In Section 11.2 we always assumed that the value of g was the same at all points on the body. This is not a good approximation if the dimensions of the body are great enough, because the value of g...
A thin, light string is wrapped around the outer rim of a uniform hollow cylinder of mass 4.75 kg having inner and outer radii as shown in Fig. 10.25. The cylinder is then released from rest. (a) How...
A 1.0-m-tall vertical tube is filled with 20C water. A tuning fork vibrating at 580 Hz is held just over the top of the tube as the water is slowly drained from the bottom. At what water heights,...
5.0 g of nitrogen gas at 20C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. a. What are the gas volume and temperature after the expansion? b. How much...
Two cars collide head-on while each is traveling at 80 km/h. Suppose all their kinetic energy is transformed into the thermal energy of the wrecks. What is the temperature increase of each car? You...
A gas cylinder holds 0.10 mol of O 2 at 150C and a pressure of 3.0 atm. The gas expands adiabatically until the pressure is halved. What are the final (a) Volume (b) Temperature?
An ideal-gas process is described by p = cV 1/2 , where c is a constant. a. Find an expression for the work done on the gas in this process as the volume changes from V 1 to V 2 . b. 0.033 mol of gas...
A small rock is thrown vertically upward with a speed of 22.0 m/s from the edge of the roof of a 30.0-m-tall building. The rock doesnt hit the building on its way back down and lands on the street...
An 8.00-kg box sits on a level floor. You give the box a sharp push and find that it travels 8.22 m in 2.8 s before coming to rest again. (a) You measure that with a different push the box traveled...
Explain why it would not make sense to use a full-size glass thermometer to measure the temperature of a thimbleful of hot water.
If you heat the air inside a rigid, sealed container until its Kelvin temperature doubles, the air pressure in the container will also double. Is the same thing true if you double the Celsius...
Two bodies made of the same material have the same external dimensions and appearance, but one is solid and the other is hollow. When their temperature is increased, is the overall volume expansion...
The inside of an oven is at a temperature of 200C (392F). You can put your hand in the oven without injury as long as you dont touch anything. But since the air inside the oven is also at 200C, why...
A newspaper article about the weather states that the temperature of a body measures how much heat the body contains. Is this description correct? Why or why not?
In some household air conditioners used in dry climates, air is cooled by blowing it through a water-soaked filter, evaporating some of the water. How does this cool the air? Would such a system work...
If you are told the initial and final states of a system and the associated change in internal energy, can you determine whether the internal energy change was due to work or to heat transfer?...
How can the thermal conduction of heat from a hot object to a cold object increase entropy when the same amount of heat that flows out of the hot object flows into the cold one?
(See Exercise 21.21.) (a) Calculate the electric potential energy of the adeninethymine bond, using the same combinations of molecules (O-H-N and N-H-N) as in Exercise 21.21. (b) Compare this energy...
Charge Q = +4.00 C is distributed uniformly over the volume of an insulating sphere that has radius R = 5.00 cm. What is the potential difference between the center of the sphere and the surface of...
In the circuit shown in Fig. P26.64, ε = 24.0 V, R 1 = 6.00 Ω, R 3 = 12.0 Ω, and R 2 can vary between 3.00 Ω and 24.0 Ω. For what value of...
The amount of meat in prehistoric diets can be determined by measuring the ratio of the isotopes 15 N to 14 N in bone from human remains. Carnivores concentrate 15 N, so this ratio tells...
The large magnetic fields used in MRI can produce forces on electric currents within the human body. This effect has been proposed as a possible method for imaging biocurrents flowing in the body,...
Two closed loops A and C are close to a long wire carrying a current I (Fig. E29.17). (a) Find the direction (clockwise or counterclockwise) of the current induced in each loop if I is steadily...
A toroidal solenoid has mean radius 12.0 cm and crosssectional area 0.600 cm 2 . (a) How many turns does the solenoid have if its inductance is 0.100 mH? (b) What is the resistance of the solenoid if...
Medical x rays are taken with electromagnetic waves having a wavelength of around 0.10 nm in air. What are the frequency, period, and wave number of such waves?
Light is incident in air at an angle ua (Fig. P33.54) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other. (a) Prove that θ a =...
Water flows steadily through the horizontal 30° pipe bend shown below. At station 1, the diameter is 0.3 m, the velocity is 12 m/s, and the pressure is 128 kPa gage. At station 2, the diameter is...
An open tank car as shown travels to the right at a uniform velocity of 4.5 m/s. At the instant shown the car passes under a jet of water issuing from a stationary 0.1-m-diameter pipe with a velocity...
During the flow of 200 ft 3 /s of water through the hydraulic turbine shown, the pressure indicated by gage A is 12 psig. What should gage B read if the turbine is delivering 600 hp at 82%...
The pressurized tank shown has a circular cross section of 6 ft in diameter. Oil is drained through a nozzle 2 in. in diameter in the side of the tank. Assuming that the air pressure is maintained...
Water flows steadily up the vertical pipe and is then deflected to flow outward with a uniform radial velocity. If friction is neglected, what is the flow rate of water through the pipe if the...
The tank in the previous problem feeds two lines, a 4-cm pipe that exits 10 m below the water level in the tank and a second line, also 4 cm in diameter runs from the tank to a station 20 m below the...
Rework Problem 6.28 with the assumption that the momentum of the incoming air at section (1) is zero. Determine the exit velocity, v, and the magnitude of the pressure drop at section (1). Data From...
In using the von Kármán approximate method for analyzing the turbulent boundary layer over a flat plate, the following velocity and concentration profiles were assumed:...
Determine the velocity profile for fluid flowing between two parallel plates separated by a distance 2h. The pressure drop is constant.
A viscous film drains uniformly down the side of a vertical rod of radius R. At some distance down the rod, the film approaches a terminal or fully developed flow such that the film thickness, h, is...
In an in-compressible flow, the volume of the fluid is constant. Using the continuity equation, v = 0, show that the fluid volume change is zero.
For flow at very low speeds and with large viscosity (the so-called creeping flows) such as occur in lubrication, it is possible to delete the inertia terms, Dv/Dt from the Navier- Stokes equation....
For the stream function given by = 6x 2 - 6y 2 determine whether this flow is rotational or irrotational.
The mass M of drops formed by liquid discharging by gravity from a vertical tube is a function of the tube diameter D, liquid density, surface tension, and the acceleration of gravity. Determine the...
In polar coordinates, the continuity equation for steady in-compressible flow becomes Derive equations (10-10), using this relation. 1 dve = 0 r 0 : (rv,) + - r r 1 Ur V r 0 r
For the fully developed flow of water in a smooth 0.15-m pipe at a rate of 0.006 m 3 /s, determine the thickness of a. The laminar sub layer b. The buffer layer c. The turbulent core
Oil having a kinematic viscosity of 6.7 10 -6 m 2 /s and density of 801 kg/m 3 is pumped through a pipe of 0.71 m diameter at an average velocity of 1.1 m/s. The roughness of the pipe is equivalent...
A 2.20-m diameter pipe carries water at 15C. The head loss due to friction is 0.500 m per 300 m of pipe. Determine the volumetric flow rate of the water leaving the pipe.
A 1-in.-nominal-diameter steel pipe with its outside surface at 400F is located in air at 90F with the convective heat-transfer coefficient between the surface of the pipe and the air equal to 1.5...
Show that equation (16-10) reduces to the form DT V kVT + + A = pcy- +vV?v Dt
Heat is generated in a cylindrical fuel rod in a nuclear reactor according to the relationship where qÌ is the volumetric heat generation rate, kW/m 3 , and r o is the outside cylinder radius....
It is desired to transport liquid metal through a pipe embedded in a wall at a point where the temperature is 650 K. A 1.2-m-thick wall constructed of a material having a thermal conductivity varying...
A furnace wall is to be designed to transmit a maximum heat flux of 200 Btu/h ft 2 of wall area. The inside and outside wall temperatures are to be 2000F and 300F, respectively. Determine the most...
The steady-state expression for heat conduction through a plane wall is q =(kA/L) ÎT as given by equation (17-4). For steady-state heat conduction through a hollow cylinder, an expression...
Evaluate the appropriate mean area for steady-state heat conduction in a hollow sphere that satisfies an equation of the form Repeat part (b) of Problem 17.2 for the spherical case. Data From Problem...
A double-pane insulated window unit consists of two 1-cm-thick pieces of glass separated by a 1.8 cm layer of air. The unit measures 4 m in width and is 3 m wide. Under conditions where the extreme...
Determine the percent in heat flux if, in addition to the conditions specified in Problem 17.11, there are two 3/4-in.- diameter steel bolts extending through the wall per square foot of wall area (k...
Water, initially at 40F, is contained within a thin-walled cylindrical vessel having a diameter of 18 in. Plot the temperature of the water vs. time up to 1 h if the water and container are immersed...
Radioactive waste (k = 20 W/m K) is stored in a cylindrical stainless steel (k = 15W/m K) container with inner and outer diameters of 1.0 and 1.2 m, respectively. Thermal energy is generated...
Soil, having a thermal diffusivity of 5.16 10 -7 m 2 /s, has its surface temperature suddenly raised and maintained at 1100 K from its initial uniform value of 280 K. Determine the temperature at a...
Consider a section of muscle tissue of cylindrical shape with a radius of 1.5 cm. During highly rigorous exercise, metabolic processes generate 15 kW/m 3 of bulk tissue. The outer surface of the...
If the heat flux into a solid is given as F(t), show that the penetration depth d for a semi-infinite solid is of the form 1/2 [LF(1)di] F(t) 8 = (constant)/a
A masonry brick wall 0.45 m thick has a temperature distribution at time, t = 0 which may be approximated by the expression T(K) = 520 + 330 sin (x/L) where L is the wall width and x is the distance...
It is known that oranges can be exposed to freezing temperatures for short periods of time without sustaining serious damage. As a representative case, consider a 0.10-m-diameter orange, originally...
This problem involves using heat-transfer principles as a guide for cooking a pork roast. The roast is to be modeled as a cylinder, having its length and diameter equal to each other, with properties...
Work Problem 19.29 for the case in which the flowing fluid is air at 15 fps. Data From Problem 19.29 Water at 60F enters a 1-in.-ID tube that is used to cool a nuclear reactor. The water flow rate is...
Nitrogen at 100F and 1 atm flows at a velocity of 100 fps. A flat plate 6 in. wide, at a temperature of 200F, is aligned parallel to the direction of flow. At a position 4 ft from the leading edge,...
Ammonia (NH 3 ) and hydrogen sulfide (H 2 S) must both be stripped from wastewater in a packed tower before the wastewater can be treated for reuse. Individual mass-transfer coefficients for ammonia...
Shown in the figure is the case of a fluid flowing parallel to a flat plate, where for a distance X from the leading edge, the plate and fluid are at the same temperature. For values of x > X, the...
Air at atmospheric pressure and 10C enters a rectangular duct that is 6 m long having dimensions of 7.5 and 15 cm in cross section. The surfaces are maintained at 70C by solar irradiation. If the...
A 1.905-cm-diameter brass tube is used to condense steam on its outer surface at 10.13 kPa pressure. Water at 290 K is circulated through the tube. Inside and outside surface coefficients are 1700...
Four immersion heaters in the shape of cylinders 15 cm long and 2 cm in diameter are immersed in a water bath at 1 atm total pressure. Each heater is rated at 500 W. If the heaters operate at rated...
A circular pan has its bottom surface maintained at 200F and is situated in saturated steam at 212F. Construct a plot of condensate depth in the pan vs. time up to 1 h for this situation. The sides...
A square pan with sides measuring 1 ft and a perpendicular lip extending 1 in. above the base is oriented with its base at an angle of 20 degrees from the horizontal. The pan surface is kept at 180F...
Consider a continuous-flow device described below used to pasteurize liquid milk, whose properties approach those of water. Milk at 20C enters a preheater tube at a volumetric flow rate of 6 L/min....
A shell-and-tube heat exchanger with two shell passes and four tube passes is used to exchange energy between two pressurized water streams. One stream flowing at 5000 lb m /h is heated from 75 to...
The sun is approximately 93 million miles distant from Earth, and its diameter is 860,000 miles. On a clear day solar irradiation at Earths surface has been measured at 360 Btu/h ft 2 and an...
The circular base of the cylindrical enclosure shown may be considered a re-radiating surface. The cylindrical walls have an effective emissivity of 0.80 and are maintained at 540°F. The top of...
A shell-and-tube heat exchanger is used for the heating of oil from 20C to 30C ; the oil flow rate is 12 kg/s (C po = 2.2 kJ/kg K). The heat exchanger has one shell pass and two tube passes. Hot...
The StokesEinstein equation is often used to estimate the molecular diameter of large spherical molecules from the molecular diffusion coefficient. The measured molecular diffusion coefficient of the...
The diffusion of oxygen (O 2 ) through living tissue is often first approximated as the diffusion of dissolved O 2 in liquid water. Estimate the diffusion coefficient of O 2 in water by the...
A cylindrical cavity is closed at the bottom and has an opening centered in the top surface. A cross section of this configuration is shown in the sketch. For the conditions stated below, determine...
The general form of the StefanMaxwell equation for mass transfer of species i in an n-component ideal gas mixture along the z-direction for flux is given by Show that for a gas-phase binary mixture...
Tetrachlorosilane (SiCl 4 ) gas is reacted with hydrogen gas (H 2 ) to produce electronic-grade polycrystalline silicon at 800C and 1.5 10 5 Pa according to the reaction equation: SiCl 4 (g) + 2H 2...
A gas separation process has been proposed to remove selectively two pollutants, hydrogen sulfide (H 2 S) and sulfur dioxide (SO 2 ), from an exhaust gas stream containing 3.0 mole% H 2 S, 5.0 mole%...
Compare the effective diffusion coefficient for a dilute mixture of oxygen gas (O 2 , species A) in nitrogen gas (N 2 , species B) at 20C and 1.0 atm within the following materials: a. Straight 10 nm...
A microchannel reactor is being developed for the reforming of methane gas (CH 4 ) to CO 2 and H 2 gas using steam (H 2 O vapor) at high temperature. Prior to entering the reforming reactor, CH 4...
Show that the (25-11) may be written in the form + (V-Pav) DABV 3D r
The design of artificial organs for growing transplant able human tissues require that the cell type of interest, for example pancreatic cells, be grown and sustained within a three-dimensional array...
The electric potential in a region of space is V = 200/x 2 + y 2 , where x and y are in meters. What are the strength and direction of the electric field at (x, y) = (2.0 m, 1.0 m)? Give the...
Consider the diffusion of solute A into the single cylindrical pore shown in the figure below. The end of the pore at z = L is sealed. The pore space is initially filled with inert fluid B. As solute...
One hundred thousand pounds per hour of water are to pass through a heat exchanger, which is to raise the water temperature from 140 to 200F. Combustion products having a specific heat of 0.24 Btu/lb...
A common process for increasing the moisture content of air is to bubble it through a column of water. The air bubbles are assumed to be spheres having a radius of 1.0 mm, and are in thermal...
A preheated piece of mild steel, having an initial concentration of 0.20% by weight of carbon, is exposed to a carbonizing atmosphere for 1.0 h. Under the processing conditions, the surface...
A 10-cm-long spring is attached to the ceiling. When a 2.0 kg mass is hung from it, the spring stretches to a length of 15 cm. a. What is the spring constant? b. How long is the spring when a 3.0 kg...
A 60 kg student is standing atop a spring in an elevator as it accelerates upward at 3.0 m/s 2 . The spring constant is 2500 N/m. By how much is the spring compressed?
A flat surface containing many parallel pores is clogged with coke from a manufacturing process, as shown in the figure below. Pure oxygen gas (O 2 ) at high temperature is used to oxidize the coke,...
a. Starting from rest, a crate of mass m is pushed up a frictionless slope of angle by a horizontal force of magnitude F. Use work and energy to find an expression for the crates speed v when it is...
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...
A 50 g rock is placed in a slingshot and the rubber band is stretched. The magnitude of the force of the rubber band on the rock is shown by the graph in FIGURE P9.55. The rubber band is stretched 30...
A common procedure for increasing the moisture content of air is to bubble it through a column of water. The air bubbles are assumed to be spheres, each having a radius of 1.0 mm, and are in thermal...
A novel metal ion adsorbent material based on the bio polymer poly glucosamine is cast into a gel bead. The amine groups on the bio polymer have a high affinity for transition metal ions at...
A polymer coating of 6.0 mm thickness is cast onto a nonporous flat surface. The coating contains a residual amount of casting solvent, which is uniform at 1.0 wt % within the coating. The mass...
Consider a rectangular-shaped gel tablet of thickness 0.125 cm and width 0.50 cm. The edges of the gel tablet are sealed so that diffusion only occurs along the thickness of the tablet. The initial...