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engineering
fluid mechanics

Fluid Mechanics Fundamentals And Applications 4th Edition Yunus Cengel, John Cimbala - Solutions

In Chap. 9, we discuss the differential equation for conservation of mass, the continuity equation. In cylindrical coordinates, and for steady flow,Write the primary dimensions of each additive term in the equation, and verify that the equation is dimensionally homogeneous. Show all your work. 1
The Reynolds transport theorem (RTT) is discussed in Chap. 4. For the general case of a moving and/or deforming control volume, we write the RTT as follows:where Vr(vector) is the relative velocity, i.e., the velocity of the fluid relative to the control surface. Write the primary dimensions of
An important application of fluid mechanics is the study of room ventilation. In particular, suppose there is a source S (mass per unit time) of air pollution in a room of volume V (Fig. P7–25). Examples include carbon monoxide from cigarette smoke or an unvented kerosene heater, gases like
In Chap. 4 we defined volumetric strain rate as the rate of increase of volume of a fluid element per unit volume (Fig. P7–26). In Cartesian coordinates we write the volumetric strain rate asWrite the primary dimensions of each additive term, and verify that the equation is dimensionally
Cold water enters a pipe, where it is heated by an external heat source (Fig. P7–27). The inlet and outlet water temperatures are Tin and Tout, respectively. The total rate of heat transfer Q̇ from the surroundings into the water in the pipe iswhere ṁ is the mass flow rate of water through the
What is the primary reason for nondimensionalizing an equation?
Recall from Chap. 4 that the volumetric strain rate is zero for a steady incompressible flow. In Cartesian coordinates we express this asSuppose the characteristic speed and characteristic length for a given flow field are V and L, respectively (Fig. P7–29). Define the following dimensionless
In an oscillating compressible flow field the volumetric strain rate is not zero, but varies with time following a fluid particle. In Cartesian coordinates we express this asSuppose the characteristic speed and characteristic length for a given flow field are V and L, respectively. Also suppose
In Chap. 9, we define the stream function ψ for two-dimensional incompressible flow in the xy-plane,where u and v are the velocity components in the x- and y-directions, respectively. (a) What are the primary dimensions of ψ? (b) Suppose a certain two-dimensional flow has a characteristic
In an oscillating incompressible flow field the force per unit mass acting on a fluid particle is obtained from Newton’s second law in intensive formSuppose the characteristic speed and characteristic length for a given flow field are V∞ and L, respectively. Also suppose that ω is a
A wind tunnel is used to measure the pressure distribution in the airflow over an airplane model (Fig. P7–33). The air speed in the wind tunnel is low enough that compressible effects are negligible. As discussed in Chap. 5, the Bernoulli equation approximation is valid in such a flow situation
Consider ventilation of a well-mixed room as in Fig. P7–25. The differential equation for mass concentration in the room as a function of time is given in Prob. 7–25 and is repeated here for convenience,There are three characteristic parameters in such a situation: L, a characteristic length
List the three primary purposes of dimensional analysis.
Repeat Prob. 7–37 with all the same conditions except that the only facility available to the students is a much smaller wind tunnel. Their model submarine is a one-twenty-fourth scale model instead of a one-fifth scale model. At what air speed do they need to run the wind tunnel in order to
List and describe the three necessary conditions for complete similarity between a model and a prototype.
A student team is to design a human-powered submarine for a design competition. The overall length of the prototype submarine is 4.85 m, and its student designers hope that it can travel fully submerged through water at 0.440 m/s. The water is freshwater (a lake) at T = 15°C. The design team
This is a follow-up to Prob. 7–37. The students measure the aerodynamic drag on their model submarine in the wind tunnel (Fig. P7–37). They are careful to run the wind tunnel at conditions that ensure similarity with the prototype submarine. Their measured drag force is 5.70 N. Estimate the
A lightweight parachute is being designed for military use (Fig. P7–40E). Its diameter D is 24 ft and the total weight W of the falling payload, parachute, and equipment is 230 lbf. The design terminal settling speed Vt of the parachute at this weight is 18 ft/s. A one-twelfth scale model of the
Some wind tunnels are pressurized. Discuss why a research facility would go through all the extra trouble and expense to pressurize a wind tunnel. If the air pressure in the tunnel increases by a factor of 1.8, all else being equal (same wind speed, same model, etc.), by what factor will the
The aerodynamic drag of a new sports car is to be predicted at a speed of 60.0 mi/h at an air temperature of 25°C. Automotive engineers build a one-third scale model of the car (Fig. P7–42E) to test in a wind tunnel. The temperature of the wind tunnel air is also 25°C. The drag force is
This is a follow-up to Prob. 7–42E. The aerodynamic drag on the model in the wind tunnel (Fig. P7–42E) is measured to be 33.5 lbf when the wind tunnel is operated at the speed that ensures similarity with the prototype car. Estimate the drag force (in lbf) on the prototype car at the conditions
Water is compressed from 100 kPa to 5000 kPa at constant temperature. The initial density of water is 1000 kg/m3 and the isothermal compressibility of water is α = 4.8 × 10–5 atm–1 . The final density of the water is(a) 1000 kg/m3 (b) 1001.1 kg/m3 (c) 1002.3 kg/m3(d ) 1003.5 kg/m3 (e)
When an airplane is flying at a constant speed relative to the ground, is it correct to say that the Mach number of this airplane is also constant?
What is a fluid? How does it differ from a solid? How does a gas differ from a liquid?
How is the Mach number of a flow defined? What does a Mach number of 2 indicate?
Consider the flow of air at a Mach number of 0.12. Should this flow be approximated as being incompressible?
What is a steady-flow process?
When is a system a closed system, and when is it a control volume?
What are system, surroundings, and boundary?
What is the difference between kg-mass and kg-force?
What is the difference between pound-mass and pound-force?
In a news article, it is stated that a recently developed geared turbofan engine produces 15,000 pounds of thrust to propel the aircraft forward. Is “pound” mentioned here lbm or lbf? Explain.
A 6-kg plastic tank that has a volume of 0.18 m3 is filled with liquid water. Assuming the density of water is 1000 kg/m3, determine the weight of the combined system.
While solving a problem, a person ends up with the equation E = 16 kJ + 7 kJ/kg at some stage. Here E is the total energy and has the unit of kilojoules. Determine how to correct the error and discuss what may have caused it.
A 195-lbm astronaut took his bathroom scale (a spring scale) and a beam scale (compares masses) to the moon where the local gravity is g = 5.48 ft/s2. Determine how much he will weigh (a) On the spring scale (b) On the beam scale.
A 4-kW resistance heater in a water heater runs for 2 hours to raise the water temperature to the desired level. Determine the amount of electric energy used in both kWh and kJ.
Based on unit considerations alone, show that the power needed to accelerate a car of mass m (in kg) from rest to velocity V (in m/s) in time interval t (in s) is proportional to mass and the square of the velocity of the car and inversely proportional to the time interval.
An airplane flies horizontally at 70 m/s. Its propeller delivers 1500 N of thrust (forward force) to overcome aerodynamic drag (backward force). Using dimensional reasoning and unity converstion ratios, calculate the useful power delivered by the propeller in units of kW and horsepower.
If the airplane of Problem 1–38 weighs 1450 lbf, estimate the lift force produced by the airplane’s wings (in lbf and newtons) when flying at 70.0 m/s.Data from Problem 38An airplane flies horizontally at 70 m/s. Its propeller delivers 1500 N of thrust (forward force) to overcome aerodynamic
The boom of a fire truck raises a fireman (and his equipment—total weight 280 lbf) 40 ft into the air to fight a building fire. (a) Showing all your work and using unity conversion ratios, calculate the work done by the boom on the fireman in units of Btu. (b) If the useful power supplied by
A man goes to a traditional market to buy a steak for dinner. He finds a 12-oz steak (1 lbm = 16 oz) for $3.15. He then goes to the adjacent international market and finds a 320-g steak of identical quality for $3.30. Which steak is the better buy?
Water at 20°C from a garden hose fills a 2.0 L container in 2.85 s. Using unity converstion ratios and showing all your work, calculate the volume flow rate in liters per minute (Lpm) and the mass flow rate in kg/s.
A forklift raises a 90.5 kg crate 1.80 m. (a) Showing all your work and using unity conversion ratios, calculate the work done by the forklift on the crane, in units of kJ. (b) If it takes 12.3 seconds to lift the crate, calculate the useful power supplied to the crate in kilowatts.
What is the difference between the analytical and experimental approach to engineering problems? Discuss the advantages and disadvantages of each approach.
What is the difference between precision and accuracy? Can a measurement be very precise but inaccurate? Explain.
Solve this system of three equations with three unknowns using EES:2x – y + z = 93x2 + 2y = z + 2xy + 2z = 14
The speed of an aircraft is given to be 260 m/s in air. If the speed of sound at that location is 330 m/s, the flight of aircraft is(a) Sonic (b) Subsonic (c) Supersonic (d) Hypersonic
For liquids, the dynamic viscosity μ, which is a measure of resistance against flow is approximated as μ = a10b/(T–c), where T is the absolute temperature, and a, b and c are experimental constants. Using the data listed in Table A-7 for methanol at 20ºC, 40ºC and 60ºC, determine the
An important design consideration in two-phase pipe flow of solid-liquid mixtures is the terminal settling velocity below, which the flow becomes unstable and eventually the pipe becomes clogged. On the basis of extended transportation tests, the terminal settling velocity of a solid particle in
A student buys a 5000 Btu window air conditioner for his apartment bedroom. He monitors it for one hour on a hot day and determines that it operates approximately 60 percent of the time (duty cycle = 60 percent) to keep the room at nearly constant temperature. (a) Showing all your work and using
The speed of an aircraft is given to be 1250 km/h. If the speed of sound at that location is 315 m/s, the Mach number is(a) 0.5 (b) 0.85 (c) 1.0 (d) 1.10 (e) 1.20
If mass, heat, and work are not allowed to cross the boundaries of a system, the system is called(a) Isolated (b) Isothermal (c) Adiabatic (d) Control mass(e) Control volume
The weight of a l0-kg mass at sea level is (a) 9.81 N (b) 32.2 kgf (c) 98.1 N (d) 10 N (e) l00 N
The weight of a 1-lbm mass is(a) 1 lbm∙ft/s2 (b) 9.81 lbf (c) 9.81 N (d) 32.2 lbf (e) 1 lbf
One kJ is NOT equal to(a) 1 kPa∙m3 (b) 1 kN∙m (c) 0.001 MJ (d) 1000 J (e) 1 kg∙m2/s2
Which is a unit for the amount of energy?(a) Btu/h (b) kWh (c) kcal/h (d) hp (e) kW
A hydroelectric power plant operates at its rated power of 7 MW. If the plant has produced 26 million kWh of electricity in a specified year, the number of hours the plant has operated that year is(a) 1125 h (b) 2460 h (c) 2893 h (d) 3714 h (e) 8760 h
Search the Internet to find out how to properly add or subtract numbers while taking into consideration the number of significant digits. Write a summary of the proper technique, then use the technique to solve the following cases: (a) 1.006 + 23.47, (b) 703,200 – 80.4, and (c) 4.6903 –
A fluid that occupies a volume of 24 L weighs 225 N at a location where the gravitational acceleration is 9.80 m/s2. Determine the mass of this fluid and its density.
What is the specific volume of oxygen at 40 psia and 80°F?
The density of saturated liquid refrigerant–134a for –20°C ≤ T ≤ 100°C is given in Table A– 4. Using this value develop an expression in the form ρ = aT2 + bT + c for the density of refrigerant–134a as a function of absolute temperature, and determine relative error for each data
The air in an automobile tire with a volume of 2.60 ft3 is at 90°F and 20 psig. Determine the amount of air that must be added to raise the pressure to the recommended value of 30 psig. Assume the atmospheric pressure to be 14.6 psia and the temperature and the volume to remain constant.
A spherical balloon with a diameter of 9 m is filled with helium at 20°C and 200 kPa. Determine the mole number and the mass of the helium in the balloon.
A cylindrical tank of methanol has a mass of 40 kg and a volume of 51 L. Determine the methanol’s weight, density, and specific gravity. Take the gravitational acceleration to be 9.81 m/s2. Also, estimate how much force is needed to accelerate this tank linearly at 0.25 m/s2.
Using average specific heats, explain how internal energy changes of ideal gases and incompressible substances can be determined.
Using average specific heats, explain how enthalpy changes of ideal gases and incompressible substances can be determined
Saturated water vapor at 150°C (enthalpy h = 2745.9 kJ/kg) flows in a pipe at 50 m/s at an elevation of z = 10 m. Determine the total energy of vapor in J/kg relative to the ground level.
What does the coefficient of compressibility of a fluid represent? How does it differ from isothermal compressibility?
What does the coefficient of volume expansion of a fluid represent? How does it differ from the coefficient of compressibility?
Can the coefficient of compressibility of a fluid be negative? How about the coefficient of volume expansion?
Water at 15°C and 1 atm pressure is heated to 100°C at constant pressure. Using coefficient of volume expansion data, determine the change in the density of water.
It is observed that the density of an ideal gas increases by 10 percent when compressed isothermally from 10 atm to 11 atm. Determine the percent increase in density of the gas if it is compressed isothermally from 1000 atm to 1001 atm.
Using the definition of the coefficient of volume expansion and the expression bideal gas = 1/T, show that the percent increase in the specific volume of an ideal gas during isobaric expansion is equal to the percent increase in absolute temperature.
Water at 1 atm pressure is compressed to 400 atm pressure isothermally. Determine the increase in the density of water. Take the isothermal compressibility of water to be 4.80 × 10–5 atm–1.
The volume of an ideal gas is to be reduced by half by compressing it isothermally. Determine the required change in pressure.
Saturated refrigerant-134a liquid at 10°C is cooled to 0°C at constant pressure. Using coefficient of volume expansion data, determine the change in the density of the refrigerant.
A water tank is completely filled with liquid water at 20°C. The tank material is such that it can withstand tension caused by a volume expansion of 0.8 percent. Determine the maximum temperature rise allowed without jeopardizing safety. For simplicity, assume β = constant = β at 40°C.
Repeat Prob. 2–46 for a volume expansion of 1.5 percent for water.Data from Problem 46A water tank is completely filled with liquid water at 20°C. The tank material is such that it can withstand tension caused by a volume expansion of 0.8 percent. Determine the maximum temperature rise allowed
The density of seawater at a free surface where the pressure is 98 kPa is approximately 1030 kg/m3. Taking the bulk modulus of elasticity of seawater to be 2.34 × 109 N/m2 and expressing variation of pressure with depth z as dP = ρg dz determine the density and pressure at a depth of 2500 m.
Taking the coefficient of compressibility of water to be 7 × 105 psia, determine the pressure increase required to reduce the volume of water by (a) 1 percent (b) 2 percent.
Ignoring any losses, estimate how much energy (in units of Btu) is required to raise the temperature of water in a 75-gallon hot-water tank from 60°F to 110°F.
The ideal gas equation of state is very simple, but its range of applicability is limited. A more accurate but complicated equation is the Van der Waals equation of state given bywhere a and b are constants depending on critical pressure and temperatures of the gas. Predict the coefficient of
Prove that the coefficient of volume expansion for an ideal gas is βideal gas = 1/T.
A frictionless piston-cylinder device contains 10 kg of water at 20°C at atmospheric pressure. An external force F is then applied on the piston until the pressure inside the cylinder increases to 100 atm. Assuming the coefficient of compressibility of water remains unchanged during the
Reconsider Prob. 2–53. Assuming a linear pressure increase during the compression, estimate the energy needed to compress the water isothermally.Data from Problem 53.A frictionless piston-cylinder device contains 10 kg of water at 20°C at atmospheric pressure. An external force F is then applied
A cylinder of mass m slides down from rest in a vertical tube whose inner surface is covered by a viscous oil of film thickness h. If the diameter and height of the cylinder are D and L, respectively, derive an expression for the velocity of the cylinder as a function of time, t. Discuss what will
A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of 5 m/s. The two stationary surfaces are spaced 4 cm apart, and the medium between them is filled with oil whose viscosity is 0.9 N·s/m2. The part of the plate immersed in oil at any given time is
Reconsider Prob. 2–94. If the viscosity of the oil above the moving plate is 4 times that of the oil below the plate, determine the distance of the plate from the bottom surface (h2) that will minimize the force needed to pull the plate between the two oils at constant velocity.Data from Problem
A rigid tank contains an ideal gas at 300 kPa and 600 K. Half of the gas is withdrawn from the tank and the gas is at 100 kPa at the end of the process. Determine (a) The final temperature of the gas (b) The final pressure if no mass were withdrawn from the tank and the same final temperature
The absolute pressure of an automobile tire is measured to be 320 kPa before a trip and 335 kPa after the trip. Assuming the volume of the tire remains constant at 0.022 m3, determine the percent increase in the absolute temperature of the air in the tire.
The composition of a liquid with suspended solid particles is generally characterized by the fraction of solid particles either by weight or mass, Cs, mass = ms/mm or by volume, Cs, vol = Vs/Vm where m is mass and V is volume. The subscripts s and m indicate solid and mixture, respectively. Develop
The specific gravities of solids and carrier fluids of a slurry are usually known, but the specific gravity of the slurry depends on the concentration of the solid particles. Show that the specific gravity of a water-based slurry can be expressed in terms of the specific gravity of the solid SGs
A 10-m3 tank contains nitrogen at 25°C and 800 kPa. Some nitrogen is allowed to escape until the pressure in the tank drops to 600 kPa. If the temperature at this point is 20°C, determine the amount of nitrogen that has escaped.
A closed tank is partially filled with water at 60°C. If the air above the water is completely evacuated, determine the absolute pressure in the evacuated space. Assume the temperature to remain constant.
Although liquids, in general, are hard to compress, the compressibility effect (variation in the density) may become unavoidable at the great depths in the oceans due to enormous pressure increase. At a certain depth the pressure is reported to be 100 MPa and the average coefficient of
A newly produced pipe with diameter of 2 m and length 15 m is to be tested at 10 MPa using water at 15°C. After sealing both ends, the pipe is first filled with water and then the pressure is increased by pumping additional water into the test pipe until the test pressure is reached. Assuming no
A shaft with a diameter of D = 80 mm and a length of L = 400 mm, shown in Fig. P2–127 is pulled with a constant velocity of U = 5 m/s through a bearing with variable diameter. The clearance between shaft and bearing, which varies from h1 = 1.2 mm to h2 = 0.4 mm, is filled with a Newtonian
Reconsider Prob. 2–127. The shaft now rotates with a constant angular speed of n =1450 rpm in a bearing with variable diameter. The clearance between shaft and bearing, which varies from h1 = 1.2 mm to h2 = 0.4 mm, is filled with a Newtonian lubricant whose dynamic viscosity is 0.1 Pa·s.
The specific gravity of a fluid is specified to be 0.82. The specific volume of this fluid is(a) 0.00100 m3/kg (b) 0.00122 m3/kg (c) 0.0082 m3/kg(d ) 82 m3/kg (e) 820 m3/kg
The specific gravity of mercury is 13.6. The specific weight of mercury is(a) 1.36 kN/m3 (b) 9.81 kN/m3 (c) 106 kN/m3 (d) 133 kN/m3(e) 13,600 kN/m3

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