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engineering
engineering fluid mechanics
Engineering Fluid Mechanics 11th Edition Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Robertson - Solutions
A cylindrical block of wood 1 m in diameter and 1 m long has a specific weight of 5000 N/m3. Will it float in water with the ends horizontal?
Is the block in this figure stable floating in the position shown? Show your calculations. L= 3H - W= 2H- H H Water
If somehow you could attach a light to a fluid particle and take a time exposure photo, would the image you photographed be a path line or a streak line? Explain based on the definition of each.
Is the pattern produced by smoke rising from a chimney on a windy day analogous to a path line or a streak line? Explain based on the definition of each.
A windsock is a sock-shaped device attached to a swivel on top of a pole. Windsocks at airports are used by pilots to see instantaneous shift s in the direction of the wind. If one drew a line colinear with a windsock’s orientation at any instant, the line would best approximate (a) A path
For streamlines, streak lines, and streamlines to all be colinear, the flow must bea. Dividingb. Stagnantc. Steadyd. A tracer
At time t = 0, dye was injected at point A in a flow field of a liquid. When the dye had been injected for 4 s, a path line for a particle of dye that was emitted at the 4 s instant was started. The streak line at the end of 10 s is shown ahead. Assume that the speed (but not the velocity) of flow
At time t = 0, a dye streak was started at point A in a flow field of liquid. The speed of the flow is constant over a 10s period, but the flow direction is not necessarily constant. At any particular instant, the velocity in the entire field of flow is the same. The streak line produced by the dye
A velocity field is given mathematically as V = (2x + 3y)j. The velocity field isa. 1-D in xb. 1-D in yc. 2-D in x and y
There is a gasoline spill in a major river. The mayor of a large downstream city demands an estimate of how many hours it will take for the spill to get to the water supply plant intake. The emergency responders measure the speed of the leading edge of the spill, effectively focusing on one
Identify five examples of an unsteady flow and explain what features classify them as an unsteady flow.
You are pouring a heavy syrup on your pancakes. As the syrup spreads over the pancakes, would the thin film of syrup be a laminar or turbulent flow? Why?
A velocity field is given by V = 10xyti. It isa. 1-D and steadyb. 1-D and unsteadyc. 2-D and steadyd. 2-D and unsteady
Which is the most correct way to characterize turbulent flow?a. 1-Db. 2-Dc. 3-D
In the system in the figure, the valve at C is gradually opened in such a way that a constant rate of increase in discharge is produced. How would you classify the flow at B while the valve is being opened? How would you classify the flow at A? A B
Water flows in the passage shown. If the flow rate is decreasing with time, the flow is classified as (a) Steady, (b) Unsteady,(c) Uniform, or (d) Nonuniform. (Select all that apply.)
If a flow pattern has converging streamlines, how would you classify the flow?
Correctly match the items in column A with those in column B. A B Steady flow Unsteady flow aVlds = 0 aVlds + 0 Uniform flow av,ldt + 0 Nonuniform flow av,ldt = 0
Classify each of the following as a one-dimensional, two–dimensional, or three-dimensional flow.a. Water flow over the crest of a long spillway of a dam.b. Flow in a straight horizontal pipe.c. Flow in a constant-diameter pipeline that follows the contour of the ground in hilly country.d. Airflow
Acceleration is the rate of change of velocity with time. Is the acceleration vector always aligned with the velocity vector? Explain.
For a rotating body, is the acceleration toward the center of rotation a centripetal or centrifugal acceleration? Justify your answer. You may also want to look up word meanings and word roots.
In a flowing fluid, acceleration means that a fluid article isa. Changing directionb. Changing speedc. Changing both speed and directiond. Any of the above
The flow passing through a nozzle is steady. The speed of the fluid increases between the entrance and the exit of the nozzle. The acceleration halfway between the entrance and the nozzle isa. Convectiveb. Localc. Both
Local accelerationa. Is close to the originb. Occurs in unsteady flowc. Is always nonuniform
The velocity along a path-line is given by V (m/s) = s2t1/2 where s is in meters and t is in seconds. The radius of curvature is 0.5 m. Evaluate the acceleration tangent and normal to the path at s = 3 m and t = 0.5 seconds.
Tests on a sphere are conducted in a wind tunnel at an air speed of U0. The velocity of flow toward the sphere along the longitudinal axis is found to be u = –U0 (1 – r30/x3), where r0 is the radius of the sphere and x the distance from its center. Determine the acceleration of an air particle
At one end of a rectangular tank 1 m wide is a sharp-crested rectangular weir 1 m high. In the bottom of the tank is a 10 cm sharp-edged orifice. If 0.10 m3/s of water flows into the tank and leaves the tank both through the orifice and over the weir, what depth will the water in the tank attain?
What is the water discharge over a rectangular weir 4 ft high and 18 ft long in a rectangular channel 18 ft wide if the head on the weir is 2.2 ft?
A reservoir is supplied with water at 60°F by a pipe with a venturi meter as shown. The water leaves the reservoir through a triangular weir with an included angle of 60°. The flow coefficient of the venturi is unity, the area of the venturi throat is 12 in.2, and the measured Δp is 10 psi. Find
At a particular instant water flows into the tank shown through pipes A and B, and it flows out of the tank over the rectangular weir at C. The tank width and weir length (dimensions normal to page) are 2 ft. Then, for the given conditions, is the water level in the tank rising or falling? 1 ft
Water flows from the first reservoir to the second over a rectangular weir with a width-to-head ratio of 3. The height P of the weir is twice the head. The water from the second reservoir flows over a 60° triangular weir to a third reservoir. Th e discharge across both weirs is the same. Find the
The head on a 60° triangular weir is 1.8 ft . What is the discharge of water over the weir?
An engineer is designing a triangular weir for measuring the flow rate of a stream of water that has a discharge of 6 cfm. The weir has an included angle of 45° and a coefficient of discharge of 0.6. Find the head on the weir.
A pump is used to deliver water at 10°C from a well to a tank. The bottom of the tank is 2 m above the water surface in the well. The pipe is commercial steel 2.5 m long with a diameter of 5 cm. The pump develops a head of 20 m. A triangular weir with an included angle of 60° is located in a wall
Explain why the thrust of a fixed-pitch propeller decreases with increasing forward speed.
What limits the rotational speed of a propeller?
What thrust is obtained from a propeller 3 m in diameter that has the characteristics given in Fig. 14.3 when the propeller is operated at an angular speed of 1100 rpm and an advance velocity of zero? Assume ρ = 1.05 kg/m3. 0.06 60 0.05 50 0.04 40 0.03 Ст 0.02 20 Cp 0.01 10 0.1 0.2 0.3 0.4 0.5
What thrust is obtained from a propeller 3 m in diameter that has the characteristics given in Fig. 14.3 when the propeller is operated at an angular speed of 1400 rpm and an advance velocity of 80 km/h? What power is required to operate the propeller under these conditions? Assume ρ = 1.05 kg/m3.
A propeller 8 ft in diameter has the characteristics shown in Fig. 14.3. What thrust is produced by the propeller when it is operating at an angular speed of 1200 rpm and a forward speed of 30 mph? What power input is required under these operating conditions? If the forward speed is reduced
For the propeller and conditions described in Problem 14.6, determine the thrust and the power input.Data from Problem 14.6A propeller 8 ft in diameter, like the one for which characteristics are given in Fig. 14.3, is to be used on a swamp boat and is to operate at maximum efficiency when
A propeller is being selected for an airplane that will cruise at 2000 m altitude, where the pressure is 60 kPa absolute and the temperature is 10°C. The mass of the airplane is 1200 kg, and the planform area of the wing is 10 m2. Th e lift -to-drag ratio is 30:1. The lift coefficient is 0.4. The
If the tip speed of a propeller is to be kept below 0.8c, where c is the speed of sound, what is the maximum allowable angular speed of propellers having diameters of 2 m, 3 m, and 4 m? Take the speed of sound as 335 m/s.
A propeller 2 m in diameter, like the one for which characteristics are given in Fig. 14.3, is to be used on a swamp boat and is to operate at maximum efficiency when cruising. If the cruising speed is to be 40 km/h, what should the angular speed of the propeller be? 0.06 60 0.05 50 0.04 40 0.03
A propeller 2 m in diameter and like the one for which characteristics are given in Fig. 14.3 is used on a swamp boat. If the angular speed is 1000 rpm and if the boat and passengers have a combined mass of 300 kg, estimate the initial acceleration of the boat when starting from rest. Assume ρ =
Answer the following questions about axial-flow pumps. a. Axial-flow pumps are best suited for what conditions of head produced and discharge?b. For an axial-flow pump, how does the head produced by the pump and the power required to operate a pump vary with flow rate through the pump?
If a pump having the characteristics shown in Fig. 14.7 has a diameter of 40 cm and is operated at a speed of 1000 rpm, what will be the discharge when the head is 3 m? 5.00 100 4.00 80 3.00 2.00 40 CH 1.00 CP 20 p.2 0.6 0.8 0.4 Co Cp and CH Efficiency, percent
The pump used in the system shown has the characteristics given in Fig. 14.8. What discharge will occur under the conditions shown, and what power is required? 100 10 80 Power Efficiency 60 40 Нead 20 N = 690 rpm n= 11.5 rps D = 35.6 cm 0.05 0.10 0.15 0.20 0.25 0.30 Discharge, m'/s Head, m; power,
If the conditions are the same as in Problem 14.15 except that the speed is increased to 900 rpm, what discharge will occur, and what power is required for the operation?Data from Problem 14.15The pump used in the system shown has the characteristics given in Fig. 14.8. What discharge will occur
For a pump with the characteristics given in Fig. 14.7 or 14.8, what water discharge and head will be produced at maximum efficiency if the pump diameter is 20 in. and the angular speed is 1100 rpm? What power is required under these conditions?In Fig 14.8Fig 14.7 100 10 80 Power Efficiency 60 40
A pump has the characteristics given by Fig. 14.7. What discharge and head will be produced at maximum efficiency if the pump size is 50 cm and the angular speed is 45 rps? What power is required when pumping water at 10°C under these conditions? 100 5.000 80 4.00 3.00 40 2.00 CH 1.00 CP 20 p.2
For a pump with the characteristics of Fig. 14.7, plot the head-discharge curve if the pump is 14 in. in diameter and is operated at a speed of 1000 rpm. 100 5.00 80 4.00 3.00 40 2.00 CH CP 20 1.00 p.2 0.4 0.6 0.8 Co Cp and CH Efficiency, percent
For a pump having the characteristics of Fig. 14.7, plot the head-discharge curve if the pump diameter is 60 cm and the speed is 690 rpm. 100 5.00 80 4.00 3.00 40 2.00 CH CP 20 1.00 p.2 0.4 0.6 0.8 Co Cp and CH Efficiency, percent
An axial-flow blower is used for a wind tunnel that has a test section measuring 60 cm by 60 cm and is capable of airspeeds up to 40 m/s. If the blower is to operate at maximum efficiency at the highest speed and if the rotational speed of the blower is 2000 rpm at this condition, what are the
An axial-flow blower is used to air-condition an office building that has a volume of 105 m3. It is decided that the air at 60°F in the building must be completely changed every 15 min. Assume that the blower operates at 600 rpm at maximum efficiency and has the characteristics shown in Fig. 14.7.
An axial fan 2 m in diameter is used in a wind tunnel as shown (test section 1.2 m in diameter; test section velocity of 60 m/s). The rotational speed of the fan is 1800 rpm. Assume the density of the air is constant at 1.2 kg/m3. There are negligible losses in the tunnel. The performance curve of
The radial flow pump is best suited for what conditions of head produced and discharge?
A pump is used to pump water out of a reservoir. What limits the depth for which the pump can draw water?
If a pump with the characteristics given in Fig. 14.10 is doubled in size but halved in speed, what will be the head and discharge at maximum efficiency? 250 100 Efficiency 200 80 Power input, kW 150 Head (ΔΗ, m. 100 40 50 20 N = 2133.5 rpm n = 35.6 rps D = 37.1 cm 0.05 0.10 0.15 0.20 0.25
A pump having the characteristics given in Fig. 14.10 pumps water at 20°C from a reservoir at an elevation of 366 m to a reservoir at an elevation of 450 m through a 36 cm steel pipe. If the pipe is 610 m long, what will be the discharge through the pipe? 250 100 Efficiency 200 80 Power input, kW
If a pump with the characteristics given in Fig. 14.10 or 14.11 is operated at a speed of 1600 rpm, what will be the discharge when the head is 135 ft ? 250 100 Efficiency 200 80 Power input, kW 150 Head (ΔΗ, m. 100 40 50 20 N = 2133.5 rpm n = 35.6 rps D = 37.1 cm 0.05 0.10 0.15 0.20 0.25
If a pump with the performance curve shown is operated at a speed of 1600 rpm, what will be the maximum possible head developed? 140 120 100 N = 1000 rpm 80 60 40 20 500 1000 1500 2000 2500 Q. gpm AH, ft
If a pump with the characteristics given in Fig. 14.10 is operated at a speed of 30 rps, what will be the shutoff head? 250 100 Efficiency 200 80 Power input, kW 150 Head (ΔΗ , m. 100 40 50 20 N = 2133.5 rpm n = 35.6 rps D = 37.1 cm 0.05 0.10 0.15 0.20 0.25 Discharge, m/s Head, m; power, kW
If a pump with the characteristics given in Fig. 14.11 is 40 cm in diameter and is operated at a speed of 25 rps, what will be the discharge when the head is 50 m? CH 1.00 5 4 Efficiency, n 0.75 CH 3 0.50 0.25 0.12 0.16 0.04 0.08 Co 2. Cp and efficien cy
A centrifugal pump 20 cm in diameter is used to pump kerosene at a speed of 5000 rpm. Assume that the pump has the characteristics shown in Fig. 14.11. Calculate the flow rate, the pressure rise across the pump, and the power required if the pump operates at maximum efficiency. Сн 1.00 5 4
Answer the following questions regarding pump sizing and selection.a. What is the difference between a system curve and a pump curve? Explain.b. The operating point for a pump system is established by what condition?
The value of the specific speed suggests the type of pump to be used for a given application. A high specific speed suggests the use of what kind of pump?
The pump curve for a given pump is represented bywhere hp,pump is the head provided by the pump in feet and Q is the discharge in gpm. The system curve for a pumping application is hp, sys = 5 + 0.002Q2 where hp,sys is the head in feet required to operate the system and Q is the discharge in
What is the suction specific speed for the pump that is operating under the conditions given in Problem 14.15? Is this a safe operation with respect to susceptibility to cavitation?Data from Problem 14.15The pump used in the system shown has the characteristics given in Fig. 14.8. What discharge
What type of pump should be used to pump water at a rate of 10 cfs and under a head of 30 ft ? Assume N = 1500 rpm.
For the most efficient operation, what type of pump should be used to pump water at a rate of 0.10 m3/s and under a head of 30 m? Assume n = 25 rps.
What type of pump should be used to pump water at a rate of 0.40 m3/s and under a head of 70 m? Assume N = 1100 rpm.
An axial-flow pump is to be used to lift water against a head (friction and static) of 15 ft . If the discharge is to be 4000 gpm, what maximum speed in revolutions per minute is allowed if the suction head is 5 ft ?
A pump is needed to pump water at a rate of 0.2 m3/s from the lower to the upper reservoir shown in the figure. What type of pump would be best for this operation if the impeller speed is to be 600 rpm? Assume f = 0.02 and Ke = 0.5. Elevation = 18 m Elevation = 15 m 20 m Pump 100 cm
Plot the five performance curves in Fig. 14.15 for the different impeller diameters in terms of the head and discharge coefficients. Use the impeller diameter for D. Capacity in liters per second 12 G0% 40% Sos 65% 55% 67% 68% 16 1750 50 pm 69.9% 69% 6 1/2 40 67% 65% 6 10 5 1/2 30 30 3 hp (2.24 kw)
When a gas is compressed adiabatically, there is a pressure rise and a temperature rise. The ratio of final temperature to initial temperature is less than the ratio of final pressure to initial pressure. Will the final density be (a) Less or (b) Greater than the initial density?
Methane flowing at the rate of 1 kg/s is to be compressed by a noncooled centrifugal compressor from 100 kPa to 165 kPa. The temperature of the methane entering the compressor is 27°C. The efficiency of the compressor is 70%. Calculate the shaft power necessary to run the compressor.
A 36 kW (shaft output) motor is available to run a noncooled compressor for carbon dioxide. The pressure is to be increased from 100 kPa to 150 kPa. If the compressor is 60% efficient, calculate the volume flow rate into the compressor.
A water-cooled centrifugal compressor is used to compress air from 100 kPa to 600 kPa at the rate of 2 kg/s. The temperature of the inlet air is 15°C. Th e efficiency of the compressor is 50%. Calculate the necessary shaft power.
An impulse turbine will produce no power if the velocity of the jet striking the bucket is the same as the bucket velocity. Explain.
A penstock 1 m in diameter and 10 km long carries water at 10°C from a reservoir to an impulse turbine. If the turbine is 85% efficient, what power can be produced by the system if the upstream reservoir elevation is 650 m above the turbine jet and the jet diameter is 16.0 cm? Assume that f =
Consider an idealized bucket on an impulse turbine that turns the water through 180°. Prove that the bucket speed should be one-half the incoming jet speed for a maximum power production. Set up the momentum equation to solve for the force on the bucket in terms of Vj and Vbucket; then the power
Consider a single jet of water striking the buckets of the impulse wheel as shown. Assume ideal conditions for power generation [Vbucket = (1/2)Vj and the jet is turned through 180° of arc]. With the foregoing conditions, solve for the jet force on the bucket and then solve for the power
Answer the following questions about reaction turbines.a. How does a reaction turbine differ from a centrifugal pump?b. What is meant by the “runner” in a reaction turbine?
For a given Francis turbine, β1 = 60°, β2 = 90°, r1 = 5 m, r2 = 3 m, and B = 1 m. Th e discharge is 126 m3/s, and the rotational speed is 60 rpm. Assume T = 10°C.a. What should α1 be for a non separating flow condition at the entrance to the runner?b. What is the maximum attainable power with
To produce a discharge of 3.3 m3/s, a Francis turbine will be operated at a speed of 60 rpm, r1 = 1.5 m, r2 = 1.20 m, B = 33 cm, β1 = 85°, and β2 = 165°. What should (a) α1 be for non-separating flow to occur through the runner? What(b) Power (c) Torque should result with this
A Francis turbine is to be operated at a speed of 120 rpm and with a discharge of 200 m3/s. If r1 = 3 m, B = 0.90 m, and β1 = 45°, what should α1 be for non-separating flow at the runner inlet?
Shown is a preliminary layout for a proposed small hydroelectric project. The initial design calls for a discharge of 8 cfs through the penstock and turbine. Assume 80% turbine efficiency. For this setup, what power output could be expected from the power plant? Draw the HGL and EGL for the system.
What determines the minimum and maximum wind speeds at which a wind turbine can operate?
Using the Internet and other resources, identify at least four types of wind turbines. For each type, describe its distinguishing characteristics and its relative advantages and disadvantages.
Calculate the minimum capture area necessary for a wind turbine that will be required to power the 2 kW demands of an energy-efficient home. Assume a wind velocity of 10 mph and an air density of 1.2 kg/m3.
Calculate the maximum power derivable from a conventional horizontal-axis wind turbine with a propeller 2.3 m in diameter in a 47 km/h wind with density 1.2 kg/m3.
A wind farm consists of 20 Darrieusturbine, each 15 m high. The total output from the turbines is to be 2 MW in a wind of 20 m/s and an air density of 1.2 kg/m3. The Darrieusturbine shown has the shape of an arc of a circle. Find the minimum width, W, of the turbine needed to provide this power
A windmill is connected directly to a mechanical pump that is to pump water from a well 10 ft deep as shown. The windmill is a conventional horizontal-axis type with a fan diameter of 10 ft. The efficiency of the mechanical pump is 80%. The density of the air is 0.07 lbm/ft 3. Assume the windmill
Why is the Reynolds number for onset of turbulence given by Re > 2000 in fully flowing pipes and Re > 500 in partly flowing pipes and other open channels?
A rectangular open channel has a base of length 2b, and the water is flowing with a depth of b.a. Sketch this channel.b. What is the hydraulic radius of this channel?
Two channels have the same cross-sectional area, but different geometry, as shown.a. Which channel has the largest wetted perimeter?b. Which channel has more contact between water and channel wall?c. Which channel will have more energy loss to friction?
Consider uniform flow of water in the two channels shown. They both have the same slope, the same wall roughness, and the same cross-sectional area. Therefore, is (a) QA = QB, (b) QA < QB, or (c) QA > QB? 5 ft 7.07 ft 10 ft 7.07 ft A B
This wood flume has a slope of 0.0019. What will be the discharge of water in it for a depth of 1 m? The wood is planed. 1 m 45° 45°
A mountain stream flows over a rocky streambed. Apply the Limerinos and Chezy equations to calculate the discharge. The stream has an intermediate rock size d 84 of 30 cm, an average depth of 2.1 m, a slope of S = 0.0037, and a width of 52 m. Choose the closest answer (m3/s): (a) 85, (b)
Water is flowing in a rectangular concrete channel. Apply the Manning equation to calculate the discharge. The channel is unfinished concrete 8 ft wide and drops 3 ft over a run of 1000 ft; the depth of flow is 2.5 ft ; T = 60°F; and the flow is uniform. Choose the closest answer (cfs): (a)
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