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Fluid mechanics cengel 4th edition solution manual pdf free download
Fluid mechanics cengel 4th edition solution manual pdf free download.Fluid mechanics fundamentals and applications 4th edition cengel solutions manual by ccc - Issuu
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Intensive properties do not depend on the size extent of the system but extensive properties do depend. Mass, number of moles, and molar mass are often confused. Molar mass is also called molecular weight.
The specific gravity, or relative density, is defined as the ratio of the density of a substance to the density. Specific gravity is dimensionless and unitless [it is just a number without dimensions or units].
Hence, specific weight is an intensive property. Air and many other gases at room temperature and pressure can be approximated as ideal gases without any. Ru is the universal gas constant that is the same for all gases, whereas R is the specific gas constant that is. Since molar mass has dimensions of mass per mole, R and Ru do not have the same dimensions or units.
An automobile tire is under-inflated with air. The amount of air that needs to be added to the tire to raise its. Notice that absolute rather than gage pressure must be used in calculations with the ideal gas law.
An automobile tire is inflated with air. The pressure rise of air in the tire when the tire is heated and the. Assumptions Properties Analysis.
The amount of air that needs to be bled off to restore pressure to its original value is kPa 0. A balloon is filled with helium gas. The number of moles and the mass of helium are to be determined. The molar mass of helium is 4.
The temperature of the helium gas is 20 C, which we must. The universal gas constant is kJ. Discussion Although the helium mass may seem large about the mass of an adult football player! The effect of the balloon diameter on the mass of helium is to be investigated, and the results are to be tabulated and plotted. A cylindrical tank contains methanol at a specified mass and volume.
The cylinder conditions before the heat addition process is specified. The pressure after the heat addition. A relation for the variation of density with elevation is to be obtained, the density at 7 km elevation is to be.
Substituting and multiplying by the factor 3. Using the data for the density of Ra in Table A-4, an expression for the density as a function of.
Chapter 2 Properties of Fluids Solution The difference between specific gravity and specific weight is to be explained and the specific weight of the substances in Table are to be determined.
Also, specific volume of a liquid is to be determined. Analysis a Specific gravity is nondimensional, and is the ratio of the density of the fluid to the density of water at 4 C. Specific weight is dimensional, and is simply the product of the density of the fluid and the gravitational acceleration. Discussion It is easy to confuse specific weight, specific gravity, and specific volume, so be careful with these terms. Excel shines in cases where there is a lot of repetition.
We are to define vapor pressure and discuss its relationship to saturation pressure. The vapor pressure Pv of a pure substance is defined as the pressure exerted by a vapor in phase. In general, the pressure of a vapor or gas, whether it exists alone or in a mixture with other gases, is called the partial pressure. During phase change processes between the liquid and vapor phases of a pure substance, the saturation pressure and the vapor pressure are equivalent since the vapor is pure.
Partial pressure is not necessarily equal to vapor pressure. For example, on a dry day low relative. The saturation temperature of a pure substance depends on pressure; in fact, it increases with pressure.
This fact is easily seen by looking at the saturated water property tables. Note that boiling temperature and. We are to determine if temperature increases or remains constant when the pressure of a boiling substance. If the pressure of a substance increases during a boiling process, the temperature also increases since the. We are assuming that the liquid will continue to boil. If the pressure is increased fast enough, boiling may. A pressure cooker uses this principle.
We are to define and discuss cavitation. In the flow of a liquid, cavitation is the vaporization that may occur at locations where the pressure. The vapor bubbles collapse as they are swept away from the low pressure regions, generating highly destructive, extremely high-pressure waves. This phenomenon is a common cause for drop in performance and even the erosion of impeller blades.
Not all. The minimum pressure on the suction side of a water pump is given. The maximum water temperature to. To avoid cavitation at a specified pressure, the fluid temperature everywhere in the flow should remain. Note that saturation temperature increases with pressure, and thus cavitation may occur at higher pressure at.
To avoid cavitation, the pressure anywhere in the system should not be allowed to drop below the vapor or. Note that the vapor pressure increases with increasing temperature, and thus the risk of cavitation is greater. To avoid cavitation, the pressure anywhere in the flow should not be allowed to drop below the vapor or. The sum of all forms of the energy a system possesses is called total energy. In the absence of magnetic,. All three constituents of total energy kinetic, potential, and internal need to be considered in an analysis of.
The internal energy of a system is made up of sensible, latent, chemical, and nuclear energies. We deal with the flow of a single phase fluid in most problems in this textbook; therefore, latent, chemical,. Thermal energy is the sensible and latent forms of internal energy. It does not include chemical or. In common terminology, thermal energy is referred to as heat. However, like work, heat is not a property, whereas thermal energy is a property.
Discussion substance. Flow energy or flow work is the energy needed to push a fluid into or out of a control volume. Fluids at. Flow energy is not a fundamental quantity, like kinetic or potential energy. However, it is a useful concept. A flowing fluid possesses flow energy, which is the energy needed to push a fluid into or out of a. The total energy of a non-flowing fluid consists of internal and potential energies. If the fluid is moving as a rigid body, but not flowing, it may also have kinetic energy e.
The total energy of a flowing fluid consists of internal, kinetic, potential, and flow energies. Flow energy is not to be confused with kinetic energy, even though both are zero when the fluid is at rest. Using specific heat values at the average temperature, the changes in the specific internal energy of ideal. If the fluid can be treated as neither incompressible nor an ideal gas, property tables must be used.
Using specific heat values at the average temperature, the changes in specific enthalpy of ideal gases can be. In fact,isc approximated remains constant 0. For 3 o 3 o this same temperature range, the density varies from We approximate the 3 o density as constant, whose value is Since this is energy per unit mass, we must multiply by the total mass of the water in the tank, i.
We give the final answer to 3 significant digits. The actual energy required will be greater than this, due to. The total energy of saturated water vapor flowing in a pipe at a specified velocity and elevation is to be. The enthalpy of the vapor at the specified temperature can be found in any thermo text to be Then the total energy is determined as. Note that only 0. The coefficient of volume expansion represents the variation of the density of a fluid with temperature at.
It differs from the coefficient of compressibility in that the latter represents the variation of pressure of a fluid with density at constant temperature.
Cengel fluid mechanics 6 edition.PDF.Fluid mechanics cengel 4th edition solution manual pdf free download
Problem E is reconsidered. The variation of Mach number with temperature as the temperature changes. Note that for a specified flow speed, the Mach number decreases with increasing temperature, as expected. The inlet state and the exit pressure of air are given for an isentropic expansion process. The ratio of the. The specific heat ratio k varies with temperature,. The inlet state and the exit pressure of helium are given for an isentropic expansion process. The Mach number of a passenger plane for specified limiting operating conditions is to be determined.
Fluids whose shear stress is linearly proportional to the velocity gradient shear strain are called. Newtonian fluids. Most common fluids such as water, air, gasoline, and oils are Newtonian fluids. In the differential analysis of fluid flow, only Newtonian fluids are considered in this textbook. It is due to the. Viscosity is caused by the cohesive forces between the molecules in liquids, and by the molecular collisions in gases.
In general, liquids have higher dynamic viscosities than gases. We are to compare the settling speed of balls dropped in water and oil; namely, we are to determine which. When two identical small glass balls are dropped into two identical containers, one filled with water and the. Oil is very viscous, with typical values of viscosity approximately times greater than that of water at.
The torque and the rpm of a double cylinder viscometer are given. The viscosity of the fluid is to be. This is the viscosity value at temperature that existed during the experiment. Viscosity is a strong. The viscosities of carbon dioxide at two temperatures are given.
The constants of Sutherland correlation for. Solution The velocity profile of a fluid flowing though a circular pipe is given. The friction drag force exerted on the pipe by the fluid in the flow direction per unit length of the pipe is to be determined. Assumptions Analysis. Substituting the given values, the viscosity of the fluid is determined to be TA 0. This is the viscosity value at the temperature that existed during the experiment.
A thin flat plate is pulled horizontally through an oil layer sandwiched between two plates, one stationary. The location in oil where the velocity is zero and the force that needs to be applied on the plate are to be determined.
The point. Note that wall shear is a friction force between a solid and a liquid, and it acts in the opposite direction of. We are to determine the torque required to rotate the inner cylinder of two concentric cylinders, with the.
We are also to explain what happens when the gap gets bigger. Inner cylinder V h. The thickness of the gap is h, and we let y be the distance from the outer wall into the fluid towards the inner wall.
But the torque is the tangential force times the moment arm Ri. Also, we are asked for the torque required to turn the inner cylinder. This applied torque is counterclockwise mathematically positive. As long as the gap is very small, and therefore the wall curvature effects are negligible, this approximation should be very good. Another way to think about this is that when the gap is very small compared to the cylinder radii, a magnified view of the flow in the gap appears similar to flow between two infinite walls Couette flow.
However, as the gap increases, the curvature effects are no longer negligible, and the linear velocity profile is not expected to be a valid approximation. We do not expect the velocity to remain linear as the gap increases.
Discussion analytically,. It is possible to solve for the exact velocity profile for this problem, and therefore the torque can be found but. A clutch system is used to transmit torque through an oil film between two identical disks. For specified. Discussion Note that the torque transmitted is proportional to the fourth power of disk diameter, and is inversely proportional to the thickness of the oil film. The previous problem is reconsidered. Using EES software, the effect of oil film thickness on the.
Film thickness varied from 0. Conclusion Torque transmitted is inversely proportional to oil film thickness, and the film thickness should be as small as possible to maximize the transmitted torque. Limited distribution permitted only to teachers and educators for course preparation.
If you are a student using this Manual, you are using it without permission. Chapter 2 Properties of Fluids Solution A block is moved at constant velocity on an inclined surface.
The force that needs to be applied in the horizontal direction when the block is dry, and the percent reduction in the required force when an oil film is applied on the surface are to be determined. Assumptions 1 The inclined surface is plane perfectly flat, although tilted. Analysis a The velocity of the block is constant, and thus its acceleration and the net force acting on it are zero.
A free body diagram of the block is given. Then the force balance gives. Then from Eq. Because of the no-slip condition, the oil film sticks to the inclined surface at the bottom and the lower surface of the block at the top. Note that the force required to push the block on the inclined surface reduces significantly by oiling the. For flow over a plate, the variation of velocity with distance is given. A relation for the wall shear stress is. The velocity profile for laminar one-dimensional flow through a circular pipe is given.
A relation for. Assumptions Properties. Then the friction drag force exerted by the fluid on the inner surface of the pipe becomes. In the entrance region and during turbulent flow, the velocity gradient is greater near the wall, and thus the. Then friction drag force exerted by the fluid on the inner surface of the pipe becomes. Chapter 2 Properties of Fluids Solution A frustum shaped body is rotating at a constant angular speed in an oil container. The power required to maintain this motion and the reduction in the required power input when the oil temperature rises are to be determined.
Assumptions The thickness of the oil layer remains constant. Then the wall shear stress anywhere on the surface of the frustum at a distance r from the axis of rotation is.
Note that the power required to overcome shear forces in a viscous fluid greatly depends on temperature. We are to determine the torque required to rotate the outer cylinder of two concentric cylinders, with the.
Inner cylinder h. The thickness of the gap is h, and we let y be the distance from the outer wall into the fluid towards the inner wall as sketched. But the torque is the tangential force times the moment arm Ro.
The above is only an approximation because we assumed a linear velocity profile. As long as the gap is. It is possible to solve for the exact velocity profile for this problem, and therefore the torque can be found analytically, but this has to wait until.
A thin flat plate is pulled horizontally through the mid plane of an oil layer sandwiched between two. The force that needs to be applied on the plate to maintain this motion is to be determined for this case and for the case when the plate. The velocity profile in each oil layer relative to the fixed wall is as shown in the figure.
Stationary surface. Analysis We measure vertical distance y from the lower plate. Then the distance of the moving plate is y from the lower plate and h — y from the upper plate, where y is variable. Chapter 2 Properties of Fluids Solution A cylinder slides down from rest in a vertical tube whose inner surface is covered by oil. An expression for the velocity of the cylinder as a function of time is to be derived. Chapter 2 Properties of Fluids Therefore this equation enables us to estimate dynamic viscosity of oil provided that the limit velocity of the cylinder is precisely measured.
It is caused by the attractive forces between the molecules. The surface tension is also surface energy per unit area since it represents the stretching work that needs to be done to increase the surface area of the liquid by a unit amount. Surface tension is the cause of some very interesting phenomena such as capillary rise and insects that can.
We are to define and discuss the capillary effect. The capillary effect is the rise or fall of a liquid in a small-diameter tube inserted into the liquid. It is. The capillary effect is proportional to the cosine of the contact angle, which is the angle that the tangent to the liquid surface makes with the solid surface at the point of contact. We are to determine whether the level of liquid in a tube will rise or fall due to the capillary effect.
This liquid must be a non-wetting liquid when in contact with the tube material. Mercury is an example of a o. The pressure inside a soap bubble is greater than the pressure outside, as evidenced by the stretch of. The capillary rise is inversely proportional to the diameter of the tube, and thus capillary rise is greater in.
Note however, that if the tube diameter is large enough, there is no capillary rise or fall at all. Rather, the. The soap bubble is in atmospheric air. Substituting, 4 0. Note that the gage pressure in a soap bubble is inversely proportional to the radius or diameter. Noting that surface tension is constant, the surface tension work is simply surface tension multiplied by the change in surface area,.
An air bubble in a liquid is considered. The pressure difference between the inside and outside the bubble is. Considering that an air bubble in a liquid has only one interface, the pressure difference between the inside. Substituting, the pressure difference is determined to be: 2 0.
The force acting on the movable wire of a liquid film suspended on a U-shaped wire frame is measured. Substituting the numerical values, the surface tension is determined from the surface tension force relation. A capillary tube is immersed vertically in water. The height of water rise in the tube is to be determined. A glass tube is inserted into mercury. The capillary drop of mercury in the tube is to be determined.
The maximum capillary rise and tube diameter for the. A steel ball floats on water due to the surface tension effect.
The maximum diameter of the ball is to be. The contact angle is. The height to which the water solution rises in a tree as a result of the capillary effect is to be determined. A journal bearing is lubricated with oil whose viscosity is known.
The torques needed to overcome the. Substituting the given values, the torque is determined to be. A U-tube with a large diameter arm contains water. The difference between the water levels of the two arms. Any difference in water levels between the two arms is due to surface tension effects and thus capillary rise.
Noting that capillary rise in a tube is inversely proportional to tube diameter there will be no capillary rise in the arm with a large diameter. Note that this is a significant difference, and shows the importance of using a U-tube made of a uniform. The amount of air that needs to be added to the tank to raise its pressure and temperature to the recommended values is to be determined. Treating air as an ideal gas, the initial volume and the final mass in the tank are determined to be.
A large tank contains nitrogen at a specified temperature and pressure. Now some nitrogen is allowed to. The amount of nitrogen that has escaped is to be determined. The pressure in an automobile tire increases during a trip while its volume remains constant. The percent. Noting that air is an ideal gas and the volume is constant, the ratio of absolute temperatures after and before.
Therefore, the absolute temperature of air in the tire will increase by 4. This may not seem like a large temperature increase, but if the tire is originally at 20 C The minimum pressure in a pump is given.
It is to be determined if there is a danger of cavitation. To avoid cavitation, the pressure everywhere in the flow should remain above the vapor or saturation. Therefore, there is danger of cavitation in the pump. Note that the vapor pressure increases with increasing temperature, and the danger of cavitation increases at. Air in a partially filled closed water tank is evacuated.
The absolute pressure in the evacuated space is to be. When air is completely evacuated, the vacated space is filled with water vapor, and the tank contains a. Since we have a two-phase mixture of a pure substance at a specified temperature, the vapor pressure must be the saturation pressure at this temperature.
If there is any air left in the container, the vapor pressure will be less. In that case the sum of the component. Chapter 2 Properties of Fluids Solution The specific gravities of solid particles and carrier fluids of a slurry are given. The relation for the specific gravity of the slurry is to be obtained in terms of the mass fraction Cs, mass and the specific gravity SGs of solid particles.
Assumptions 1 The solid particles are distributed uniformly in water so that the solution is homogeneous. Consider solid particles of mass ms and volume Vs dissolved in a fluid of mass mf and volume Vm. The total. The final temperature when half the mass is withdrawn and final pressure when no mass is withdrawn are to be determined. When half of the gas is withdrawn from the tank, the final. The ideal gas 1. Suspended solid particles in water are considered. A relation is to be developed for the specific gravity of.
Analysis Consider solid particles of mass ms and volume V s dissolved in a fluid of mass mf and volume Vm. The total volume of the suspension or mixture is. The variation of the dynamic viscosity of water with absolute temperature is given. Using tabular data, a th. The equations and plot are shown here. A newly produced pipe is tested using pressurized water. The additional water that needs to be pumped to. The coefficient of volume expansion of an ideal gas is not constant, but rather decreases with temperature.
The pressure is given at a certain depth of the ocean. An analytical relation between density and pressure is. The density is to be compared with that from Eq. The coefficient of compressibility is given to be MPa. The liquid density at the free surface is given to 3. Therefore we conclude that linear approximation Eq. The specific heat ratio k varies with. A shaft is pulled with a constant velocity through a bearing. The space between the shaft and bearing is. The force required to maintain the axial movement of the shaft is to be determined.
The varying clearance h can be expressed as a function of axial coordinate x see figure. A shaft rotates with a constant angual speed in a bearing.
The space between the shaft and bearing is filled. A relation is to be derived for the capillary rise of a liquid between two large parallel plates a distance t. The magnitude of the capillary rise between two large parallel plates can be determined from a force. The bottom of the liquid column is at the same level as the free surface of the liquid reservoir, and thus the pressure there must be atmospheric pressure. This will balance the atmospheric pressure acting from the top surface, and thus these two effects will cancel each other.
The weight of the liquid column is t. A cylindrical shaft rotates inside an oil bearing at a specified speed. The power required to overcome. Note the power dissipated in journal bearing is proportional to the cube of the shaft radius and to the square.
A large plate is pulled at a constant speed over a fixed plate. The space between the plates is filled with. The shear stress developed on the upper plate and its direction are to be determined for parabolic and linear velocity profile cases. Therefore we conclude that the linear assumption is not realistic since it gives over prediction.
Chapter 2 Properties of Fluids Solution Air spaces in certain bricks form air columns of a specified diameter. The height that water can rise in those tubes is to be determined. Assumptions 1 The interconnected air pockets form a cylindrical air column.
Properties The surface tension is given to be 0. Air Brick h Mercury. Therefore, the value determined may change with temperature. Chapter 2 Properties of Fluids Solution A fluid between two long parallel plates is heated as the upper plate is moving. A relation for the fluid velocity is to be obtained and velocity profile is to be plotted.
Also the shear stress is to be calculated and its direction is to be shown. Assumptions 1 Flow is parallel to plates. Analysis a Taking an infinitesimal fluid element and applying force balance assuming one dimensional flow ,. The viscosity is changing linearly with respect to y. The velocity vectors are also shown. For comparison, a linear profile is also plotted.
This is expected. The viscosity decreases towards the moving plate. To keep the shear stress constant as was founded earlier , the velocity should increase more and more not a constant rate as one approaches the moving plate. As found earlier, the shear stress is constant throughout the flow. The shear stress directions on the top surface of the fluid element adjacent to the moving plate, and on the moving plate are:. Chapter 2 Properties of Fluids Solution A thrust bearing is operated with a thin film of oil.
The ratio of lost power in the thrust bearing to the produced power is to be determined. A relationship for the torque transmitted by the clutch is to be obtained, and the numerical value of the torque is to be calculated. This is the torque transmitted by one surface of a plate mounted on the input shaft. A relationship for the torque transmitted by the clutch is to be obtained, and the m. Assumptions 1 The thickness of the oil layer between the disks is constant. The laminar flow of a Bingham plastic fluid in a horizontal pipe of radius R is considered.
The shear stress. A circular disk immersed in oil is used as a damper, as shown in the figure. It is to be shown that the. Then the wall shear stress anywhere on the upper surface of the disk at a distance r from the axis of rotation. Note that the damping torque and thus damping power is inversely proportional to the thickness of oil th. A thin oil film is sandwiched between two large parallel plates with top plate stationary and bottom plate. A third plate is dragged through the oil.
The velocity profile is to be sketched and the vertical distance where the velocity is zero is to be determined. Also, the force required to keep the middle plate at constant speed is to be determined. Analysis a The velocity profiles are expected to be linear with respect to y, and independent of x. You should be able to calculate these yourself. The specific volume of this fluid is 3. Answer b 0. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen.
Similar problems and their solutions can be obtained easily by modifying numerical values. Chapter 2 Properties of Fluids A 0. The mass of the air in the tank is 3. Answer a 0. Answer e 0. The density of the gas is 1. The pressure of the gas is a 13 kPa. Liquid water vaporizes into water vapor as it flows in the piping of a boiler.
The temperature of water also increases by 0. Answer b 1. An ideal gas is compressed isothermally from kPa to kPa. The final density of the water is 3. Then, the coefficient of compressibility value of water is a atm. The coefficient of volume expansion of this fluid is a 0.
The Mach number of this flow is a Answer d 1. The kinematic viscosity of air at this state is a 0. A viscometer constructed of two cm-long concentric cylinders is used to measure the viscosity of a fluid. The outer diameter of the inner cylinder is 9 cm, and the gap between the two cylinders is 0. The inner cylinder is rotated at rpm, and the torque is measured to be 1.
The viscosity of the fluid is 2. The contact angle can be taken as zero degrees. The capillary rise of water in the tube is a 2. Answer c 5. Chapter 2 Properties of Fluids A liquid film suspended on a U-shaped wire frame with a 6-cm-long movable side is used to measure the surface tension of a liquid. If the force needed to move the wire is 0. Answer d 0. The maximum diameter of the tube in which water rises is a 0.
We are to determine the inlet water speed at which cavitation is likely to occur in the throat of a converging-. So, the minimum inlet velocity at which cavitation is likely to occur is 0.
The velocity at the throat is much faster than this, of course. Using Eq. As might be expected, at higher temperature, a lower inlet velocity is required to generate cavitation, since the water is warmer and already closer to its boiling point.
Discussion is. Cavitation is usually undesirable since it leads to noise, and the collapse of the bubbles can be destructive. It often. We are to explain how objects like razor blades and paper clips can float on water, even though they are. Just as some insects like water striders can be supported on water by surface tension, surface tension is the. If we think of surface tension like a skin on top of the water, somewhat like a stretched piece of balloon, we can understand how something heavier than water pushes down on the surface, but the surface tension forces counteract the weight to within limits by providing an upward force.
Since soap decreases surface tension, we expect that it would be harder to float objects like this on a soapy surface; with a high enough soap concentration, in fact, we would expect that the razor blade or paper clip could not float at all.
If the razor blade or paper clip is fully submerged breaking through the surface tension , it sinks. See More. No part of this Manual may be reproduced, displayed or distributed in any form or by any means, electronic or otherwise, without the prior written permission of McGraw-Hill Education.
Density and Specific Gravity C Solution We are to discuss the difference between intensive and extensive properties. Analysis Intensive properties do not depend on the size extent of the system but extensive properties do depend on the size extent of the system. Discussion An example of an intensive property is temperature. An example of an extensive property is mass.
Discussion Mass, number of moles, and molar mass are often confused. Discussion Specific gravity is dimensionless and unitless [it is just a number without dimensions or units]. Discussion If specific weight were an extensive property, its value for half of the system would be halved.
Discussion Air and many other gases at room temperature and pressure can be approximated as ideal gases without any significant loss of accuracy.
Analysis Ru is the universal gas constant that is the same for all gases, whereas R is the specific gas constant that is different for different gases. Discussion Since molar mass has dimensions of mass per mole, R and Ru do not have the same dimensions or units.
Assumptions At specified conditions, air behaves as an ideal gas. Assumptions At specified conditions, argon behaves as an ideal gas. Assumptions At specified conditions, oxygen behaves as an ideal gas. Solution The volume and the weight of a fluid are given. Its mass and density are to be determined. The amount of air that needs to be added to the tire to raise its pressure to the recommended value is to be determined.
Assumptions 1 At specified conditions, air behaves as an ideal gas. Solution An automobile tire is inflated with air. The pressure rise of air in the tire when the tire is heated and the amount of air that must be bled off to reduce the temperature to the original value are to be determined. Assumptions Properties Analysis 1 At specified conditions, air behaves as an ideal gas. Assumptions At specified conditions, helium behaves as an ideal gas. Properties The molar mass of helium is 4.
Properties o The molar mass of helium is 4. Assumptions 1 The volume of the tank remains constant. The pressure after the heat addition process is to be determined. Assumptions 1 The contents of cylinder are approximated by the air properties. Combustion chamber 1. Assumptions 1 Atmospheric air behaves as an ideal gas. Solution Using the data for the density of Ra in Table A-4, an expression for the density as a function of temperature in a specified form is to be obtained.
Analysis An Excel sheet gives the following results. Chapter 2 Properties of Fluids Vapor Pressure and Cavitation C Solution Analysis We are to define vapor pressure and discuss its relationship to saturation pressure.
The vapor pressure Pv of a pure substance is defined as the pressure exerted by a vapor in phase equilibrium with its liquid at a given temperature. Discussion Partial pressure is not necessarily equal to vapor pressure. For example, on a dry day low relative humidity , the partial pressure of water vapor in the air is less than the vapor pressure of water. Analysis Yes. The higher the pressure, the higher the saturation or boiling temperature. Discussion This fact is easily seen by looking at the saturated water property tables.
Note that boiling temperature and saturation pressure at a given pressure are equivalent. Analysis If the pressure of a substance increases during a boiling process, the temperature also increases since the boiling or saturation temperature of a pure substance depends on pressure and increases with it. Discussion We are assuming that the liquid will continue to boil.
If the pressure is increased fast enough, boiling may stop until the temperature has time to reach its new higher boiling temperature. In the flow of a liquid, cavitation is the vaporization that may occur at locations where the pressure drops below the vapor pressure. Not all cavitation is undesirable.
The maximum water temperature to avoid the danger of cavitation is to be determined. Properties The saturation temperature of water at 0. Discussion Note that saturation temperature increases with pressure, and thus cavitation may occur at higher pressure at locations with higher fluid temperatures.
Analysis To avoid cavitation, the pressure anywhere in the system should not be allowed to drop below the vapor or saturation pressure at the given temperature. Discussion Note that the vapor pressure increases with increasing temperature, and thus the risk of cavitation is greater at higher fluid temperatures.
Chapter 2 Properties of Fluids Solution The minimum pressure in a piping system to avoid cavitation is to be determined. Analysis To avoid cavitation, the pressure anywhere in the flow should not be allowed to drop below the vapor or saturation pressure at the given temperature.
Analysis The sum of all forms of the energy a system possesses is called total energy. In the absence of magnetic, electrical, and surface tension effects, the total energy of a system consists of the kinetic, potential, and internal energies.
Discussion All three constituents of total energy kinetic, potential, and internal need to be considered in an analysis of a general fluid flow. Analysis The internal energy of a system is made up of sensible, latent, chemical, and nuclear energies. The sensible internal energy is due to translational, rotational, and vibrational effects.
Discussion We deal with the flow of a single phase fluid in most problems in this textbook; therefore, latent, chemical, and nuclear energies do not need to be considered. Analysis Thermal energy is the sensible and latent forms of internal energy. It does not include chemical or nuclear forms of energy. Analysis Flow energy or flow work is the energy needed to push a fluid into or out of a control volume.
Fluids at rest do not possess any flow energy. Discussion Flow energy is not a fundamental quantity, like kinetic or potential energy. However, it is a useful concept in fluid mechanics since fluids are often forced into and out of control volumes in practice. Analysis A flowing fluid possesses flow energy, which is the energy needed to push a fluid into or out of a control volume, in addition to the forms of energy possessed by a non-flowing fluid. Discussion Flow energy is not to be confused with kinetic energy, even though both are zero when the fluid is at rest.
Discussion If the fluid can be treated as neither incompressible nor an ideal gas, property tables must be used. Chapter 2 Properties of Fluids E Solution We are to estimate the energy required to heat up the water in a hot-water tank. Assumptions 1 There are no losses.
The actual energy required will be greater than this, due to heat transfer losses and other inefficiencies in the hot-water heating system. Analysis The total energy of a flowing fluid is given by Eq. Analysis The coefficient of volume expansion represents the variation of the density of a fluid with temperature at constant pressure. Discussion The coefficient of volume expansion of an ideal gas is equal to the inverse of its absolute temperature.
Analysis The coefficient of compressibility represents the variation of pressure of a fluid with volume or density at constant temperature.
Discussion The coefficient of compressibility of an ideal gas is equal to its absolute pressure. Analysis The coefficient of compressibility of a fluid cannot be negative, but the coefficient of volume expansion can be negative e. Discussion This is the reason that ice floats on water. Chapter 2 Properties of Fluids E Solution We are to estimate the density as water is heated, and we are to compare to the actual density.
Assumptions 1 The coefficient of volume expansion is constant in the given temperature range. The change in pressure is to be determined. Assumptions The process is isothermal and thus the temperature remains constant. Solution Water at a given temperature and pressure is compressed to a high pressure isothermally. The increase in the density of water is to be determined. Assumptions 1 The isothermal compressibility is constant in the given pressure range.
Solution The percent increase in the density of an ideal gas is given for a moderate pressure. The percent increase in density of the gas when compressed at a higher pressure is to be determined.
Assumptions The gas behaves an ideal gas. Therefore, the coefficient of compressibility of an ideal gas is equal to its absolute pressure, and the coefficient of compressibility of the gas increases with increasing pressure. Discussion If temperature were also allowed to change, the relationship would not be so simple. Molar mass is also called molecular weight.
Specific gravity is dimensionless and unitless [it is just a number without dimensions or units]. Hence, specific weight is an intensive property. Air and many other gases at room temperature and pressure can be approximated as ideal gases without any. Ru is the universal gas constant that is the same for all gases, whereas R is the specific gas constant that is. Since molar mass has dimensions of mass per mole, R and Ru do not have the same dimensions or units. Chapter 2 Properties of Fluids In ideal gas calculations, it saves time to write the gas constant in appropriate units.
An automobile tire is under-inflated with air. The amount of air that needs to be added to the tire to raise its. Notice that absolute rather than gage pressure must be used in calculations with the ideal gas law. An automobile tire is inflated with air. The pressure rise of air in the tire when the tire is heated and the. Treating air as an ideal gas and assuming the volume of the tire to remain constant, the final pressure in the tire is determined from K PV PV T 1 1.
The amount of air that needs to be bled off to restore pressure to its original value is kPa 0. A balloon is filled with helium gas. The number of moles and the mass of helium are to be determined. The molar mass of helium is 4. The temperature of the helium gas is 20 C, which we must. Discussion Although the helium mass may seem large about the mass of an adult football player! Chapter 2 Properties of Fluids Solution A balloon is filled with helium gas. The effect of the balloon diameter on the mass of helium is to be investigated, and the results are to be tabulated and plotted.
A cylindrical tank contains methanol at a specified mass and volume. The cylinder conditions before the heat addition process is specified. The pressure after the heat addition. Limited distribution permitted only to teachers and educators for course preparation.
If you are a student using this Manual, you are using it without permission. A relation for the variation of density with elevation is to be obtained, the density at 7 km elevation is to be. Substituting and multiplying by the factor 3. Using the data for the density of Ra in Table A-4, an expression for the density as a function of.
Chapter 2 Properties of Fluids Solution The difference between specific gravity and specific weight is to be explained and the specific weight of the substances in Table are to be determined.
Also, specific volume of a liquid is to be determined. Analysis a Specific gravity is nondimensional, and is the ratio of the density of the fluid to the density of water at 4 C. Specific weight is dimensional, and is simply the product of the density of the fluid and the gravitational acceleration. Discussion It is easy to confuse specific weight, specific gravity, and specific volume, so be careful with these terms.
Excel shines in cases where there is a lot of repetition. We are to define vapor pressure and discuss its relationship to saturation pressure. The vapor pressure Pv of a pure substance is defined as the pressure exerted by a vapor in phase. In general, the pressure of a vapor or gas, whether it exists alone or in a mixture with other gases, is called the partial pressure. During phase change processes between the liquid and vapor phases of a pure substance, the saturation pressure and the vapor pressure are equivalent since the vapor is pure.
Partial pressure is not necessarily equal to vapor pressure. For example, on a dry day low relative. The saturation temperature of a pure substance depends on pressure; in fact, it increases with pressure. This fact is easily seen by looking at the saturated water property tables. Note that boiling temperature and. We are to determine if temperature increases or remains constant when the pressure of a boiling substance.
If the pressure of a substance increases during a boiling process, the temperature also increases since the. We are assuming that the liquid will continue to boil. If the pressure is increased fast enough, boiling may. A pressure cooker uses this principle.
We are to define and discuss cavitation. In the flow of a liquid, cavitation is the vaporization that may occur at locations where the pressure. The vapor bubbles collapse as they are swept away from the low pressure regions, generating highly destructive, extremely high-pressure waves. This phenomenon is a common cause for drop in performance and even the erosion of impeller blades. Not all.
The minimum pressure on the suction side of a water pump is given. The maximum water temperature to. To avoid cavitation at a specified pressure, the fluid temperature everywhere in the flow should remain. Note that saturation temperature increases with pressure, and thus cavitation may occur at higher pressure at. To avoid cavitation, the pressure anywhere in the system should not be allowed to drop below the vapor or. Note that the vapor pressure increases with increasing temperature, and thus the risk of cavitation is greater.
To avoid cavitation, the pressure anywhere in the flow should not be allowed to drop below the vapor or. The sum of all forms of the energy a system possesses is called total energy. In the absence of magnetic,. All three constituents of total energy kinetic, potential, and internal need to be considered in an analysis of. The internal energy of a system is made up of sensible, latent, chemical, and nuclear energies. We deal with the flow of a single phase fluid in most problems in this textbook; therefore, latent, chemical,.
Thermal energy is the sensible and latent forms of internal energy. It does not include chemical or. In common terminology, thermal energy is referred to as heat. However, like work, heat is not a property, whereas thermal energy is a property.
