Analysis The flow of air over the wings of an aircraft is external since this is an unbounded fluid flow over a surface. The flow of gases through a jet engine is internal flow since the fluid is completely bounded by the solid surfaces of the engine. Discussion If we consider the entire airplane, the flow is both internal through the jet engines and external over the body and wings. We are also to discuss whether wind-driven flows are forced or natural. Analysis In forced flow, the fluid is forced to flow over a surface or in a tube by external means such as a pump or a fan.
In natural flow, any fluid motion is caused by natural means such as the buoyancy effect that manifests itself as the rise of the warmer fluid and the fall of the cooler fluid. The flow caused by winds is natural flow for the earth, but it is forced flow for bodies subjected to the winds since for the body it makes no difference whether the air motion is caused by a fan or by the winds.
Discussion As seen here, the classification of forced vs. Analysis The Mach number of a flow is defined as the ratio of the speed of flow to the speed of sound in the flowing fluid. A Mach number of 2 indicate a flow speed that is twice the speed of sound in that fluid.
Discussion Mach number is an example of a dimensionless or nondimensional parameter. Analysis No. The speed of sound, and thus the Mach number, changes with temperature which may change considerably from point to point in the atmosphere. Therefore, air flow with a Mach number of 0.
Discussion Air is of course a compressible fluid, but at low Mach numbers, compressibility effects are insignificant.
Analysis A fluid in direct contact with a solid surface sticks to the surface and there is no slip. This is known as the no-slip condition, and it is due to the viscosity of the fluid.
Discussion There is no such thing as an inviscid fluid, since all fluids have viscosity. Analysis The region of flow usually near a wall in which the velocity gradients are significant and frictional effects are important is called the boundary layer. When a fluid stream encounters a solid surface that is at rest, the fluid velocity assumes a value of zero at that surface. The velocity then varies from zero at the surface to some larger value sufficiently far from the surface.
The development of a boundary layer is caused by the no-slip condition. Discussion As we shall see later, flow within a boundary layer is rotational individual fluid particles rotate , while that outside the boundary layer is typically irrotational individual fluid particles move, but do not rotate. Analysis A process is said to be steady if it involves no changes with time anywhere within the system or at the system boundaries.
Discussion The opposite of steady flow is unsteady flow, which involves changes with time. Analysis Stress is defined as force per unit area, and is determined by dividing the force by the area upon which it acts.
The normal component of a force acting on a surface per unit area is called the normal stress, and the tangential component of a force acting on a surface per unit area is called shear stress. In a fluid at rest, the normal stress is called pressure.
Discussion Fluids in motion may have both shear stresses and additional normal stresses besides pressure, but when a fluid is at rest, the only normal stress is the pressure, and there are no shear stresses. Analysis A system is defined as a quantity of matter or a region in space chosen for study.
The mass or region outside the system is called the surroundings. The real or imaginary surface that separates the system from its surroundings is called the boundary.
This has been a source of confusion for students for many years. Analysis When analyzing the acceleration of gases as they flow through a nozzle, a wise choice for the system is the volume within the nozzle, bounded by the entire inner surface of the nozzle and the inlet and outlet cross-sections. This is a control volume or open system since mass crosses the boundary. Discussion It would be much more difficult to follow a chunk of air as a closed system as it flows through the nozzle.
Analysis Systems may be considered to be closed or open, depending on whether a fixed mass or a volume in space is chosen for study. A closed system also known as a control mass or simply a system consists of a fixed amount of mass, and no mass can cross its boundary. An open system, or a control volume, is a selected region in space. Mass may cross the boundary of a control volume or open system. Discussion In thermodynamics, it is more common to use the terms open system and closed system, but in fluid mechanics, it is more common to use the terms system and control volume to mean the same things, respectively.
Analysis We would most likely take the system as the air contained in the piston-cylinder device. This system is a closed or fixed mass system when it is compressing and no mass enters or leaves it. However, it is an open system during intake or exhaust.
Discussion In this example, the system boundary is the same for either case — closed or open system. Analysis Pound-mass lbm is the mass unit in English system whereas pound-force lbf is the force unit in the English system. One pound-force is the force required to accelerate a mass of In other words, the weight of a 1-lbm mass at sea level on earth is 1 lbf. Discussion It is not proper to say that one lbm is equal to one lbf since the two units have different dimensions.
Analysis In this unit, the word light refers to the speed of light. The light-year unit is then the product of a velocity and time. Hence, this product forms a distance dimension and unit. Analysis There is no acceleration car moving at constant velocity , thus the net force is zero in both cases.
If there is zero acceleration, there must be zero net force. The steak that is a better buy is to be determined. Assumptions The steaks are of identical quality. Analysis To make a comparison possible, we need to express the cost of each steak on a common basis. We choose 1 kg as the basis for comparison. Discussion Notice the unity conversion factors in the above equations. Its weight is to be determined. Its weight is to be determined in various units. The mass and weight of the air in the room are to be determined.
Assumptions The density of air is constant throughout the room. Considering that the mass of an average man is about 70 to 90 kg, the mass of air in the room is probably larger than you might have expected.
The amount of electric energy used in kWh and kJ are to be determined. It is to be determined how much he weighs on the spring and beam scales on the moon. Which scale would you consider to be more accurate? The net upward force acting on a man in the aircraft is to be determined. Discussion The man feels like he is six times heavier than normal. You get a similar feeling when riding an elevator to the top of a tall building, although to a much lesser extent.
The acceleration of the rock is to be determined. The entire software solution is to be printed out, including the numerical results with proper units. Units are in square brackets. Rock The percent reduction in the weight of an airplane cruising at 13, m is to be determined.
Properties The gravitational acceleration g is 9. Analysis Weight is proportional to the gravitational acceleration g, and thus the percent reduction in weight is equivalent to the percent reduction in the gravitational acceleration, which is determined from 9. Discussion Note that the weight loss at cruising altitudes is negligible. Sorry, but flying in an airplane is not a good way to lose weight. The best way to lose weight is to carefully control your diet, and to exercise.
Discussion This is more than three times higher than the altitude at which a typical commercial jet flies, which is about 30, ft m. So, flying in a jet is not a good way to lose weight — diet and exercise are always the best bet. Sea level z 0 The weight of an astronaut in the International Space Station is to be determined.
Analysis At the altitude of the Space Station, 6 2 2 9. This is the astronauts weight if he were at that elevation, but not in orbit. However, since the satellite and its occupants are in orbit, the astronaut feels weightless. In other words, if the person were to step on a bathroom scale, the reading would be zero. The astronaut feels a gravitational acceleration of 8.
But since the satellite and its occupants are in orbit, they are in free fall — constantly accelerating falling at this rate, but also moving horizontally at a speed such that the elevation of the satellite remains constant, and its circular orbit is maintained. The astronaut feels weightless only because he or she is in a steady circular orbit around the earth.
The gravitational acceleration on a satellite is in fact the centripetal acceleration towards the earth, i. It is a common misconception that space has zero gravity. In fact, if you think about it, satellites could not maintain an orbit at all without gravity acting on them.
The simple linear equation we used here for gravitational decay with elevation breaks down at high elevation, and a more appropriate equation should be used. Analysis The total volume of air breathed in per day is 3L min hr 1 m 7. Discussion This is a lot more air than you probably thought! We breathe in more air in terms of mass than the mass of food that we eat!
A correction is to be found, and the probable cause of the error is to be determined. Multiplying the last term by mass will eliminate the kilograms in the denominator, and the whole equation will become dimensionally homogeneous; that is, every term in the equation will have the same unit.
Discussion Obviously this error was caused by forgetting to multiply the last term by mass at an earlier stage. Assumptions 1 The airplane flies at constant altitude and constant speed. Energy is force times distance, and power is energy per unit time. Discussion We used two unity conversion ratios in the above calculation. Discussion The answer is valid at any speed, since lift must balance weight in order to sustain straight, horizontal flight.
As the fuel is consumed, the overall weight of the aircraft will decrease, and hence the lift requirement will also decrease. If the pilot does not adjust, the airplane will climb slowly in altitude. Assumptions 1 The vertical speed of the fireman is constant.
Analysis a Work W is a form of energy, and is equal to force times distance. One unity conversion ratio is used in each of the above calculations. The weight of the combined system is to be determined.
Assumptions The density of water is constant throughout. Assumptions 1 The volume flow rate, temperature, and density of water are constant over the measured time.
Analysis The volume flow rate is equal to the volume per unit time, i. Since density is mass per unit volume, mass flow rate is equal to volume flow rate times density. If we were interested only in the mass flow rate, we could have eliminated the intermediate calculation by solving for mass flow rate directly, i.
Assumptions 1 The vertical speed of the crate is constant. Discussion The actual required power will be greater than calculated here, due to frictional losses and other inefficiencies in the forklift system.
Three unity conversion ratios are used in the above calculations. Based on unit considerations alone, a relation is to be obtained for the filling time. Assumptions Gasoline is an incompressible substance and the flow rate is constant.
Analysis The filling time depends on the volume of the tank and the discharge rate of gasoline. Therefore, the independent quantities should be arranged such that we end up with the unit of seconds. Based on unit considerations, a relation is to be obtained for the volume of the pool.
Assumptions Water is an incompressible substance and the average flow velocity is constant. Analysis The pool volume depends on the filling time, the cross-sectional area which depends on hose diameter, and flow velocity.
Dynamics 6th edition, Solution manual to Thermodynamics an engineering approach sixth edition By Yunus A. Cengel, Michael A. Cengel, Yunus, Cimbala, John If you are a student using this Manual, you are using it without permission.
Solutions Manual for. Fluid Mechanics: Fundamentals and Applications. Second Edition. Yunus A. McGraw-Hill, Chapter Solutions manual. The instructor's manual contains solutions to most end-of- chapter nondesign problems. Slides of important figures and tables Determine the variation of pressure in a fluid at rest. Nov 5, Cimbala at or [email protected] edu to report it.
Fluid Mechanics. Semester 2. Colin Caprani. Chartered Engineer It helps achieve some practically Sections 1. Fundamentals of Thermal-Fluid Sciences. Engineering Design: A Materials I will generally be in class at a. Cengel and John M. Cimbala, Fluid Mechanics Fundamentals and Applications, 1st edition This textbook has a website Final answers must be clearly marked underlined, boxed, or Our intension here is generalized the one- dimensional Bernoulli equation for viscous flow.
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