Questions and Answers of Fundamentals Momentum Heat

Freon-12 is flowing at 10 ft/sec through a pipe made of galvanized iron at 100°F. If the pipe is 100 ft long and 4 in. in diameter, what is the head loss in this system?
Your boss comes to you with an important project where you are to determine the pressure drop in a rough horizontal high-pressure pipe made of cast iron. The pipe has a diameter of 0.25 ft and a
You have been hired to consult on a pilot plant project that requires the installation of a rough horizontal pipe made from commercial steel into a flow system. The pipe has a diameter of 4 in. and a
A system consists of three pipes in parallel with a total head loss of 24 m. Data for the three pipes are as follows: For water at 20°C, neglect minor losses and determine the volumetric
A 0.2-m-diameter cast-iron pipe and a 67-mm diameter commercial steel pipe are parallel, and both run from the same pump to a reservoir. The pressure drop is 210 kPa and the lines are 150 m long.
Two concrete pipes are connected in series. The flow rate of water at 20°C through the pipes is 0.18 m3/s, with a total head loss of 18 m for both pipes. Each pipe has a length of 312.5 m and a
A system consists of three pipes in series. The total pressure drop is 180 kPa, and the decrease in elevation is 5 m. Data for the three pipes are as follows:Determine the total flow rate of
Water flows at a volumetric flow rate of 0.25 m3/s from reservoir 1 to reservoir 2 through three concrete pipes connected in series. Pipe 1 is 900 m long and has a diameter of 0.16 m. Pipe 2 has a
Determine the depth of water behind the dam in the figure that will provide a flow rate of 5.675 Ã— 10-4m3/s through a 20-m-long, 1.30 cm commercial steel pipe. 1.30 cm -L-
A level 10-m-long water pipe has a manometer at both the inlet and the outlet. The manometers indicate pressure head of 1.5 and 0.2 m, respectively. The pipe diameter is 0.2 m and the pipe roughness
A 15-cm diameter wrought-iron pipe is to carry water at 20°C. Assuming a level pipe, determine the volumetric flow rate at the discharge if the pressure loss is not permitted to exceed 30.0 kPa per
Water at 20°C is being drained from an open tank through a cast-iron pipe 0.6 m diameter and 30 m long. The surface of the water in the pipe is at atmospheric pressure and at an elevation of 46.9 m,
A 2.20-m diameter pipe carries water at 15°C. The head loss due to friction is 0.500 m per 300 m of pipe. Determine the volumetric flow rate of the water leaving the pipe.
Water at 20°C flows through a cast-iron pipe at a velocity of 34 m/s. The pipe is 400 m long and has a diameter of 0.18 m. Determine the head loss due to friction.
Determine the flow rate through a 0.2-m gate valve with upstream pressure of 236 kPa when the valve isa. Openb. 1/4 closedc. 1/2 closedd. 3/4 closed
An 8-km-long, 5-m-diameter head race tunnel at the Paute river hydroelectric project in Ecuador supplies a power station 668 m below the entrance of the tunnel. If the tunnel surface is concrete,
Two water reservoirs of height h1= 60 m and h2= 30 m are connected by a pipe that is 0.35 m in diameter. The exit of the pipe is submerged at distance h3= 8 m from the reservoir surface.a. Determine
Estimate the flow rate of water through 50 ft of garden hose from a 40-psig source fora. A 1/2-in.-ID hoseb. A 3/4-in.-ID hose
A cast-iron pipeline 2 m long is required to carry 3 million gal of water per day. The outlet is 175 ft higher than the inlet. The costs of three sizes of pipe when in place are as follows:10-in.
A galvanized rectangular duct 8 in. square is 25 ft long and carries 600 ft3/min of standard air. Determine the pressure drop in inches of water.
The siphon of Problem 6.31 is made of smooth rubber hose and is 23 ft long. Determine the flow rate and the pressure at point B.
The pipe in Problem 6.33 is 35 m long and made of commercial steel. Determine the flow rate.Data from 6.33Assume that the level of water in the tank remains the same and that there is no friction
Calculate the inlet pressure to a pump 3 ft above the level of a sump. The pipe is 6 in. in diameter, 6 ft long, and made of commercial steel. The flow rate through the pump is 500 gal/min. Use the
Water at the rate of 118 ft3/min flows through a smooth horizontal tube 250 ft long. The pressure drop is 4.55 psi. Determine the tube diameter.
The cold-water faucet in a house is fed from a water main through the following simplified piping system:a. A 160 ft length of 3/4-in.-ID copper pipe leading from the main line to the base of the
Oil having a kinematic viscosity of 6.7 × 10-6 m2/s and density of 801 kg/m3 is pumped through a pipe of 0.71 m diameter at an average velocity of 1.1 m/s. The roughness of the pipe is equivalent to
In the previous problem, a 10-km-long section of the pipeline is replaced during a repair process with a pipe with internal diameter of 0.42 m. Determine the total pumping power required when using
A 280-km-long pipeline connects two pumping stations. If 0.56 m3/s are to be pumped through a 0.62-m-diameter line, the discharge station is 250 m lower in elevation than the upstream station, and
The pressure drop in a section of a pipe is determined from tests with water. A pressure drop of 13 psi is obtained at a flow rate of 28.3 lbm/s. If the flow is fully turbulent, what will be the
A lubricating line has an inside diameter of 0.1 in. and is 30 in. long. If the pressure drop is 15 psi, determine the flow rate of the oil. Use the properties given in Problem 13.1.Data From Problem
An oil with kinematic viscosity of 0.08 × 10-3 ft2/s and a density of 57 lbm/ft3 flows through a horizontal tube 0.24 in. in diameter at the rate of 10 gal/h. Determine the pressure drop in 50 ft of
In the case of carbon monoxide at 100°F flowing along a plane surface at a velocity of 4 ft/s, will the boundary layer flow at a position 0.5 ft from the leading edge be laminar, or turbulent? What
Water at 20°C is flowing along a 5-m-bng flat plate with a velocity of 50 m/s. What will be the boundary layer thickness at a position 5 m from the leading edge? Is the boundary layer flow at
Air, water, and glycerin, each at 80°F, are flowing through separate 0.5-in. diameter tubes at a velocity of 40 ft/s. Determine, for each case, whether the follow is laminar or turbulent.
Using the Blasius shear-stress relation (12??68) and the power-law velocity profile, determine the boundary-layer thickness on a flat plate as a function of the Reynolds number and the exponent n.
Evaluate the velocity derivative, ∂v̅x/∂y, for the power law velocity profile at y = 0 and y = R.
The turbulent shear stress in a two-dimensional flow is given by Expanding v'x and v'y in a Taylor series in x and y near the wall and with the aid of the continuity equation show that,
Use the one-seventh power-law profile and compute the drag force and boundary layer thickness on a plate 20 ft long and 10 ft wide (for one side) if it is immersed in a flow of water of 20 ft/s
Compare the boundary-layer thicknesses and local skin friction coefficients of a laminar boundary layer and a turbulent boundary layer on a smooth flat plate at a Reynolds number of 106. Assume both
Estimate the friction drag on a wing by considering the following idealization. Consider the wing to be a rectangular flat plate, 7 ft by 40 ft, with a smooth surface. The wing is flying at 140 mph
Using a sine profile the laminar flow and a one-seventh power law for turbulent flow, make a dimensionless plot of the momentum and kinetic energy profiles in the boundary layer a Reynolds number of
For a thin a plate 6 in. wide and 3 ft long, estimate the friction force in air at a velocity of 40 fps, assuminga. Turbulent flowb. Laminar flowThe flow is parallel to the 6-in. dimension
Using Blasius€™ correlation for shear stress (equation (12-68)), develop an expression for the local skin-friction coefficient in pipes. In pipes, the average velocity is used for the
For the fully developed flow of water in a smooth 0.15-m pipe at a rate of 0.006 m3/s, determine the thickness ofa. The laminar sub layerb. The buffer layerc. The turbulent core
Plot the boundary-layer thickness along a flat plate for the flow of air at 30 m/s assuminga. Laminar flowb. Turbulent flowIndicate the probable transition point.
In a house, water flows through a copper tube with a 0.75-in. ID, at a flow rate of 2 gpm. Determine the Reynolds number fora. Hot water (T ≅ 120°F)b. Cold water (T ≅ 45°F)
If the turbulence intensity is 10%, what fraction of the total kinetic energy of the flow is due to the turbulence?
If the vertical velocity at the wall is not zero such as would be the case with suction or blowing, what modifications occur to equation (12-33)? dP ,2 ly=0 y=0 dx
The lift coefficient on a rotating sphere is very approximately given by over the range of Here R is the sphere radius and W is rotation rate of the sphere. For the baseball in Problem
Golfball €œdimples€ cause the drag drop (see Figure 12.4 and the illustration for Problem 12.7) to occur at a lower Reynolds number. The table below gives the drag coefficient
A baseball has a circumference of 9¼ in. and a weight of 5¼ ounces. At 95 mph determinea. The Reynolds numberb. The drag forcec. The type of flow (see the illustration for Problem
A 1998 Lexus LS400 has a drag coefficient of 0.28 and a reference area of 2.4 m2. Determine the horsepower required to overcome drag when driving at 70 mph at sea level.a. On a hot summer
Estimate the normal force on a circular sign 8 ft in diameter during a hurricane wind (120 mph).
What diameter circular plate would have the same drag as the auto of Problem 12.11?Data From Problem 12.11A 2007 Toyota Prius has a drag coefficient of 0.26 at road speeds, using a reference
The auto in Problem 12.11 has shown a sensitivity to yaw angle. At a yaw angle of 20°, the lift coefficient increased to 1.0. What is the lift force at 100 mph for this case?Data From Problem 12.11A
The lift coefficient is defined as CL = (lift force) = 1/2ρv2xAr. If the lift coefficient for the auto in the previous problem is 0.21, determine the lift force at a road speed of 100 mph.
A 2007 Toyota Prius has a drag coefficient of 0.26 at road speeds, using a reference area of 2.33 m2. Determine the horsepower required to overcome drag at a velocity of 30 m/s. Compare this figure
Estimate the drag force on a 3-ft radio antenna with an average diameter of 0.2 in. at a speed of 60 mph.
For what wind velocities will a 12.7-mm-diameter cable be in the unsteady wake region of Figure 12.2?Figure 12.2 100 10 Съ 0.1 Regimes -П Ш FIV 0.01 10-1 10-0 101 102 103 104 105 106 puD Reynolds
Plot a curve of drag vs. velocity for a 1.65-in.-diameter sphere in air between velocities of 50 fps and 400 fps.
The drag coefficient for a smooth sphere is shown below. Determine the speed at the critical Reynolds number for a 42-mm-diameter sphere in air. 0.5 0.4 0.3 CD 0.2 0.1 103 104 105 107 106 Re = Dv/v
There is fluid evaporating from a surface at which vx|y=0 = 0, but vx|y=0 ≠ 0. Derive the von Kármán momentum relation.
Evaluate and compare with the exact solution δ, Cfx, and CfL for the laminar boundary layer over a flat plate, using the velocity profile vx = α sin by.
Find a velocity profile for the laminar boundary layer of the formwhen the pressure gradient is not zero. Ux — С1 + C2у + Сзу? + сдуз Vz8
Consider the flow of air at 30 m/s along a flat plate. At what distance from the leading edge will transition occur?
Modern subsonic aircraft have been refined to such an extent that 75% of the parasite drag (portion of total aircraft drag not directly associated with producing lift) can be attributed to friction
If Reynolds’s experiment was performed with a 38-mmID pipe, what flow velocity would occur at transition?
A pump in a manufacturing plant is transferring viscous fluids to a series of delivery tanks. This critical transfer requires careful monitoring of the solution mass flow rate, the power (work) that
A coating operation is creating materials for the electronics industry. The coating requires a specific volumetric flow rate Q, solution density ρ, solution viscosity μ, substrate coating velocity
A model ship propeller is to be tested in water at the same temperature that would be encountered by a full-scale propeller. Over the speed range considered, it is assumed that there is no dependence
A 40% scale model of an airplane is to be tested in a flow regime where unsteady flow effects are important. If the full scale vehicle experiences the unsteady effects at a Mach number of 1 at an
A model of a harbor is made on the length ratio of 360:1. Storm waves of 2 m amplitude and 8 m/s velocity occur on the breakwater of the prototype harbor. Significant variables are the length scale,
An estimate is needed on the lift provided by a hydrofoil wing section when it moves through water at 60 mph. Test data are available for this purpose from experiments in a pressurized wind tunnel
A falling liquid film within a gas–liquid contactor of 1.50 m length is in contact with 100% carbon dioxide gas at 1.0 atm and 25°C. The wetted surface area is 0.50 m2, and the liquid film
A 25% scale model of an undersea vehicle that has a maximum speed of 16 m/s is to be tested in a wind tunnel with a pressure of 6 atm to determine the drag characteristics of the full scale vehicle.
During the development of a 300-ft ship, it is desired to test a 10% scale model in a towing tank to determine the drag characteristics of the hull. Determine how the model is to be tested if the
A 1/6-scale model of a torpedo is tested in a water tunnel to determine drag characteristics. What model velocity corresponds to a torpedo velocity of 20 knots? If the model resistance is 10 lb, what
In natural-convection problems, the variation of density due to the temperature difference Î”T creates an important buoyancy term in the momentum equation. If a warm gas at THmoves through
A car is traveling along a road at 22.2 m/s. Calculate the Reynolds numbera. Based on the length of the carb. Based on the diameter of the radio antennaThe car length is 5.8 m and the antenna
Identify the variables associated with Problem 8.13 and find the dimensionless parameters.Data from 8.13The device in the schematic diagram on the next page is a viscosity pump. It consists of a
The size d of droplets produced by a liquid spray nozzle is thought to depend upon the nozzle diameter D, jet velocity V, and the properties of the liquid ρ, μ, and σ. Rewrite this relation in
A large amount of energy E is suddenly released in the air as in a point of explosion. Experimental evidence suggests that the radius r of the high-pressure blast wave depends on time t as well as
The power P required to run a compressor varies with compressor diameter D, angular velocity ω, volume flow rate Q, fluid density ρ, and fluid viscosity μ. Develop a relation between these
The functional frequency n of a stretched string is a function of the string length L, its diameter D, the mass density ρ, and the applied tensile force T. Suggest a set of dimensionless parameters
The mass M of drops formed by liquid discharging by gravity from a vertical tube is a function of the tube diameter D, liquid density, surface tension, and the acceleration of gravity. Determine the
The performance of a journal bearing around a rotating shaft is a function of the following variables: Q, the rate of flow lubricating oil to the bearing in volume per unit time; D, the bearing
The rate at which metallic ions are electroplated from a dilute electrolytic solution onto a rotating disk electrode is usually governed by the mass diffusion rate of ions to the disk. This process
Refer to Example 1. What is the required bulk velocity for the air over the surface of the film, assuming laminar flow? The molecular diffusion coefficient of MEK in air is 0.090 cm2/s at 27°C and
In a spray column, a liquid is sprayed into a gas stream, and mass is transferred between the liquid and gas phases. The formation of liquid drops from the spray nozzle is considered to be a function
The maximum pitching moment that is developed by the water on a flying boat as it lands is noted as cmax The following are the variables involved in this action:α = angle made by flight path of
A “cooling bag” is commonly used for storing water in hot, arid outdoor environments. The bag made of a thin porous fabric that allows water vapor, but not liquid water, to pass through it. A
The pressure rise across a pump P (this term is proportional to the head developed by the pump) may be considered to be affected by the fluid density ρ, the angular velocity ω, the impeller
Through a series of tests on pipe flow, H. Darcy derived an equation for the friction loss in pipe flow as in which f is a dimensionless coefficient that depends on (a) the average velocity u of
The power output of a hydraulic turbine depends on the diameter D of the turbine, the density ρ of water, the height H of water surface above the turbine, the gravitational acceleration g, the
The stream function for steady, in-compressible flow is given byψ(x,y) = 2x2 - 2y2 - xyDetermine the velocity potential for this flow.
The stream function for steady, in-compressible flow is given by ψ = y2 xy x2. Determine the velocity components for this flow, and find out whether the flow is rotational or irrotational.
A small droplet of liquid detergent, falling through air in a spray drying tower, has its diameter reduced as water evaporates from the surface. If it is assumed that the temperature of the liquid
In Example 3 we began finding the equation for the stream function by integrating equation (3). Repeat this example, but instead begin by integrating equation (4) and show that no matter which
For the stream function given byψ = 6x2 - 6y2determine whether this flow is rotational or irrotational.
A 2-m-diameter horizontal cylinder is formed by bolting two semi cylindrical channels together on the inside. There are 12 bolts per meter of width holding the top and bottom together. The inside

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