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engineering
engineering fluid mechanics
Munson Young And Okiishi's Fundamentals Of Fluid Mechanics 8th Edition Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein - Solutions
Do the head-flowrate data shown in Fig. 12.7 appear to follow the similarity laws as expressed by Eqs. 12.39 and 12.40? Explain.Eq. 12.39Eq. 12.40 (a) (b) Figure 12.7 (a) Open impeller, (b) enclosed or shrouded impeller, (c) complete pump assembly. (Courtesy of Flowserve Corporation.) 9 (c)
A centrifugal fan operating in a duct has the dimensionless parameters\[ C_{Q}=\frac{Q}{\omega D^{3}} \quad \text { and } \quad C_{H}=\frac{\Delta p}{ho \omega^{2} D^{2}} \]where \(C_{Q}\) is a flow coefficient, \(C_{H}\) is a head coefficient, \(Q\) is the volume flow rate, \(\omega\) is the fan
A centrifugal pump has the performance characteristics of the pump with the 6-in.-diameter impeller described in Fig. 12.7. Note that the pump in this figure is operating at \(3500 \mathrm{rpm}\). What is the expected head gained if the speed of this pump is reduced to \(2800 \mathrm{rpm}\) while
A prototype fan has a \(20-\mathrm{ft}\) diameter, an inlet pressure of \(14.40 \mathrm{psia}\), an inlet temperature of \(70^{\circ} \mathrm{F}\), and a speed of \(90 \mathrm{rpm}\). A \(\frac{1}{10}\)-scale model of the fan has the same inlet pressure and temperature, an inlet power of \(1.24
Use the data given in Problem 12.18 and plot the dimensionless coefficients \(C_{H}, C_{\mathscr{P}}, \eta\) versus \(C_{Q}\) for this pump. Calculate a meaningful value of specific speed, discuss its usefulness, and compare the result with data of Fig. 12.18.Fig. 12.18Problem 12.18The centrifugal
In a certain application, a pump is required to deliver \(5000 \mathrm{gpm}\) against a \(300-\mathrm{ft}\) head when operating at \(1200 \mathrm{rpm}\). What type of pump would you recommend?
A centrifugal pump operates at \(300 \mathrm{rpm}\) to deliver \(20^{\circ} \mathrm{C}\) lubricating oil. A \(\frac{1}{5}\)-size, geometrically similar pump delivering \(15^{\circ} \mathrm{C}\) water is used to model the larger pump. How fast should the smaller pump run? Discuss the accuracy of the
A certain axial-flow pump has a specific speed of \(N_{s}=5.0\). If the pump is expected to deliver \(3000 \mathrm{gpm}\) when operating against a 15 -ft head, at what speed (rpm) should the pump be run? Draw a sketch of the pump impeller (front and side views).
A certain pump is known to have a capacity of \(3 \mathrm{~m}^{3} / \mathrm{s}\) when operating at a speed of \(60 \mathrm{rad} / \mathrm{s}\) against a head of \(20 \mathrm{~m}\). Based on the information in Fig. 12.18, would you recommend a radialflow, mixed-flow, or axial-flow pump? Draw a
The system resistance for a pipeline is given by \(\Delta p_{\text {sys }}=2.0 Q^{2}\), where \(\Delta p_{\text {sys }}\) is the pressure rise required of a pump to deliver the flow rate \(Q\) through the piping system. A pump has the pressure-rise-flow characteristic given by \(\Delta
The axial-flow pump shown in Fig. 12.19 is designed to move \(5000 \mathrm{gal} / \mathrm{min}\) of water over a head rise of \(5 \mathrm{ft}\) of water. Estimate the motor power requirement and the \(U_{2} V_{\theta 2}\) needed to achieve this flowrate on a continuous basis. Comment on any
A propeller-driven airplane is traveling with a velocity \(V_{1}=200 \mathrm{mph}(294 \mathrm{ft} / \mathrm{s})\). The propeller diameter is \(10 \mathrm{ft}\) and it rotates at \(3000 \mathrm{rpm}\). Figure P12.38 shows a propeller crosssectional profile and the velocity diagrams for a short
For the fan of both Examples 5.19 and 5.28 discuss what fluid flow properties you would need to measure to estimate fan efficiency.Example 5.1A great danger to workers in confined spaces involves the consumption of breathable air (oxygen) and its replacement with other gases such as carbon dioxide
A lossless motor drives the fan shown in Fig. P12.40 at \(40 \mathrm{~Hz}\). The power input to the motor is \(40 \mathrm{amps}\) at 440 volts. For the geometry shown, what is the discharge flow rate of air through the fan? Assume that the tangential component of the velocity leaving the impeller
A centrifugal fan has a power input of \(25 \mathrm{~kW}\), an inner radius of \(R_{1}=0.5 \mathrm{~m}\), an outer radius of \(R_{2}=1.0 \mathrm{~m}\), and delivers \(100 \mathrm{~kg} / \mathrm{s}\) of air. There are no friction losses, the air inlet absolute velocity has no tangential component,
An axial fan operating at \(1000 \mathrm{rpm}\) has the characteristics shown in Fig. P12.42. It delivers \(15{ }^{\circ} \mathrm{C}\) atmospheric air through a 50-cm I.D., galvanized, sheet-metal, horizontal duct having a length of \(175 \mathrm{~m}\) and seven \(90^{\circ}\) long-radius elbows.
A model fan with wheel diameter 32 in. is tested at a speed of \(1750 \mathrm{rpm}\). The test fluid is air with density \(0.075 \mathrm{lbm} / \mathrm{ft}^{3}\). At its BEP, the fan produces \(8000 \mathrm{ft}^{3} / \mathrm{min}\) at total pressure rise of 8 in. \(\mathrm{H}_{2} \mathrm{O}\). A
A fan is to produce a total pressure rise of 6 in. \(\mathrm{H}_{2} \mathrm{O}\) and a flow of \(4000 \mathrm{ft}^{3} / \mathrm{min}\). Two motors are available, \(3550 \mathrm{rpm}\) and \(1160 \mathrm{rpm}\). For each motor, specify the best (most efficient) type of fan to use and sketch the
An inward-flow radial turbine (see Fig. P12.48) involves a nozzle angle, \(\alpha_{1}\), of \(60^{\circ}\) and an inlet rotor tip speed, \(U_{1}\), of \(3 \mathrm{~m} / \mathrm{s}\). The ratio of rotor inlet to outlet diameters is 2.0. The absolute velocity leaving the rotor at section (2) is
The frictionless converging stationary nozzle of the hydraulic turbine shown in Fig. P12.46 has an inlet pressure \(p_{0}=480 \mathrm{kPa}\), a negligible inlet velocity \(V_{0}\), and an exit pressure \(p_{1}=101 \mathrm{kPa}\). The velocity \(V_{1}\) is used to drive the axial flow turbine, which
A water turbine wheel rotates at the rate of \(100 \mathrm{rpm}\) in the direction shown in Fig. P12.47. The inner radius, \(r_{2}\), of the blade row is \(1 \mathrm{ft}\), and the outer radius, \(r_{1}\), is \(2 \mathrm{ft}\). The absolute velocity vector at the turbine rotor entrance makes an
A sketch of the arithmetic mean radius blade sections of an axial-flow water turbine stage is shown in Fig. P12.48. The rotor speed is \(1500 \mathrm{rpm}\). (a) Sketch and label velocity triangles for the flow entering and leaving the rotor row. Use \(\mathbf{V}\) for absolute velocity,
Figure P12.49 shows a piping system with frictional losses of \(h_{\mathrm{L} 1-2}=4.0 Q^{2}\), with \(h_{\mathrm{L} 1-2}\) in \(\mathrm{ft}\) and \(Q\) in \(\mathrm{gal} / \mathrm{min}\). The turbine performance characteristics are given by \(h_{t}=20+12.0 Q\), where \(h_{t}\) is the turbine head
A small Pelton wheel is used to power an oscillating lawn sprinkler as shown in Fig. P12.50. The arithmetic mean radius of the turbine is \(1 \mathrm{in}\)., and the exit angle of the blade is \(135^{\circ}\) relative to the blade motion. Water is supplied through a single 0.20 -in.-diameter nozzle
A windmill has an approach velocity \(V_{1}=24 \mathrm{mph}(35.3 \mathrm{ft} / \mathrm{s})\) and a blade diameter of \(100 \mathrm{ft}\). The blade rotates at \(15 \mathrm{rpm}\). Figure P12.51 shows a blade cross-sectional profile and the velocity diagrams for a short section of the blade at a
The single-stage, axial-flow turbomachine shown in Fig. P12.52 involves water flow at a volumetric flowrate of \(9 \mathrm{~m}^{3} / \mathrm{s}\). The rotor revolves at \(600 \mathrm{rpm}\). The inner and outer radii of the annular flow path through the stage are 0.46 and \(0.61 \mathrm{~m}\), and
Water for a Pelton wheel turbine flows from the headwater and through the penstock as shown in Fig. P12.54. The effective friction factor for the penstock, control valves, and the like is 0.032 , and the diameter of the jet is \(0.20 \mathrm{~m}\). Determine the maximum power output.Figure P12.54
A Pelton wheel has a diameter of \(2 \mathrm{~m}\) and develops \(500 \mathrm{~kW}\) when rotating \(180 \mathrm{rpm}\). What is the average force of the water against the blades? If the turbine is operating at maximum efficiency, determine the speed of the water jet from the nozzle and the mass
Water to run a Pelton wheel is supplied by a penstock of length \(\ell\) and diameter \(D\) with a friction factor \(f\). If the only losses associated with the flow in the penstock are due to pipe friction, show that the maximum power output of the turbine occurs when the nozzle diameter,
A Pelton wheel is supplied with water from a lake at an elevation \(H\) above the turbine. The penstock that supplies the water to the wheel is of length \(\ell\), diameter \(D\), and friction factor \(f\). Minor losses are negligible. Show that the power developed by the turbine is maximum when
Water flows through the Pelton wheel turbine shown in Fig. 12.25. For simplicity we assume that the water is turned \(180^{\circ}\) by the blade. Show, based on the energy equation (Eq. 5.84), that the maximum power output occurs when the absolute velocity of the fluid exiting the turbine is
A 1-m-diameter Pelton wheel rotates at \(300 \mathrm{rpm}\). Which of the following heads (in meters) would be best suited for this turbine:(a) 2,(b) 5,(c) 40,(d) 70, (e) 140? Explain.
Draft tubes as shown in Fig. P12.60 are often installed at the exit of Kaplan and Francis turbines. Explain why such draft tubes are advantageous.Figure P12.60 -Draft tube
Turbines are to be designed to develop 30,000 horsepower while operating under a head of \(70 \mathrm{ft}\) and an angular velocity of \(60 \mathrm{rpm}\). What type of turbine is best suited for this purpose? Estimate the flowrate needed.
Water at \(400 \mathrm{psi}\) is available to operate a turbine at 1750 \(\mathrm{rpm}\). What type of turbine would you suggest to use if the turbine should have an output of approximately \(200 \mathrm{hp}\) ?
It is desired to produce \(50,000 \mathrm{hp}\) with a head of \(50 \mathrm{ft}\) and an angular velocity of \(100 \mathrm{rpm}\). How many turbines would be needed if the specific speed is to be (a) 50 , (b) 100 ?
Test data for the small Francis turbine shown in Fig. P12.64 is given in the following table. The test was run at a constant \(32.8-\mathrm{ft}\)Figure P12.64head just upstream of the turbine. The Prony brake on the turbine output shaft was adjusted to give various angular velocities, and the force
Obtain photographs/images of a variety of turbo-compressor rotors and categorize them as axial-flow or radial-flow compressors. Explain briefly how they are used. Note any unusual features. Repeat for compressible flow turbines.
An axial flow compressor stage shown in Fig. P12.66 has the inlet and outlet velocity diagrams shown. Calculate the work per unit mass. Quantities are \(U_{1}=U_{2}=U=762 \mathrm{ft} / \mathrm{s}, V_{1}=440 \mathrm{ft} / \mathrm{s}, W_{1}=\) \(880 \mathrm{ft} / \mathrm{s}, \alpha_{1}=90^{\circ},
The axial flow gas turbine stage shown in Fig. P12.67 has a mean blade radius of \(R=5.0 \mathrm{in}\)., a rotational speed of \(15,000 \mathrm{rpm}\), a mass flow rate of \(10.0 \mathrm{lbm} / \mathrm{s}, W_{1}=972 \mathrm{ft} / \mathrm{s}, V_{1}=1560 \mathrm{ft} / \mathrm{s}, \alpha_{1}=\)
A centrifugal air compressor has a rotor inner diameter of \(D_{1}=2.0\) in., a rotor outer diameter of \(D_{2}=6.5\) in., a rotor depth of \(10 \mathrm{in}\)., and a rotor rotational speed of \(3600 \mathrm{rpm}\). The fluid relative velocities \((W)\) are purely radial. The compressor delivers an
The axial flow steam turbine rotor shown in Fig. P12.69 has a blade outer radius \(R_{0}=2.40 \mathrm{ft}\), a blade inner radius \(\mathrm{R}_{i}=\) \(2.00 \mathrm{ft}\), a steam inlet pressure \(p_{1}=200 \mathrm{psia}\), a steam inlet density \(ho_{1}=0.296 \mathrm{lbm} / \mathrm{ft}^{3}\), and
The figure below shows a nozzle vane and a rotor blade for an axial flow gas turbine stage. The blade speed is \(800 \mathrm{ft} / \mathrm{s}\). The absolute velocity leaving the stage is identical to the absolute velocity entering the stage and both are purely in the axial direction. (a) Draw and
Assume that water flowing past the equilateral triangular bar shown in Fig. P9.1 produces the pressure distributions indicated. Determine the lift and drag on the bar and the corresponding lift and drag coefficients (based on frontal area). Neglect shear forces.Figure P9.1 U = 5 ft/s p=0.5 pu
Fluid flows past the two-dimensional bar shown in Fig. P9.2. The pressures on the ends of the bar are as shown, and the average shear stress on the top and bottom of the bar is \(\tau_{\text {avg. }}\). Assume that the drag due to pressure is equal to the drag due to viscous effects. (a) Determine
Repeat Problem 9.1 if the object is a cone (made by rotating the equilateral triangle about the horizontal axis through its tip) rather than a triangular bar.Problem 9.1Assume that water flowing past the equilateral triangular bar shown in Fig. P9.1 produces the pressure distributions indicated.
The average pressure and shear stress acting on the surface of the 1-m-square flat plate are as indicated in Fig. P9.4. Determine the lift and drag generated. Determine the lift and drag if the shear stress is neglected. Compare these two sets of results.Figure P9.4 U Pave =-1.2 kN/m Tave 5.8 x 102
The pressure distribution on the 1-m-diameter circular disk in Fig. P9.5 is given in the table. Determine the drag on the disk.Figure P9.5 r (m) p (kN/m) 0 4.34 0.05 4.28 0.10 4.06 0.15 3.72 0.20 3.10 0.25 2.78 0.30 2.37 0.35 1.89 0.40 1.41 0.45 0.74 0.50 0.0
A nonspinning ball having a mass of 3 oz. is thrown vertically upward with a velocity of \(100 \mathrm{mph}\) and has zero velocity at a height \(250 \mathrm{ft}\) above the release point. Assume that the air drag on the ball is constant and find this constant "average" air drag. Neglect the
When you walk through still air at a rate of \(1 \mathrm{~m} / \mathrm{s}\), would you expect the character of the airflow around you to be most like that depicted in Fig. 9.6a, b, or c? Explain. Fig. 9.6 U Viscous forces important throughout Re = UD/y = 0.1 Viscosity not important (a) U
A 0.10-m-diameter circular cylinder moves through air with a speed \(U\). The pressure distribution on the cylinder's surface is approximated by the three straight-line segments shown in Fig. P9.8. Determine the drag coefficient on the cylinder. Neglect shear forces.Figure P9.8 P. N/m T 3 2 1 0 20
Typical values of the Reynolds number for various animals moving through air or water are listed below. For which cases is inertia of the fluid important? For which cases do viscous effects dominate? For which cases would the flow be laminar, turbulent? Explain. Animal Speed Re (a) large whale 10
Estimate the Reynolds numbers associated with the following objects moving through water. (a) a kayak, (b) a minnow, (c) a submarine, (d) a grain of sand settling to the bottom, (e) you swimming. Are viscous or inertial effects more dominant for each case?
Approximately how fast can the wind blow past a 0.25-in.diameter twig if viscous effects are to be of importance throughout the entire flow field (i.e., \(\operatorname{Re}
Consider the following cases. (a) A small 0.6-in.-long fish swims with a speed of \(0.8 \mathrm{in} / \mathrm{s}\). Would a boundary layer type flow be developed along the sides of the fish? Explain. (b) A 12-ft-long kayak moves with a speed of \(5 \mathrm{ft} / \mathrm{s}\). Would a boundary layer
Water flows past a flat plate that is oriented parallel to the flow with an upstream velocity of \(0.5 \mathrm{~m} / \mathrm{s}\). Determine the approximate location downstream from the leading edge where the boundary layer becomes turbulent. What is the boundary layer thickness at this location?
A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance \(1.3 \mathrm{~m}\) from the leading edge is \(12 \mathrm{~mm}\). Determine the boundary layer thickness at distances of \(0.20,2.0\), and \(20 \mathrm{~m}\) from the leading edge. Assume laminar flow.
If the upstream velocity of the flow in Problem 9.14 is \(U=\) \(1.5 \mathrm{~m} / \mathrm{s}\), determine the kinematic viscosity of the fluid.Problem 9.14A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance \(1.3 \mathrm{~m}\) from the leading edge is \(12
Water flows past a flat plate with an upstream velocity of \(U=0.02 \mathrm{~m} / \mathrm{s}\). Determine the water velocity a distance of \(10 \mathrm{~mm}\) from the plate at distances of \(x=1.5 \mathrm{~m}\) and \(x=15 \mathrm{~m}\) from the leading edge.
The typical shape of small cumulus clouds is as indicated in Fig. P9.17. Based on boundary layer ideas, explain why it is clear that the wind is blowing from right to left as indicated.Figure P9.17 U
Because of the velocity deficit, \(U-u\), in the boundary layer, the streamlines for flow past a flat plate are not exactly parallel to the plate. This deviation can be determined by use of the displacement thickness, \(\delta^{*}\). For air blowing past the flat plate shown in Fig. P9.18, plot the
Air enters a square duct through a 1 - \(\mathrm{ft}\) opening as is shown in Fig. P9.19. Because the boundary layer displacement thickness increases in the direction of flow, it is necessary to increase the cross-sectional size of the duct if a constant \(U=2 \mathrm{ft} / \mathrm{s}\) velocity is
A smooth, flat plate of length \(\ell=6 \mathrm{~m}\) and width \(b=4 \mathrm{~m}\) is placed in water with an upstream velocity of \(U=0.5 \mathrm{~m} / \mathrm{s}\). Determine the boundary layer thickness and the wall shear stress at the center and the trailing edge of the plate. Assume a laminar
An atmospheric boundary layer is formed when the wind blows over the Earth's surface. Typically, such velocity profiles can be written as a power law: \(u=a y^{n}\), where the constants \(a\) and \(n\) depend on the roughness of the terrain. As is indicated in Fig. P9.21, typical values are
A 30-story office building (each story is \(12 \mathrm{ft}\) tall) is built in a suburban industrial park. Plot the dynamic pressure, \(ho u^{2} / 2\), as a function of elevation if the wind blows at hurricane strength \((75 \mathrm{mph})\) at the top of the building. Use the atmospheric boundary
Show that by writing the velocity in terms of the similarity variable \(\eta\) and the function \(f(\eta)\), the momentum equation for boundary layer flow on a flat plate (Eq. 9.9b) can be written as the ordinary differential equation given by Eq. 9.14.Eq. 9.9bEq. 9.14(a, b) +0
Integrate the Blasius equation (Eq, 9.14) numerically to determine the boundary layer profile for laminar flow past a flat plate. Compare your results with those of Table 9.1.Eq. 9.14(a, b)Table 9.1 2f"" + ff" = 0
An airplane flies at a speed of \(400 \mathrm{mph}\) at an altitude of \(10,000 \mathrm{ft}\). If the boundary layers on the wing surfaces behave as those on a flat plate, estimate the extent of laminar boundary layer flow along the wing. Assume a transitional Reynolds number of
If the boundary layer on the hood of your car behaves as one on a flat plate, estimate how far from the front edge of the hood the boundary layer becomes turbulent. How thick is the boundary layer at this location?
A laminar boundary layer velocity profile is approximated by \(u / U=[2-(y / \delta)](y / \delta)\) for \(y \leq \delta\), and \(u=U\) for \(\mathrm{y}>\delta\).(a) Show that this parabolic profile satisfies the appropriate boundary conditions.(b) Use the momentum integral equation to determine the
Choose two of the velocity profiles and corresponding boundary layer parameter formulas presented in Table 9.2. Plot the thickness of the boundary layer and the wall shear stress versus \(x\) for values of \(x\) from zero to the laminar-turbulent transition point. The fluid is \(20^{\circ}
Air at 20 psia and \(90{ }^{\circ} \mathrm{F}\) flows over a flat plate at \(100 \mathrm{ft} / \mathrm{s}\). Find the value of \(x\) at which the Reynolds number is \(10^{4}\). Choose three velocity profile models from Table 9.2 and plot the velocity profiles ( \(u\) versus \(y\) ) on the same
A laminar boundary layer velocity profile is approximated by the two straight-line segments indicated in Fig. P9.30. Use the momentum integral equation to determine the boundary layer thickness, \(\delta=\delta(x)\), and wall shear stress, \(\tau_{w}=\tau_{w}(x)\). Compare these results with those
A laminar boundary layer velocity profile is approximated by \(u / U=2(y / \delta)-2(y / \delta)^{3}+(y / \delta)^{4}\) for \(y \leq \delta\), and \(u=U\) for \(y>\delta\). (a) Show that this profile satisfies the appropriate boundary conditions. (b) Use the momentum integral equation to determine
Consider \(20{ }^{\circ} \mathrm{C}\) water flowing over a thin, wide, smooth flat plate aligned with the flow. The approach velocity is \(60 \mathrm{~km} / \mathrm{hr}\) and the Reynolds number based on the plate length is \(2 \times 10^{5}\). Calculate the drag per unit width of the plate for
For a fluid of specific gravity \(S G=0.86\) flowing past a flat plate with an upstream velocity of \(U=5 \mathrm{~m} / \mathrm{s}\), the wall shear stress on the flat plate was determined to be as indicated in the table below. Use the momentum integral equation to determine the boundary layer
Should a canoe paddle be made rough to get a "better grip on the water" for paddling purposes? Explain.
Two different fluids flow over two identical flat plates with the same laminar free-stream velocity. Both fluids have the same viscosity, but one is twice as dense as the other. What is the relationship between the drag forces for these two plates?
Fluid flows past a flat plate with a drag force \(\mathscr{D}_{1}\). If the freestream velocity is doubled, will the new drag force, \(\mathscr{D}_{2}\), be larger or smaller than \(\mathscr{D}_{1}\) and by what amount?
A model is placed in an airflow at standard conditions with a given velocity and then placed in water flow at standard conditions with the same velocity. If the drag coefficients are the same between these two cases, how do the drag forces compare between the two fluids?
The drag coefficient for a newly designed hybrid car is predicted to be 0.21. The cross-sectional area of the car is \(30 \mathrm{ft}^{2}\). Determine the aerodynamic drag on the car when it is driven through still air at \(55 \mathrm{mph}\).
A 5-m-diameter parachute of a new design is to be used to transport a load from flight altitude to the ground with an average vertical speed of \(3 \mathrm{~m} / \mathrm{s}\). The total weight of the load and parachute is \(200 \mathrm{~N}\). Determine the approximate drag coefficient for the
A 180-1b man parachutes from a plane using a hemispherical parachute in air at \(20^{\circ} \mathrm{F}\) and \(14.60 \mathrm{psia}\). Calculate the parachute diameter required for the man's terminal velocity not to exceed \(20 \mathrm{ft} / \mathrm{s}\). Neglect the weight of the parachute.
A 70-kg soldier on a secret mission has to parachute from an airplane over the desert. It takes five seconds for him to release his parachute after he jumps. Taking the mass of the parachute as \(5 \mathrm{~kg}\), estimate the force acting on the soldier as he releases the parachute. The diameter
The aerodynamic drag on a car depends on the "shape" of the car. For example, the car shown in Fig. P9.42 has a drag coefficient of 0.35 with the windows and roof closed. With the windows and roof open, the drag coefficient increases to 0.45. With the windows and roof open, at what speed is the
An automobile engine has a maximum power output of \(70 \mathrm{hp}\), which occurs at an engine speed of \(2200 \mathrm{rpm}\). A \(10 \%\) power loss occurs through the transmission and differential. The rear wheels have a radius of \(15.0 \mathrm{in}\). and the automobile is to have a maximum
A woman is riding a bicycle down an \(18 \%\) slope. Her velocity is \(25 \mathrm{~km} / \mathrm{hr}\) into an oncoming \(25-\mathrm{km} / \mathrm{hr}\) wind. The air is at \(15{ }^{\circ} \mathrm{C}\) and \(101 \mathrm{kPa}\). Assuming that the only forces affecting the speed are the weight and
A baseball is thrown by a pitcher at \(95 \mathrm{mph}\) through standard air. The diameter of the baseball is \(2.82 \mathrm{in}\). Estimate the drag force on the baseball. Explain how the actual drag force may be different than your estimate.
A logging boat is towing a \(\log\) at \(1.5 \mathrm{~m} / \mathrm{s}\) against a river current that is \(1 \mathrm{~m} / \mathrm{s}\). The \(\log\) is \(0.5 \mathrm{~m}\) in diameter and \(2 \mathrm{~m}\) long.(a) Estimate the power required if the axis of the \(\log\) is parallel to the flow.(b)
How fast do small water droplets of \(0.06-\mu \mathrm{m}\left(6 \times 10^{-8} \mathrm{~m}\right)\) diameter fall through the air under standard sea-level conditions? Assume the drops do not evaporate. Repeat the problem for standard conditions at \(5000-\mathrm{m}\) altitude.
Determine the drag on a small circular disk of \(0.01-\mathrm{ft}\) diameter moving \(0.01 \mathrm{ft} / \mathrm{s}\) through oil with a specific gravity of 0.87 and a viscosity 10,000 times that of water. The disk is oriented normal to the upstream velocity. By what percent is the drag reduced if
The square, flat plate shown in Fig. P9.49a is cut into four equal-sized pieces and arranged as shown in Fig. P9.49b. Determine the ratio of the drag on the original plate [case (a)] to the drag on the plates in the configuration shown in (b). Assume laminar boundary flow. Explain your answer
Water flows past a triangular flat plate oriented parallel to the free stream as shown in Fig. P9.50. Integrate the wall shear stress over the plate to determine the friction drag on one side of the plate. Assume laminar boundary layer flow.Figure P9.50 U = 0.2 m/s 1.0 m 456 45%
For small Reynolds number flows, the drag coefficient of an object is given by a constant divided by the Reynolds number (see Table 9.4). Thus, as the Reynolds number tends to zero, the drag coefficient becomes infinitely large. Does this mean that for small velocities (hence, small Reynolds
A rectangular cartop carrier of \(1.6-\mathrm{ft}\) height, \(4.0-\mathrm{ft}\) length (front to back), and 4.2-ft width is attached to the top of a car. Estimate the additional power required to drive the car with the carrier at \(65 \mathrm{mph}\) through still air compared with the power
As shown in Fig. P9.53a, a kayak is a relatively streamlined object. As a first approximation in calculating the drag on a kayak, assume that the kayak acts as if it were a smooth, flat plate \(17 \mathrm{ft}\) long and \(2 \mathrm{ft}\) wide. Determine the drag as a function of speed and compare
A coal barge \(1000 \mathrm{ft}\) long and \(100 \mathrm{ft}\) wide is submerged a depth of \(12 \mathrm{ft}\) in \(60^{\circ} \mathrm{F}\) water. It is being towed at a speed of \(12 \mathrm{mph}\). Estimate the friction drag on the barge.
A three-bladed helicopter blade rotates at \(200 \mathrm{rpm}\). If each blade is \(12 \mathrm{ft}\) long and \(1.5 \mathrm{ft}\) wide, estimate the torque needed to overcome the friction on the blades if they act as flat plates.
A thin, smooth sign is attached to the side of a truck as is indicated in Fig. P9.56. Estimate the friction drag on the sign when the truck is driven at \(55 \mathrm{mph}\).Figure P9.56 5 ft 20 ft Eli Van Lines 4 ft
A 38.1-mm-diameter, \(0.0245-\mathrm{N}\) table tennis ball is released from the bottom of a 4-m-deep swimming pool. Assuming that the ball has reached its terminal velocity within \(1 \mathrm{~m}\), estimate the time required to rise the remaining distance to the surface.
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