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Problem 1.119 A soda straw with an inside diameter of 0 .125 in. is inserted into a pan of water at 6 0 °F. The water in the straw rises to a height of 0 .150 in. above the water […]

Problem 1.22 Express the following quantities in SI units: (a) 1 60 acres, (b) 1 5 gallons (U.S.), (c) 2 40 miles, (d) 7 9.1 h p , and (e) 6 0.3 °F. Solution 1.22 a) 22 4252 2 ft […]

Problem 1.45 Nitrogen is compressed to a density of 3 4 kg/m under an absolute pressure of 4 00 kPa. Determine the temperature in degrees Celsius. Solution 1.45 3 2 N 400 10 m337 K p Nm s 3 1 […]

Problem 1.1 The force, F , of the wind blowing against a building is given by 22 D F CVA , where V is the wind speed, the density of the air, A the cross-sectional area of the building, and […]

Problem 1.65 Calculate the Reynolds numbers for the flow of water and for air through a 4-mm-diameter tube, if the mean velocity is 3m/s and the temperature is 30 C in both cases. Assume the air is at standard atmospheric […]

Problem 1.104 Assume that the air volume in a small automobile tire is constant and equal to the volume between two concentric cylinders 1 3 cm high with diameters of 3 3 cm and 5 2 cm. The air in […]

Problem 1.83 Standard air flows past a flat surface, and velocity measurements near the surface indicate the following distribution: fty0.005 0.01 0.02 0.04 0.06 0.08 ft/su0.74 1.51 3.03 6.37 10.21 14.43 The coordinate y is measured normal to the surface […]

Problem 10.19 Water in a rectangular channel flows into a gradual contraction section as is indicated in the figure below. If the flowrate is =3 25ft / sQ and the upstream depth is = 10.5fty, determine the downstream depth, 2 […]

Problem 10.31 The following data are taken from measurements on Indian Fork Creek: =2 26 mA, =16 mP, and = 0 0.02 m 62 m S. Determine the average shear stress on the wetted perimeter of this channel. Solution 10.31 […]

Problem 10.1 On a distant planet small-amplitude waves travel across a 1-m– deep pond with a speed of 5 m/s. Determine the acceleration of gravity on the surface of that planet. Solution 10.1 =cgy , where =m 5 s c […]

Problem 10.50 Done without GPS or lasers Two thousand years before, the invention of such tools as the Global Positioning System (GPS) or laser surveying equipment, Roman engineers were able to design and construct structures that made a lasting contribution […]

and () == =    1 1 1 2 ft 21.6 s1.29 ft 32.2 8.7 ft s n V Fgy This root does not satisfy our problem statement since the flow upstream of the sluice gate is given […]

Problem 10.67 The symmetrical channel shown in the figure below is dug in sandy loam soil with =0.020 n . For such surface material, it is recommended that to prevent scouring of the surface, the average velocity be no more […]

Problem 11.50 Air flows in the channel as shown in the figure below. Determine the Mach number, static pressure, and stagnation pressures at station 3. Assume isentropic flow except for the normal shock wave. Solution 11.50 Let the subscript “a” […]

Problem 11.59 Supersonic airflow enters an adiabatic, constant area pipe (inside diameter 0.1 m = ) with 1 M a2.0=. The pipe friction factor is 0.02. If a standing normal shock is located right at the pipe exit, and the […]

Problem 11.42 The static pressure to stagnation pressure ratio at a point in a gas flow field is measured with a Pitot-static probe as being equal to 0.6. The stagnation temperature of the gas is 20 °C. Determine the flow […]

and   =     * 2 21 *1 VV VV V V (6) We use Eq. (2) to get    ==  ⋅  ⋅ ⋅    ⋅  1 2 m […]

Problem 11.14 Steam ( 2 HO vapor) flows in a pipeline in a power station. The steam pressure is 150 psia, its temperature is 500 °F, and it flows with velocity 750ft/s. Calculate the stagnation pressure and stagnation temperature. If […]

Chapter 11 Compressible Flow Note: Solutions presented here may refer to Isentropic Flow Tables or Charts, Shock Tables or Charts, Fanno Flow Tables or Charts, and/or Rayleigh Flow Tables or Charts. It should be understood that Tables, Charts, Mathematical Functions, […]

Problem 11.30 The Pitot tube on a supersonic aircraft cruising at an altitude of 30,000 ft senses a stagnation pressure of 12 psia . If the atmosphere is considered standard, determine the airspeed and Mach number of the aircraft. A […]

where ρ ⋅ ⋅ == =    3 3 slugs ft slugs 1.94 0.0109 0.0211 ss ft mQ Thus, and () ⋅ ⋅  =−=      ⋅ = max 222 shaft 3 slugs ft […]

Problem 12.1 The rotor shown in the figure below rotates clockwise. Assume that the fluid enters in the radial direction and the relative velocity is tangent to the blades and remains constant across the entire rotor. Is the device a […]

Problem 12.40 A lossless motor drives the fan shown in the figure below at 40 Hz. The power input to the motor is 40 A at 440 V. For the geometry shown, what is the discharge flowrate of air through […]

Problem 12.60 Draft tubes as shown in the figure below are often installed at the exit of Kaplan and Francis turbines. Explain why such draft tubes are advantageous. Solution 12.60 Draft tube Without the draft tube, there would be a […]

Now atm p pp 12 == and ≈ 10V. This gives (for α = 21.0) For screwed connections, ent K 1.0=, check K 2.0=, elb K 0.6 4 =, tee K 0.90=, gate K 0.11=, globe K 5.7= These numerical […]

Problem 12.13 The performance characteristics of a certain centrifugal pump having a 9-in.-diameter impeller and operating at 1 750 rpm are determined using an experimental setup similar to that as shown in the figure below. The following data were obtained […]

Problem 2.79 Consider the gate shown in the figure below. The gate is massless and has a width b (perpendicular to the paper). The hydrostatic pressure on the vertical side creates a counterclockwise moment about the hinge, and the hydrostatic […]

Problem 2.2 The deepest known spot in the oceans is the Challenger Deep in the Mariana Trench of the Pacific Ocean and is approximately 11,000 m below the surface. Assume that the salt-water density is constant at 3 1025kg/m and […]

For an infinite cistern area, =∞ 1 A γ γ ∞ −− ==  +   2 1 2( ) 1 2 HL HL p ppp xA A Percent error = ∞∞   −  ==−=+−   […]

Problem 2.20 Assume that a person skiing high in the mountains at an altitude of 15,000 ft takes in the same volume of air with each breath as she does while walking at sea level. Determine the ratio of the […]

To locate R F , For equilibrium, = 0 H M So that () =1ft+y RR WF And ()( ) + == 333lb 1ft 1.178ft 3.63ft 200 lb I yc = 0.3927R 4 I xyc = 0 c y x […]

Also, To determine 1, consider a unit square that consist of a quarter circle and the remainder as show in the figure. The centroids of areas (1) and (2) are as indicated. Thus, () π  −=−   211 […]

Problem 2.98 The Altus dam in the figure below is made of concrete with a density of 3 150 lbm/ft . The coefficient of friction µ between the base of the dam and the foundation is 0.65. Is the dam […]

Problem 2.154 The cylinder in the figure below accelerates to the left at the rate of 2 9.80 m/s . Find the tension in the string connecting at rod of circular cross section to the cylinder. The volume between the […]

Problem 2.40 Two pipes are connected by a manometer as shown in the figure below. Determine the pressure difference − AB p p, between the pipes. Solution 2.40 ()()() γγγ ++−+−= 2 2 AHO gf HO B 0.5m 0.6m 0.6 […]

Problem 2.141 A child’s balloon is a sphere 1 ft. in diameter. The balloon is filled with helium ρ 3 = 0.014 lbm/ft(). The balloon material weighs 2 0.008 lbf/ft of surface area. If the child releases the balloon, how […]

Also, 22 00 11 01 22 pV pV zz gg γγ ++=++ where 10z= and () 3 3 12 1 m 9.10 10 m s4.63 s 0.05 m 4 Q VA π − × == = 2 234 1 10 […]

24.48fth= or 2a negative rooth=. Clearly, it is not possible (physically) to have 20h< Thus, 20.630 fth= or 24.48fth= Problem 3.124 Water flows in a rectangular channel that is 2.0 m wide as shown in the figure below. The upstream […]

Problem 3.56 Find the water mass flow rate at the nozzle outlet O shown in the figure below, and calculate the maximum height to which the water stream will rise. The water density is 3 1.9slugs ft , and the […]

Problem 3.20 Air flows over the airfoil shown in the figure below. Sensors give the pressures shown at points ,,ABC , and D. Find the air velocities just above points ,,ABC , and D. The air density is 3 0.0020slug […]

Problem 3.42 The figure below shows a tube for siphoning water from an aquarium. Determine the rate at which the water leaves the aquarium for the conditions shown. Is there an advantage to having the large-diameter section? The water flow […]

where 22 55 AV AV= Thus, 2 22 02 02 05 11 ( ) 8ft (3ft) 7.81ft 216 16 pV zz zz zz g γ =−− =−− − = − = or 232 lb lb 62.4 (7.81ft) 488 ft ft […]

Problem 3.2 Air flows steadily along a streamline from point (1) to point (2) with negligible viscous effects. The following conditions are measured: At point (1) 12mz= and 10kPa p = ; at point (2) 210 mz= , 2 220 […]

or Thus, 2 2 3 120 33 2 ft 31.8 lb lb s 1.1 62.4 3.6 ft 42.5 (2.0 ft) ft 2ft ft 2 32.2 s V pzh g γγ          =−−= […]

or 3 m 17.9 s V= Thus, 3 2 33 mm (0.050 m) 17.9 0.0351 4ss QAV π  == =   Also, 2 233 11 13 22 pV pV zz gg γγ ++=++ where 3 133 1 A […]

With T dh Vdt =, Thus, 11 2 3 2, T dh gA h h h A dt  ++ =−  where 1,hh=2,hhL=+ 32hhL=+ and 2in.L= Hence, 0 1 0 22 t TL Adh gdt AhhLhL  −=  […]

Problem 4.33 As a valve is opened, water flows through the diffuser as shown in the figure below at an increasing flowrate so that the velocity along the centerline is given by 0(1 ) 1 ct x uV e − […]

FIND: Lagrangian expression =0 (,)VVVt where 0 V is car velocity at time =0t and 0x=. SOLUTION: The condition =0 VV at =0x gives or ×  =−=   1293.1 ln 1 1.0 0.1 88.5 B so =+ 0(1 […]

Problem 4.48 The velocity components for steady flow through the nozzle as shown in the figure below are =− and   =+     , where 0 V and are constants. Determine the ratio of the magnitude […]

Problem 4.59 In the region just downstream of a sluice gate, the water may develop a reverse flow region as is indicated in the figure below. The velocity profile is assumed to consist of two uniform regions, one with velocity […]

V = V0 + ∆V (1–e–ax) Problem 4.2 The surface velocity of a river is measured at several locations x and can be reasonably represented by 0(1 ) ax VV V e − =+Δ − , where 0 V , […]

Problem 5.1 Use the Reynolds transport theorem with volumeB= and, therefore, ==volume/mass 1/densityb to obtain the continuity equation for steady or unsteady incompressible flow through a fixed control volume: 0 CV dA⋅=  Vn . Solution 5.1 The Reynolds Transport […]

and we note that the result is independent of the fluid involved. The value of ,1 V θ can be ascertained with the help of the section (1) velocity triangle sketched below.  11 s1.8 s Ar Thus with Eq. […]

Problem 5.35 Find the force components x F and y F required to hold the box as shown in the figure below stationary. The fluid is oil and has specific gravity of 0.85. Neglect gravity effects. Atmospheric pressure acts around […]

Problem 5.97 Oil ( 1 0 psi) flows downward through a vertical pipe contraction as shown in the figure below. If the mercury manometer reading, h, is 100 mm, determine the volume flowrate for frictionless flow. Is the actual flowrate […]

Problem 5.59 Determine the magnitude of the horizontal component of the anchoring force required to Solution 5.59 The control volumes of the figures below are appropriate for use in solving this problem. h u (b)(c) Control volume Water only Control […]

Problem 5.119 Water is to be pumped from the large tank shown in the figure below with an exit velocity of 6 m/s. It was determined that the original pump (pump 1) that supplies 1kW of power to the water […]

Problem 5.127 Find the acceleration of the cart shown in the figure below as a function of the water height in the cart, which varies with time. The initial total mass is 0 m, and the fluid density is 0 […]

Problem 5.109 A pump is to move water from a lake into a large, pressurized tank as shown in the figure below at a rate of 1000 gal in 10 min or less. Will a pump that adds 3hp to […]

Using the table below, ()   ⋅     =−10        ⋅        =− =− 22 2 2 3 kg m m N s 998 […]

Problem 5.72 Thrust vector control is a technique that can be used to greatly improve the maneuverability of military fighter aircraft. It consists of using a set of vanes in the exit of a jet engine to deflect the exhaust […]

Problem 5.19 Two rivers merge to form a larger river as shown in the figure below. At a location downstream from the junction (before the two streams completely merge), the nonuniform velocity profile is as shown and the depth is […]

(c) For θ =60, we use Eq. (4) to get 22 3 2 2 2 3 kg l mm N 999 5 (0.5 m)(cos 60 ) 1000 1 m sm mkg s l 1000 (3)( mm ) m shaft T […]

Problem 6.92 We will see in Chapter 8 that the pressure drop in fully developed pipe flow is sometimes computed with the aid of a friction factor, defined by 2 1 2 p D f V ρ Δ = where […]

Also, 2 12 3 lb 0.167 lb ft 0.334 ft 6in. in. 12 ft pp p x − ∂ −= = = ∂     thus, from Eq. (1) 2 3 1.0 in. lb s ft in. 0.03 […]

Problem 6.1 The velocity in a certain two-dimensional flow field is given by the equation ˆˆ 22 V xt yt=ij – where the velocity is in ft s when x, y, and t are in feet and seconds, respectively. Determine […]

Problem 6.29 Integrate Bernoulli’s equation for compressible flow, Solution 6.29 The equation is 2 2 dp V gz C ρ ++=  From the given pressure–density relationship n p C ρ =, 1n d pnC d ρρ − =, And […]

Problem 6.70 “Stokes’s first problem” involves the instantaneous acceleration at time 0t= of a flat plate to a constant velocity 0 U while in contact with a “semi-infinite,” static fluid as shown in the figure below. For a constant fluid […]

From Eq. (1) 2 4 0.06 m 3s m 6.37 10 s2(15) A Vm π −     =× + 4m s − = 8.49×10 Problem 6.56 A Rankine oval is formed by combining a source-sink pair, each […]

and the stagnation point is on the wall to the righ0.0079 t of 6 t ft sli . The value of ψ at the stagnation point (r = 0.00796 ft, 0 θ =) is zero [Eq. (1)] so that the […]

Problem 6.16 The stream function for an incompressible, two-dimensional flow field is 3 ay by ψ =− where a and b are constants. Is this an irrotational flow? Explain. Solution 6.16 For the flow to be irrotational, 10 2 z […]

Problem 7.65 The drag characteristics of an airplane are to be determined by model tests in a wind tunnel operated at an absolute pressure of 1300 kPa. If the prototype is to cruise in standard air at 385 km/hr, and […]

Problem 7.76 Models are commonly used to study the dispersion of a gaseous pollutant from an exhaust stack located near a building complex. Similarity requirements for the pollutant source involve the following independent variables: the stack gas speed, V; the […]

Problem 7.34 Develop the Weber number by starting with estimates for the inertia and surface tension forces. Solution 7.34 Inertia force ρ 22 V and Surface tension force σ  then ρρ σσ = 22 2 Inertia force Surface tension […]

Problem 7.1 A mixing basin in a sewage filtration plant is stirred by mechanical agitation (paddlewheel) with a power input (ft lb/s ) W⋅ . The degree of mixing of fluid particles is measured by a “velocity gradient” G given […]

Problem 7.16 A cone and plate viscometer consists of a cone with a very small angle α that rotates above a flat surface as shown in the figure below. The torque, T, required to rotate the cone at an angular […]

Problem 7.46 Air at 8 0°F is to flow through a 2 -ft pipe at an average velocity of 6 ft/s. What size pipe should be used to move water at °60 F and average velocity of 3 ft/s if […]

Problem 8.127 Air at 200 °F and 60 psia flows in a 4-in.-diameter pipe at a rate of lb 0.52 s. Determine the pressure at the 2-in.-diameter throat of a Venturi meter placed in the pipe. Solution 8.127 βγ ρβ […]

Problem 8.71 As shown in the figure below, water “bubbles up” 3 in. Above the exit of the vertical pipe attached to three horizontal pipe segments. The total length of the 0.75-in.-diameter galvanized iron pipe between point (1) and the […]

Problem 8.80 Water is pumped through a 6 0-m-long, 0.3-m-diameter pipe from a lower reservoir to a higher reservoir whose surface is 1 0 m above the lower one. The sum of the minor loss coefficients for the system is […]

Thus, by combining Eqs. (3), (4), and (5), we obtain the following equation for V:   11 22 33 0.01 2.51 13.7 2.0 log 13.13 13.13 0.01365 (8290 ) 0.01365V VV   +     =− […]

Problem 8.20 Asphalt at 1 20 F, considered to be a Newtonian fluid with a viscosity 8 0000 times that of water and a specific gravity of 1.09 , flows through a pipe of diameter 2.0 in. If the pressure […]

Problem 8.2 Rainwater runoff from a parking lot flows through a 3-ft- diameter pipe, completely filling it. Whether flow in a pipe is laminar or turbulent depends on the value of the Reynolds number. Would you expect the flow to […]

Problem 8.92 Calculate the water flowrate in the system shown in the figure below. The piping system includes four gate valves, two half-open globe valves, fourteen 90° regular elbows, and 250 ft of 2-in. schedule 40 commercial steel pipe (with […]

Problem 8.109 It is necessary to deliver 270 ft3/min of water from reservoir A to reservoir B, as shown in the figure below. The connecting piping consists of four fully open gate valves, 12 regular 90° elbows, one swing check […]

Problem 8.57 Air flows though the mitered bend shown in the figure below at a rate of 5 cfs . To help straighten, the flow after the bend, a set of 0.25-in.- diameter drinking straws is placed in the pipe […]

or 1 2   Also, from Eq. (1), 312 V VV=− (11) Solution method: (a) Guess values of f1, f2, and f3 (A good starting value is the large Re value for 4 4.5 10 D ε − =× […]

Problem 8.32 Water is pumped between two tanks as shown in the figure below. The energy line is as indicated. Is the fluid being pumped from A to B or B to A? Explain. Which pipe has the larger diameter: […]

Problem 8.101 A certain process requires 2.3 cfs of water to be delivered at a pressure of 30 psi. This water comes from a large-diameter supply main in which the pressure remains at 60 psi. If the galvanized iron pipe […]

or 2 2 ft 55.6 500 ft s (0.022) 440 ft ft 1.2 ft 232.2 s L h     ==      For this horizontal pipe, γγ ++=+ ++ 22 11 2 2 12 […]

Problem 8.45 H. Blasius correlated data on turbulent friction factor in smooth pipes. His equation 14 0.3164 Re− ≈ smooth f is reasonably accurate for Reynolds numbers between 4000 and 5 1 0. Use this information for the following scenario. […]

Problem 9.96 By appropriate streamlining, the drag coefficient for an airplane is reduced by 12 % while the frontal area remains the same. For the same power output, by what percentage is the flight speed increased? Solution 9.96 2 1 […]

Problem 9.83 A shortwave radio antenna is constructed from circular tubing, as illustrated in the figure below. Estimate the wind force on the antenna in a 100- km hr wind. Solution 9.83 12 3 4 =++ DD D D Obtain […]

Hence, () ν ν δ == 22 5.83 0.1175 xx UU For the exact Blasius Solution, ν δ =5.0 x U, so the given profile estimates approximately 14% higher boundary layer thickness. Problem 9.32 Consider 2 0C° water flowing over […]

Problem 9.1 Assume that water flowing past the equilateral triangular bar shown in the figure below produces the pressure distributions indicated. Determine the lift and drag on the bar and the corresponding lift and drag coefficients (based on frontal area). […]

Thus, since Using a standard numerical integration routine with the data given, we obtain =0.327 L C ′x       2 1 u U− 0.000 −1.00 0.025 −0.0572 0.050 0.518 0.075 0.621 0.100 0.615 0.200 0.628 […]

Hence, for any x-location = A QQ or () δ =− * A Uy U y or where m x∼ 0 0.005 0.01 0.015 0.02 0.025 01234 y (m) x (m) 0.03 0.035 0.04 * 1 22 5 3 1.721 […]

Problem 9.73 Phil’s Pizza Parlor decides to place a thin, rectangular, plastic sign on top of its delivery van as shown in the figure below. The sign measures 2 ft by5 ft . (a) Estimate the extra power required to […]

Problem 9.48 Determine the drag on a small circular disk of 0.01-ft diameter moving 0.01ft 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 […]

Problem 9.61 Estimate the velocity with which you would contact the ground if you jumped from an airplane at an altitude of 5000 ft and (a) air resistance is negligible, (b) air resistance is important, but you forgot your parachute, […]