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...
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...
Calculate the total lift force on the Arctic hut shown below as a function of the location of the opening. The lift force results from the difference between the inside pressure and the outside...
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...
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...
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.
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,...
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...
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...
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
Water at 60F enters a 1-in.-ID tube that is used to cool a nuclear reactor. The water flow rate is 30 gal/min. Determine the total heat transfer, the exiting water temperature, and the wall...
A newly cast polymer sheet is laid down on a moving conveyer belt to cool. A side view of the process is shown below. The polymer sheet measures 2 m by 1.5 m and is 1.5 mm thick. Because the conveyer...
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 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...
Hookes law describes an ideal spring. Many real springs are better described by the restoring force (F Sp ) s = -ks - q(s) 3 , where q is a constant. Consider a spring with k = 250 N/m and q = 800...
The force acting on a particle is F x = F 0 e-x/L . How much work does this force do as the particle moves along the x-axis from x = 0 to x = L?
An electric dipole consists of two equal but opposite electric charges, +q and -q, separated by a small distance d. If another charge Q is distance x from the center of the dipole, in the plane...
When a 65 kg cheerleader stands on a vertical spring, the spring compresses by 5.5 cm. When a second cheerleader stands on the shoulders of the first, the spring compresses an additional 4.5 cm. What...
Two identical horizontal springs are attached to opposite sides of a box that sits on a frictionless table. The outer ends of the springs are clamped while the springs are at their equilibrium...
Hydrogen embrittlement weakens the mechanical strength of cast iron. This phenomenon frequently occurs in cast-iron pressure vessels containing hydrogen (H 2 ) gas. The H 2 gas dissolves into the...
A simple experiment is set up to measure the effective diffusion coefficient of blue dextran dye into a rigid agarose gel. An aqueous, well-mixed solution of liquid height 10 cm con taining 1.0 g/L...
The contamination of water-saturated soils with toxic organic solvents is an important environmental problem. The organic solvents can dissolve into to the water and diffuse through the...
A spring of equilibrium length L 1 and spring constant k 1 hangs from the ceiling. Mass m 1 is suspended from its lower end. Then a second spring, with equilibrium length L 2 and spring constant k 2...
Consider the porous slab shown in the figure below. Very tiny pores of 20 A diameter run through the 2.0 cm slab in parallel array. This device will ultimately serve as a drug delivery vehicle for a...
A horizontal spring with spring constant 250 N/m is compressed by 12 cm and then used to launch a 250 g box across the floor. The coefficient of kinetic friction between the box and the floor is...
A 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying a 40 kg backpack filled with gear. How much power does he need to reach the top in 55 s?
A hydroelectric power plant uses spinning turbines to transform the kinetic energy of moving water into electric energy with 80% efficiency. That is, 80% of the kinetic energy becomes electric...
The block of mass M in FIGURE P7.36 slides on a frictionless surface. Find an expression for the tension in the string. Massless string Massless, fric- tionless pulley FIGURE P7.36
A farmer uses a tractor to pull a 150 kg bale of hay up a 15 incline to the barn at a steady 5.0 km/h. The coefficient of kinetic friction between the bale and the ramp is 0.45. What is the tractors...
A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1480 kg, and two-thirds of the...
One step in the processing of cucumbers to pickles is the pickling process itself. In one method of making pickles, young cucumbers with no waxy skins are soaked in a NaC1 solution overnight. To...
A 5.0 kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in FIGURE EX9.29. The scale reads in newtons. a. What does the spring scale read just before the mass...
The coefficient of static friction is 0.60 between the two blocks in FIGURE P7.35. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force F causes both blocks to...
Two 3.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 100 V battery. a. What is the capacitance? b. What is the magnitude of the charge on each electrode?
Light from the sun allows a solar cell to move electrons from the positive to the negative terminal, doing 2.4 10 -19 J of work per electron. What is the emf of this solar cell?
Figure Q26.10 shows a 3 V battery with metal wires attached to each end. What are the potential differences ÎV 12 = V 2 - V 1 , ÎV 23 = V 3 - V 2 , ÎV 34 = V 4 - V 3 , and ÎV...
Figure Q26.8 shows a negatively charged electroscope. The gold leaf stands away from the rigid metal post. Is the electric potential of the leaf higher than, lower than, or equal to the potential of...
The electron drift speed in a wire is exceedingly slow typically only a fraction of a millimeter per second. Yet when you turn on a flashlight switch, the light comes on almost instantly. Resolve...