0.15 ft 2 at the stern. Determine the tension in the... If the plate shown is inclined at an angle as shown, what are the forces F x and F y necessary to maintain its position? The flow is friction less. 4 3 v = 100 fps - Fx m = 2 slugs/s Fy Consider the differential control volume shown below. By applying the conservation of mass and the momentum theorem, show that dP + pv dv + g dy = 0 2, 2 V2, A2 s (1) P1, P1 V1, A1 For the pipe-flow-reducing section D 1 = 8 cm, D 2 = 5 cm, and p 2 = 1 atm. If v 1 = 5 m/s and the manometer reading is h = 58 cm, estimate the total force resisted by the flange bolts. Water Hg An open tank L ft long as shown below travels to the right at a velocity v c fps. A jet of area A j exhausts fluid of density r at a velocity v j fps relative to the car. The tank car, at the same... The velocity profile in the annular control volume of Example 3 is approximately linear, varying from a velocity of zero at the outer boundary to a value of d/2 at the inner boundary. Develop an... Sea water, p = 1025 kg/m 3 , flows through a pump at 0:21 m 3 /s. The pump inlet is 0.25 m in diameter. At the inlet the pressure is -0.15 m of mercury. The pump outlet, 0.152 m in diameter, is 1.8 m... Air at 70F, Flows into a 10-ft 3 reservoir at a velocity of 110 fps. If the reservoir pressure is 14 psig and the reservoir temperature 70F, find the rate of temperature increase in the reservoir.... Water flows through a 2-in.-diameter horizontal pipe at a flow rate of 35 gal/min. The heat transfer to the pipe can be neglected, and frictional forces result in a pressure drop of 10 psi. What is... During the test of a centrifugal pump, a Bourdon pressure gage just outside the casing of the 12-in.-diameter suction pipe reads -6 psig (i.e., vacuum). On the 10-in.-diameter discharge pipe, another... A liquid flows from A to B in a horizontal pipe line shown at a rate of 3 ft 3 /s with a friction loss of 0.45 ft of flowing fluid. For a pressure head at B of 24 in., what will be the pressure head... Water at 100°C flows through a 10 cm diameter pipe that has a 180 degree vertical turn as shown in the figure below. The volumetric flow rate is constant at 0.2 m 3 /s. The absolute pressure at... Boundary-layer analysis for fluid flow over a flat plate predicts the following relationships between the local Sherwood (Sh x ), Reynolds (Re), and Schmidt (Sc) numbers: with the transition... A Venturi meter with an inlet diameter of 0.6 m is designed to handle 6 m 3 /s of standard air. What is the required throat diameter if this flow is to give a reading of 0.10 m of alcohol in a... An automobile is driving into a 45-mph headwind at 40 mph. If the barometer reads 29 in. Hg and the temperature is 40F, what is the pressure at a point on the auto where the wind velocity is 120 fps... A fan draws air from the atmosphere through a 0.30-m diameter round duct that has a smoothly rounded entrance. A differential manometer connected to an opening in the wall of the duct shows a vacuum... Find the change in temperature between stations (1) and (2) in terms of the quantities A 1 , A 3 , v 1 , v 3 , c v , and θ. The internal energy is given by c v T . The fluid is water and... The solution to 5.22 is Show that Bernoulli's equation applied between sections 1 and 2 does not give this result. Derive all expressions for the change in total head across a hydraulic jump. 1/2 h... Residential water use, exclusive of fire protection, runs about 80 gallons per person per day. If the water is delivered to a residence at 60 psig, estimate the monthly energy required to pump the... A 1968 Volkswagen sedan is driving over a 7300-ft-high mountain pass at a speed of v m/s into a headwind of W m/s. Compute the gage pressure in mPa at a point on the auto where the velocity relative... A liquid is heated in a vertical tube of constant diameter, 15 m long. The flow is upward. At the entrance the average velocity is 1 m/s, the pressure 340,000 Pa, and the density is 1001 kg/m 3 . If... For fully developed turbulent flow over a flat plate of length L, the local Sherwood number at position x(0 < x ¤ L) is estimated by Develop an expression for the average Sh over length L of... In Problem 6.26, compute the upward force on the device from water and air. Use the results of Problem 6.26 as well as any other data given in that problem that you may need. Explain why you cannot... Water is discharged from a 1.0-cm-diameter nozzle that is inclined at a 30° angle above the horizontal. If the jet strikes the ground at a horizontal distance of 3.6 m and a vertical distance of... In the previous problem, determine the flow rate at which the pump inlet pressure is equal to the vapor pressure of the water. Assume that friction causes a head loss of 4 ft. The vapor pressure of... Water flows through the pipe contraction shown at a rate of 1 ft 3 /s. Calculate the differential manometer reading in inches of mercury, assuming no energy loss in the flow. Be sure to give the... Consider a 4-cm pipe that runs between a tank open to the atmosphere and a station open to the atmosphere 10 m below the water surface in the tank. Assuming friction less flow, what will be the mass... A fluid of density Ï 1 enters a chamber where the fluid is heated so that the density decreases to Ï 2 The fluid then escapes through a vertical chimney that has a height L. Neglecting... A common type of viscosimeter for liquids consists of a relatively large reservoir with a very slender outlet tube, the rate of outflow being determined by timing the fall in the surface level. If... A Newtonian oil with a density of 60 lb m /ft 3 , viscosity of 0.206 à 10 -3 Ib m /ft-s and kinematic viscosity of 0.342 à 10 -5 ft 2 /s undergoes steady shear between a horizontal... Find Dv/Dt in polar coordinates by taking the derivative of the velocity. (v = v r (r, , t)e r + v (r, , t)e . Remember that the unit vectors have derivatives.) Does the velocity distribution in Example 2 satisfy continuity? The atmospheric density may be approximated by the relation = 0 exp(-y/), where = 22,000 ft. Determine the rate at which the density changes with respect to body falling at v fps. If v = 20,000... In polar coordinates, the continuity equation is Show that a. if v θ = 0, then v r = F(θ)/r b. if v r = 0, then v θ = f(r) |1 1 (rv,) +- r 0 r Obtain the equations for a one-dimensional steady, viscous, compressible flow in the x direction from the Navier Stokes equations. (These equations, together with an equation of state and the energy... Using the laws for the addition of vectors and equation (9-19), show that in the absence of gravity, a. The fluid acceleration, pressure force, and viscous force all lie in the same plane b. In the... Determine the velocity profile in a fluid situated between two coaxial rotating cylinders. Let the inner cylinder have radius R 1 , and angular velocity 1 ; let the outer cylinder have radius R 2... Beginning with the appropriate form of the Navier Stokes equations, develop an equation in the appropriate coordinate system to describe the velocity of a fluid that is flowing in the annular space... In Example 3 we began finding the equation for the stream function by integrating equation (3). Repeat this example, but instead begin by integrating equation (4) and show that no matter which... Refer to Example 1. What is the required bulk velocity for the air over the surface of the film, assuming laminar flow? The molecular diffusion coefficient of MEK in air is 0.090 cm 2 /s at 27C and... The power P required to run a compressor varies with compressor diameter D, angular velocity , volume flow rate Q, fluid density , and fluid viscosity . Develop a relation between these variables by... An oil with kinematic viscosity of 0.08 10 -3 ft 2 /s and a density of 57 lb m /ft 3 flows through a horizontal tube 0.24 in. in diameter at the rate of 10 gal/h. Determine the pressure drop in 50... For the same pump and system operation described in Problem 14.20 determine (a) the discharge rate and (b) power required when the pump operates at 900 rpm. The pump having the characteristics shown in Problem 14.14 is used to pump water from one reservoir to another that is 95 m higher in elevation. The water will flow through a steel pipe that is 0.28... A composite wall is to be constructed of 1/4-in. stainless steel (k = 10 Btu/h ft F), 3 in. of cork board (k = 0.025 Btu/hft F) and 1/2 in. of plastic (k = 1.5 Btu/h ft F). a. Draw the thermal... The cross section of a storm window is shown in the sketch. How much heat will be lost through a window measuring 1.83 m by 3.66 m on a cold day when the inside and outside air temperatures are,... One-dimensional steady-state conduction, with no internal heat generation, occurs across a plane wall having a constant thermal conductivity of 30 W/m K. The material is 30 cm thick. For each case... Starting with the Fourier field equation in cylindrical coordinates, a. Reduce this equation to the applicable form for steady-state heat transfer in the θ direction. b. For the... A furnace wall consisting of 0.25 m of fire clay brick, 0.20 m of kaolin, and a 0.10-m outer layer of masonry brick is exposed to furnace gas at 1370 K with air at 300 K adjacent to the outside wall.... A heater composed of Nichrome wire wound back and forth and closely spaced is covered on both sides with 1/8 - in. thickness of asbestos (k = 0.15 Btu/h ft F) and then with a 1/8 -in. thickness of... Given the conditions of Problem 17.9, except that the outside temperature of the masonry brick cannot exceed 325 K, by how much must the thickness of kaolin be adjusted to satisfy this requirement?... For an asbestos cylinder with both height and diameter of 13 cm initially at a uniform temperature of 295 K placed in a medium at 810 K with an associated convective heat-transfer coefficient of 22.8... A steel I-beam with a cross-sectional area as shown has its lower and upper surfaces maintained at 700 and 370 K, respectively. a. Assuming a negligible temperature change through both flanges,... In a thermal heat sink the heat flux variation along the axis of a cooling passage is approximated as A 1-in., 16-BWG copper tube has its outside surface maintained at 240F. If this tube is located in still air at 60F, what heat flux will be achieved if the tube is oriented a. Horizontally? b.... A swimming-pool nuclear reactor, consisting of 30 rectangular plates measuring 1 ft in width and 3 ft in height, spaced 21/2 in. apart, is immersed in water at 80F. If 200F is the maximum allowable... A cooking oven has a top surface temperature of 45C when exposed to still air. At this condition the inside oven temperature and room air temperature are 180C and 20C, respectively, and heat is... A 1-in., 16-BWG copper tube, 10ft long, has its outside surface maintained at 240F. Air at 60F and atmospheric pressure is forced past this tube with a velocity of 40 fps. Determine the heat flux... Two thousand watts of electrical energy are to be dissipated through copper plates measuring 5 cm by 10 cm by 0.6 cm immersed in water at 390 K. How many plates would you recommend? Substantiate all... A vertical flat surface 2 ft high is maintained at 60F. If saturated ammonia at 85F is adjacent to the surface, what heat- transfer coefficient will apply to the condensation process? What total heat... Water at 50F is available for cooling at a rate of 400 Ib m /h. It enters a double-pipe heat exchanger with a total area of 18 ft 2 . Oil, with c p = 0.45 Btu/1b m , F, enters the exchanger at 250F.... The distribution of solar energy incident on Earth can be approximated as being from a black body at 5800 K. Two kinds of glass, plain and tinted, are being considered for use in windows. The... Derive equation (25-11) for component A in terms of molar units, starting with the control-volume expression for the conservation of mass. CA - RA = 0 V NA +: (25-11) a. Find an expression for the capacitance of a spherical capacitor, consisting of concentric spherical shells of radii R 1 (inner shell) and R 2 (outer shell). b. A spherical capacitor with a 1.0 mm... You are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem. +... Estimate the value of the gas-phase diffusion coefficient for the following gas pairs using the Hirschfelder equation: a. Carbon dioxide and air at 310 K and 1:5 10 5 Pa b. Ethanol and air at 325 K... A vacuum-insulated parallel-plate capacitor with plate separation d has capacitance C 0 . What is the capacitance if an insulator with dielectric constant k and thickness d/2 is slipped between the... The label rubbed off one of the capacitors you are using to build a circuit. To find out its capacitance, you place it in series with a 10 F capacitor and connect them to a 9.0 V battery. Using your... An isolated 5.0 F parallel-plate capacitor has 4.0 mC of charge. An external force changes the distance between the electrodes until the capacitance is 2.0 F. How much work is done by the external... Capacitors C 1 = 10 F and C 2 = 20 F are each charged to 10 V, then disconnected from the battery without changing the charge on the capacitor plates. The two capacitors are then connected in... A hemispherical droplet of liquid water, lying on a flat surface, evaporates by molecular diffusion through still air surrounding the droplet. The droplet initially has a radius R. As the liquid... Six identical capacitors with capacitance C are connected as shown in FIGURE P26.60. a. What is the equivalent capacitance of these six capacitors? b. What is the potential difference between points... Suppose a time machine has just brought you forward from 1750 (post-Newton but pre-electricity) and youve been shown the lightbulb demonstration of Figure Q27.1. Do observations or simple... The electric potential is 40 V at point A near a uniformly charged sphere. At point B, 2.0 m farther away from the sphere, the potential has decreased by 0.16 mV. How far is point A from the center... Metal sphere 1 has a positive charge of 6.0 nC. Metal sphere 2, which is twice the diameter of sphere 1, is initially uncharged. The spheres are then connected together by a long, thin metal wire.... The 90 F capacitor in a defibrillator unit supplies an average of 6500 W of power to the chest of the patient during a discharge lasting 5.0 ms. To what voltage is the capacitor charged? 50 pJ of energy is stored in a 2.0 cm 2.0 cm 2.0 cm region of uniform electric field. What is the electric field strength? You need a capacitance of 50 F, but you dont happen to have a 50 F capacitor. You do have a 75 F capacitor. What additional capacitor do you need to produce a total capacitance of 50 F? Should you... What is the equivalent capacitance of the three capacitors in Figure EX26.28? 20 F 13 F 30 F FIGURE EX26.28 A 150 g particle at x = 0 is moving at 2.00 m/s in the +x-direction. As it moves, it experiences a force given by F x = (0.250 N) sin (x/2.00 m). What is the particles speed when it reaches x = 3.14... A horizontal spring with spring constant 750 N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it 5.0 cm. How hard is the athlete pushing? A spherical ball of solid, nonporous naphthalene, a mothball, is suspended in still air. The naphthalene ball slowly sublimes, releasing the naphthalene vapor into the surrounding air by molecular... A 35-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant? A horizontal spring with spring constant 85 N/m extends outward from a wall just above floor level. A 1.5 kg box sliding across a frictionless floor hits the end of the spring and compresses it 6.5... One mole (6.02 10 23 atoms) of helium atoms in the gas phase has 3700 J of microscopic kinetic energy at room temperature. If we assume that all atoms move with the same speed, what is that speed?... A baggage handler throws a 15 kg suitcase along the floor of an airplane luggage compartment with a speed of 1.2 m/s. The suitcase slides 2.0 m before stopping. Use work and energy to find the... At midday, solar energy strikes the earth with an intensity of about 1 kW/m 2 . What is the area of a solar collector that could collect 150 MJ of energy in 1 h? This is roughly the energy content of... A 50 kg sprinter, starting from rest, runs 50 m in 7.0 s at constant acceleration. a. What is the magnitude of the horizontal force acting on the sprinter? b. What is the sprinters power output at... A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s. During the same time interval, a 30 kg greyhound can go from rest to 20 m/s. What is the average power output of each? Average... A 1000 kg elevator accelerates upward at 1.0 m/s 2 for 10 m, starting from rest. a. How much work does gravity do on the elevator? b. How much work does the tension in the elevator cable do on the... Susans 10 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30 above the floor. The tension is a constant 30 N and the coefficient of friction is... A particle of mass m moving along the x-axis has velocity v x = v 0 sin (x/2L). How much work is done on the particle as it moves (a) From x = 0 to x = L (b) From x = 0 to x = 2L? A ball shot straight up with kinetic energy K 0 reaches height h. What height will it reach if the initial kinetic energy is doubled? A pile driver lifts a 250 kg weight and then lets it fall onto the end of a steel pipe that needs to be driven into the ground. A fall of 1.5 m drives the pipe in 35 cm. What is the average force... A 50 kg ice skater is gliding along the ice, heading due north at 4.0 m/s. The ice has a small coefficient of static friction, to prevent the skater from slipping sideways, but k = 0. Suddenly, a... Youre fishing from a tall pier and have just caught a 1.5 kg fish. As it breaks the surface, essentially at rest, the tension in the vertical fishing line is 16 N. Use work and energy to find the... Recall from example 3, Chapter 25, that the differential model for the radial concentration profile of dissolved oxygen within one cylindrical engineered tissue bundle (Figure 25.8) is with boundary...
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