- A torpedo-like device is being designed to travel just below the water surface. Which dimensionless numbers in Section 8.4 would be significant in this problem? Give a rationale for your answer.
- What is f for the flow of water at 10°C through a 30-cm cast iron pipe with a mean velocity of 24 m/s?
- Briefly explain each of the following ideas.a. Post processorb. Verificationc. Validation
- Briefly explain each of the following ideas.a. DNSb. k-epsilon methodc. LES
- Briefly explain each of the following ideas.a. Gridb. Time stepc. Solution time for a CFD program versus the accuracyd. Boundary conditione. Initial condition
- Using the Internet, find one example of a publicly available CFD program (either a commercial or noncommercial code) and describe the code so that others can understand it. Address the following
- Would you prefer to write your own CFD programs, or would you prefer to use codes that have been written by others? Discuss the advantages and disadvantages of each approach.
- If someone asked you why CFD codes are useful for engineers, how would you answer? List your top three reasons in priority order.
- Stress, as introduced in the derivation of the Navier-Stokes equation, is a second-order tensor. Using the Internet, find some articles on tensors and answer the following questions:a. Why do people
- For the propeller and conditions described in Problem 14.10, determine the thrust and the power input. Assume ρ = 1.2 kg/m3.Data from Problem 14.10A propeller 2 m in diameter, like the one for which
- A 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 cruising. If the cruising speed
- Water at 50°F is piped from a reservoir to a channel like that shown. The pipe from the reservoir to the channel is a 4 in. steel pipe 100 ft in total length. There are two 90° bends, r/D = 1, in
- Consider the rectangular weir described in Prob. 13.50. When the head is doubled, the discharge is (a) Doubled, (b) Less than doubled(c) More than doubled.Data from Prob. 13.50A 3 m long
- A 3 m long rectangular weir is to be constructed in a 3 m wide rectangular channel, as shown (a). The maximum flow in the channel will be 4 m3/s. What should be the height P of the weir to yield a
- A 1 ft high rectangular weir (weir 1) is installed in a 2 ft wide rectangular channel, and the head on the weir is observed for a discharge of 10 cfs. Then the 1 ft weir is replaced by a 2 ft high
- Water flows over two rectangular weirs. Weir A is 5 ft long in a channel 10 ft wide; weir B is 5 ft long in a channel 5 ft wide. Both weirs are 2 ft high. If the head on both weirs is 1.00 ft , then
- The head on a 60° triangular weir is 25 cm. What is the discharge over the weir in cubic meters per second?
- Water flows over a rectangular weir that is 3 m wide and 35 cm high. If the head on the weir is 15 cm, what is the discharge in cubic meters per second?
- On the Internet, locate technically reliable resources about weirs to answer the following questions. a. What are five important considerations for using weirs?b. What variables influence flow
- Ultrasonic flowmeters are used to measure velocity in systems where it is important to not disrupt the flow, such as for blood velocity. One mode of operation of ultrasonic flowmeters is to measure
- A rotameter is used to measure the flow rate of a gas with a density of 1.0 kg/m3. The scale on the rotameter indicates 5 liters/s. However, the rotameter is calibrated for a gas with a density of
- A rotameter operates by aerodynamic suspension of a weight in a tapered tube. The scale on the side of the rotameter is calibrated in scfm of air—that is, cubic feet per minute at standard
- A vortex flowmeter is used to measure the discharge in a duct 5 cm in diameter. The diameter of the shedding element is 1 cm. The Strouhal number based on the shedding frequency from one side of the
- What is the head loss in terms of V0 2/2g for the flow nozzle shown? Vo D 3
- Water flows through an annular venturi consisting of a body of revolution mounted inside a pipe. The pressure is measured at the minimum area and upstream of the body. The pipe is 5 cm in diameter,
- A flow nozzle has a throat diameter of 2 cm and a beta ratio (d/D) of 0.5. Water flows through the nozzle, creating a pressure difference across the nozzle of 8 kPa. The viscosity of the water is
- The differential-pressure gage on the venturi meter reads 40 kPa, d = 20 cm, D = 40 cm, and h = 75 cm. What is the discharge of gasoline (SG = 0.69; μ = 3 × 10−4 N∙s/m2) in the system? D - Ap h
- The differential-pressure gage on the venturi meter shown reads 5.4 psi, h = 25 in., d = 7 in., and D = 12 in. What is the discharge of water in the system? Assume T = 50°F.
- The pressure differential across this venturi meter is 92 kPa. What is the discharge of water (T = 20°C) through it? The value of flow coefficient you calculate should be K = 1.02. Ap d= 1.00 m D =
- When no flow occurs through the venturi meter, the indicator on the differential-pressure gage is straight up and indicates a Δp of zero. When 5 cfs of water flows to the right, the
- Estimate the rate of flow of water through the venturi meter shown. Air (y = 0.20 lbf/ft') 48 in 30° Diameter = 4 in Diameter = 12 in
- Water flows through a venturi meter that has a 40 cm throat. The venturi meter is in a 70 cm pipe. What deflection will occur on a mercury-water manometer connected between the upstream and throat
- What is the throat diameter required for a venturi meter in a 61 cm horizontal pipe carrying water with a discharge of 0.76 m3/s if the differential pressure between the throat and the upstream
- What is the main advantage of a venturi meter versus an orifice meter? The main disadvantage?
- An orifice is to be designed to have a change in pressure of 48 kPa across it (measured with a differential-pressure transducer) for a discharge of 4.0 m3/s of water in a pipe 1.2 m in diameter. What
- What is the discharge of gasoline (SG = 0.68) in a 20 cm horizontal pipe if the differential pressure across a 10 cm orifice in the pipe is 100 kPa?
- Determine the size of orifice required in a 15-cm pipe to measure 0.03 m3/s of water with a deflection of 1 m on a mercury-water manometer.
- Water (T = 50°F) is pumped at a rate of 20 cfs through the system shown in the figure. What differential pressure will occur across the orifice? What power must the pump supply to the flow for the
- A pressure transducer is connected across an orifice as shown. The pressure at the upstream pressure tap is p1, and the pressure at the downstream tap is p2. The pressure at the transducer connected
- If water (20°C) is flowing through this 4.3 cm orifice, estimate the rate of flow. Assume flow coefficient K = 0.6. -50 cm 60 kPa Vertical 30 cm 50 kPa
- A 15 cm plate orifice at the end of a 30 cm pipe is enlarged to 20 cm. With the same pressure drop across the orifice (approximately 50 kPa), what will be the percentage of increase in discharge?
- The 10 cm orifice in the horizontal 30 cm pipe shown is the same size as the orifice in the vertical pipe. The manometers are mercury-water manometers, and water (T = 20°C) is flowing in the system.
- A 6 in. orifice is placed in a 10 in. pipe, and a mercury manometer is connected to either side of the orifice. If the flow rate of water (60°F) through this orifice is 4.5 cfs, what will be the
- Determine the discharge of water (T = 60°F) through the orifice shown if h = 4 ft , D = 6 in., and d = 3 in. Water d D
- Determine the discharge of water through this 7 in. orifice that is installed in a 12 in. pipe. Assume T = 60°F and v = 1.22 × 10−5 ft 2/s. 12 in 2 ft 1.0 ft Mercury
- Figure 13.14 in §13.2 shows a sharp-edged orifice. Note that the metal surface immediately downstream of the leading edge makes an acute angle with the metal of the upstream face of the orifice. Do
- A fluid jet discharging from a 10.2 cm orifice has a diameter of 8 cm at its vena contracta. What is the coefficient of contraction?
- For the jet and orifice shown, determine Cv, Cc, and Cd. 2 m 1.90 m Vena contracta d = 8 cm d = 10.0 cm -
- Theory and experimental verification indicate that the mean velocity along a vertical line in a wide stream is closely approximated by the velocity at 0.6 depth. If the indicated velocities at 0.6
- A velocity traverse in a 24 cm oil pipe yields the data in the table. What are the discharge, mean velocity, and ratio of maximum to mean velocity? Does the flow appear to be laminar or turbulent? r
- Water from a test apparatus is diverted into a calibrated volumetric tank for 6 min. If the volume of diverted water is measured to be 67 m3, what is the discharge in cubic meters per second, gallons
- Water from a pipe is diverted into a tank for 5 min. If the weight of diverted water is measured to be 10 kN, what is the discharge in cubic meters per second? Assume the water temperature is 20°C.
- List five different instruments or approaches that engineers use to measure flow rate (discharge). For each instrument or approach, list two advantages and two disadvantages.
- Classify the following devices as to whether they are used to measure velocity (V), pressure (P), or discharge (Q).a. Hot-wire anemometerb. Venturi meterc. Differential manometerd. Orifice metere.
- A laser-Doppler anemometer (LDA) system is being used to measure the velocity of air in a tube. The laser is an argon-ion laser with a wavelength of 4880 angstroms. The angle between the laser beams
- On the Internet, locate technically sound resources relevant to the LDA. Skim these resources, and thena. Write down five findings that are relevant to engineering practice and interesting to you.b.
- A velocity-measuring probe used frequently for measuring smokestack gas velocities is shown. The probe consists of two tubes bent away from and toward the flow direction and cut off on a plane normal
- Without exceeding an error of 1%, what is the minimum water velocity that can be obtained using a 1.5 mm circular stagnation tube if the formulaV = √2Δpstag/ρ = √2ghstagis used for computing
- Without exceeding an error of 2.5%, what is the minimum air velocity that can be obtained using a 1 mm circular stagnation tube if the formula V = √2Δpstag/ρ = √2ghstag is used for
- An ultralight airplane has a wing with an aspect ratio of 5 and with lift and drag coefficients corresponding to Fig. 11.24. The planform area of the wing is 200 ft2. The weight of the airplane and
- The wing loading on an airplane is defined as the aircraft weight divided by the wing area. An airplane with a wing loading of 2000 N/m2 has the aerodynamic characteristics given by Fig. 11.25. Under
- An airplane wing having the characteristics shown in Fig. 11.24 is to be designed to lift 1800 lbf when the airplane is cruising at 200 ft /s with an angle of attack of 3°. If the chord length is to
- Apply the grid method to each situation that follows.a. Use Eq. (11.17) to predict the lift force in newtons for a spinning baseball. Use a coefficient of lift of CL = 1.2. The speed of the baseball
- Estimate the energy in joules and kcal (food calories) that a runner supplies to overcome aerodynamic drag during a 10 km race. The runner runs a 6:30 pace (i.e., each mile takes 6 minutes and 30
- Consider trends from Table 11.1 and Fig. 11.9 in order to classify these statements as true or false:In table a. A value of CD = 0.35 for a sports car would be a reasonable estimate.b. A value
- Consider a large rock situated at the bottom of a river and acted on by a strong current. Estimate a typical speed of the current that will cause the rock to move downstream along the bottom of the
- A circular billboard with a diameter of 4 m is exposed to the wind. Estimate the total force exerted on the structure by a wind that has a direction normal to the structure and a speed of 20 m/s.
- As shown, wind is blowing on a 55-gallon drum. Estimate the wind speed needed to tip the drum over. Work in SI units. The mass of the drum is 48 lbm, the diameter is 22.5 in., and the height is 34.5
- Estimate the drag of a thin square plate (3 m by 4 m) when it is towed through water (10°C). Assume a towing speed of about 5 m/s. Use Table 11.1 in §11.3. In Table 11.1a. The plate is
- Apply the grid method to each situation that follows.a. Use Eq. (11.5) to predict the drag force in newtons for an automobile that is traveling at V = 60 mph on a summer day. Assume that the frontal
- Determine whether the following statements are true or false. a. Regarding CD, the primary dimensions are: M∙L/T2b. In the context of calculating the drag force for a sphere, the formula for
- Determine whether the following statement is true or false: In general, the lift force is upward, and the drag force is horizontal with respect to gravity.
- Determine whether the following statement is true or false: In general, the drag force and the lift force are perpendicular. FDrag Lift
- Fill in the blanks for the following two statements:A. ___________ is associated with the viscous shear stress distribution.a. Form dragb. Friction dragB. ____________ is associated with the pressure
- Flow is occurring past the square rod. The pressure coefficient values are as shown. From which direction do you think the flow is coming? (a) SW direction, (b) SE direction, (c) NW
- A hypothetical pressure coefficient variation over a long (length normal to the page) plate is shown. What is the coefficient of drag for the plate in this orientation and with the given pressure
- Frequently in the design of pump systems, a bypass line will be installed in parallel to the pump so that some of the fluid can recirculate as shown. The bypass valve then controls the flow rate in
- The pipes shown in the system are all concrete. With a flow of 25 cfs of water, find the head loss and the division of flow in the pipes from A to B. Assume f = 0.030 for all pipes. L= 3000 ft D = 14
- Two pipes are connected in parallel. One pipe is twice the diameter of the other and four times as long. Assume that f in the larger pipe is 0.010 and f in the smaller one is 0.012. Determine the
- Pipes 1 and 2 are the same kind (cast-iron pipe), but pipe 2 is three times as long as pipe 1. They are the same diameter (1 ft). If the discharge of water in pipe 2 is 1.5 cfs, then what will be the
- In the parallel system shown, pipe 1 is 1200 m long and is 50 cm in diameter. Pipe 2 is 1500 m long and 35 cm in diameter. Assume f is the same in both pipes. What is the division of the flow of
- A flow is divided into two branches as shown. A gate valve, half open, is installed in line A, and a globe valve, fully open, is installed in line B. The head loss due to friction in each branch is
- A pipe system consists of a gate valve, wide-open (Kv = 0.2), in line A and a globe valve, wide-open (Kv = 10), in line B. The cross-sectional area of pipe A is half of the cross-sectional area of
- A pump that has the characteristic curve shown in the accompanying graph is to be installed as shown. What will be the discharge of water in the system? Elevation = 20 ft L = 50 ft D = 10 in. f =
- If the pump for Fig. 10.20b is installed in the system of Prob. 10.90, what will be the rate of discharge of water from the lower tank to the upper one?Data from Prob. 10.90,What power must be
- What power must be supplied by the pump to the flow if water (T = 20°C) is pumped through the 300-mm steel pipe from the lower tank to the upper one at a rate of 0.75 m3/s? Elevation = 235 m 10 m 50
- Air (20°C) flows with a speed of 10 m/s through a horizontal rectangular air-conditioning duct. The duct is 20 m long and has a cross section of 4 by 10 in. (102 by 254 mm). Calculate (a) The
- A cold-air duct 120 cm by 15 cm in cross section is 100 m long and made of galvanized iron. This duct is to carry air at a rate of 6 m3/s at a temperature of 15°C and atmospheric pressure. What is
- The cross section of an air duct has the dimensions shown in the sketch. Find the hydraulic diameter in units of cm. Choose the closest answer (cm): (a) 0.9, (b) 3.0, (c) 3.2, (d)
- Air at 60°F and atmospheric pressure flows in a horizontal duct with a cross section corresponding to an equilateral triangle (all sides equal). The duct is 100 ft long, and the dimension of a side
- If the water surface elevation in reservoir B is 110 m, what must be the water surface elevation in reservoir A if a flow of 0.03 m3/s is to occur in the cast iron pipe? Draw the HGL and the EGL,
- The steel pipe shown carries water from the main pipe A to he reservoir and is 2 in. in diameter and 300 ft long. What must be the pressure in pipe A to provide a flow of 70 gpm? Elevation = 90
- Liquid discharges from a tank through the piping system shown. There is a venturi section at A and a sudden contraction at B. The liquid discharges to the atmosphere. Sketch the energy and hydraulic
- Both pipes in the system shown have an equivalent sand roughness ks of 0.10 mm and a flow rate of 0.1 m3/s, with D1 = 12 cm, L1 = 60 m, D2 = 24 cm, and L2 = 120 m. Determine the difference in the
- Water is pumped at a rate of 32 m3/s from the reservoir and out through the pipe, which has a diameter of 1.50 m. What power must be supplied to the water to effect this discharge? Elevation = 140 m
- The 12 cm galvanized steel pipe shown is 800 m long and discharges water into the atmosphere. The pipeline has an open globe valve and four threaded elbows; h1 = 3 m and h2 = 15 m. What is the
- Find the loss coefficient Kv of the partially closed valve that is required to reduce the discharge to 50% of the flow with the valve wide-open as shown. Threaded elbows 10 cm diameter steel pipe
- Gasoline (T = 50°F) is pumped from the gas tank of an automobile to the carburetor through a 1/4-in. fuel line of drawn tubing 10 ft long. The line has five 90° smooth bends with an r/d of 6. The
- A heat exchanger consists of 15 m of copper tubing with an internal diameter of 15 mm. There are 14 return elbows in the system with a loss coefficient of 2.2 for each elbow. The pump in the system
- A heat exchanger consists of a closed system with a series of parallel tubes connected by 180° elbows as shown in the figure. There are a total of 14 return elbows. The pipe diameter is 2 cm, and