Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 3, Problem 58P
To determine
The value of
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We consider a laminar flow induced by an impulsively started infinite flat
plate. The y-axis is normal to the plate. The x- and z-axes form a plane parallel
to the plate. The plate is defined by y = 0. For time t <0, the plate and the flow
are at rest. For t≥0, the velocity of the plate is parallel to the 2-coordinate;
its value is constant and equal to uw. At infinity, the flow is at rest. The flow
induced by the motion of the plate is independent of z.
(a) From the continuity equation, show that v=0 everywhere in the flow and
the resulting momentum equation is
მu
Ət
Note that this equation has the form of a diffusion equation (the same form as
the heat equation).
(b) We introduce the new variables T, Y and U such that
T=kt, Y=k/2y, U = u
where k is an arbitrary constant. In the new system of variables, the solution
is U(Y,T). The solution U(Y,T) is expressed by a function of Y and T and the
solution u(y, t) is expressed by a function of y and t. Show that the functions are
identical.…
Part A: Suppose you wanted to drill a 1.5 in diameter hole through a piece of 1020 cold-rolled steel that is 2 in thick, using an HSS twist drill. What values if feed and cutting speed will you specify, along with an appropriate allowance?
Part B: How much time will be required to drill the hole in the previous problem using the HSS drill?
1.1 m
1.3 m
B
60-mm diameter
Brass
40-mm diameter
Aluminum
PROBLEM 2.52
-
A rod consisting of two cylindrical portions AB and BC is restrained at both
ends. Portion AB is made of brass (E₁ = 105 GPa, α = 20.9×10°/°C) and
portion BC is made of aluminum (Ę₁ =72 GPa, α = 23.9×10/°C).
Knowing that the rod is initially unstressed, determine (a) the normal
stresses induced in portions AB and BC by a temperature rise of 42°C, (b)
the corresponding deflection of point B.
Chapter 3 Solutions
Fluid Mechanics Fundamentals And Applications
Ch. 3 - Someone claims that the absolute pressure in a...Ch. 3 - A tinysteel cube is suspended in water by a...Ch. 3 - Express Pascal’s law, and give a real-world...Ch. 3 - Consider two identical fans, one at sea level and...Ch. 3 - What is the difference between gage pressure and...Ch. 3 - Explain why some people experience nose bleeding...Ch. 3 - Prob. 7PCh. 3 - A vacuum gage connected to a chamber reads 36 kPa...Ch. 3 - The pressure at the exit of an air compressor is...Ch. 3 - The pressure in a water line is 1500 kPa. What is...
Ch. 3 - A manometer is used to measure the air pressure in...Ch. 3 - The water in a tank is pressurized by air, and the...Ch. 3 - Determine the atmospheric pressure at a location...Ch. 3 - The gagepressure in a liquid at a depth of 2.5 m...Ch. 3 - The absolute pressure in water at a depth of 8 m...Ch. 3 - Show that 1kgf/cm2=14.223psi .Ch. 3 - Prob. 17EPCh. 3 - Consider a 55-kg woman who has a total foot...Ch. 3 - A vacuum gage connected to a tank reads 45 kPa at...Ch. 3 - Prob. 20EPCh. 3 - A pressure gage connected to a tank reads 500kPa...Ch. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Water from a reservoir is raised in a vertical...Ch. 3 - The barometer of a mountain hiker reads 980 mbars...Ch. 3 - The basic barometer can be used to measure the...Ch. 3 - Prob. 28PCh. 3 - Prob. 29EPCh. 3 - A gas is contained in a vertical, frictionless...Ch. 3 - Both a gage and a manometer are attached to a gas...Ch. 3 - The variation of pressure P in a gas with density ...Ch. 3 - The system shown in the figure is used to...Ch. 3 - The manometer shown in the figure is designed to...Ch. 3 - A manometer containing ( =850kg/m3 ) attached to a...Ch. 3 - A mercury ( =13,600kg/m3 ) is connected to an air...Ch. 3 - Repeat Prob. 3-37 for a differential mercury...Ch. 3 - Blood pressure is usually measured by rapping a...Ch. 3 - The maximum blood pressure in the upper arm of a...Ch. 3 - Consider a 1.73-m-tall man standing vertically in...Ch. 3 - Consider a U-tube whose arms are open to the...Ch. 3 - Prob. 44PCh. 3 - Freshwater and seamier flowing in parallel...Ch. 3 - Repeat Prob. 3-48 by replacing the air with oil...Ch. 3 - The pressure in a natural gas pipeline is measured...Ch. 3 - Repeat Prob. 3-42E by replacing air by oil with a...Ch. 3 - The gage pressure of the air in the tank shown in...Ch. 3 - Repeat Prob. 3-44 for a gage pressure of 40 kPa.Ch. 3 - The 500-kg load on the hydraulic lift show in Fig....Ch. 3 - Prob. 52EPCh. 3 - Pressure is often given in terms of a liquid...Ch. 3 - Prob. 54PCh. 3 - Consider a double-fluid manometer attached to an...Ch. 3 - The pressure difference between an oil pipe and...Ch. 3 - Consider the system shown in Fig. P3-51. If a...Ch. 3 - Prob. 58PCh. 3 - Prob. 59PCh. 3 - Define the resultant hydrostatic force acting on a...Ch. 3 - Someone claims that she can determine the...Ch. 3 - A submersed horizontal flat plate is suspended in...Ch. 3 - You may have noticed that dams are much thicker at...Ch. 3 - Consider a submerged curved surface. Explain how...Ch. 3 - Consider a submersed curved surface. Explain how...Ch. 3 - Consider a circular surface subjected to...Ch. 3 - Consider a heavy car submerged in water in a lake...Ch. 3 - A long, solid cylinder of radius 2 ft hinged at...Ch. 3 - Consider a 8-m-long, 8-m-wide, and 2-m-high...Ch. 3 - Consider a 200-ft-high, dam filled to capacity....Ch. 3 - A room the lower level of a cruise ship has a...Ch. 3 - The water side of the wall of a 70-m-long dam is a...Ch. 3 - For a gate width of 2 m into the paper (Fig....Ch. 3 - Determine the resultant force acting on the...Ch. 3 - A 6-m-high, 5-m-wide rectangular plate blocks the...Ch. 3 - The flow of water from a reservoir is controlled...Ch. 3 - Repeat Prob. 3-76E for a water height of 6 ft.Ch. 3 - A water trough of semicircular cross section of...Ch. 3 - Prob. 80PCh. 3 - An open settling tank shown in the figure contains...Ch. 3 - From Prob. 3-80, knowing that the density of the...Ch. 3 - Prob. 83PCh. 3 - The two sides of a V-shaped water trough are...Ch. 3 - Repeat Prob. 3-82 for the case of a partially...Ch. 3 - A retaining wall against a mud slide is to be...Ch. 3 - Prob. 87PCh. 3 - A 4-m-long quarter-circular gate of radius 3 m and...Ch. 3 - Repeat Prob. 3-90 for a radius of 2 m for the...Ch. 3 - Consider a flat plate of thickness t, width w into...Ch. 3 - Prob. 91PCh. 3 - Consider a 1-m wide inclined gate of negligible...Ch. 3 - Prob. 93PCh. 3 - What is buoyant force? What causes it? What is the...Ch. 3 - Consider two identical spherical bails submerged...Ch. 3 - Consider two 5-cm-diaineter spherical balls-one...Ch. 3 - Prob. 97CPCh. 3 - Prob. 98CPCh. 3 - The density of a liquid is to be determined by an...Ch. 3 - A crane is used to lower weights into a lake for...Ch. 3 - Prob. 101PCh. 3 - Prob. 102PCh. 3 - Prob. 103PCh. 3 - It is estimated that 90 percent of an iceberg’s...Ch. 3 - The weight of a body is usually measured by...Ch. 3 - Prob. 106PCh. 3 - Prob. 107PCh. 3 - The hull of a boat has a volume of 180 m3, and the...Ch. 3 - Under what conditions can a moving body of fluid...Ch. 3 - Consider a glass of water. Compare the water...Ch. 3 - Consider two identical glasses of water, one...Ch. 3 - Consider a vertical cylindrical container...Ch. 3 - Prob. 113PCh. 3 - Consider two water tanks filled with water. The...Ch. 3 - Prob. 115PCh. 3 - A 3-ft-diameter vertical cylindrical lank open to...Ch. 3 - Prob. 117PCh. 3 - A 30-cm-diameter, 90-cm-high vertical cylindrical...Ch. 3 - A fish tank that contains 60-cm-high water is...Ch. 3 - A 3-m-diameter vertical cylindrical milk tank...Ch. 3 - Consider a tank of rectangular cross-section...Ch. 3 - The bottom quarter of a vertical cylindrical tank...Ch. 3 - Milk with a density of 1020 kg/m3 is transported...Ch. 3 - Prob. 124PCh. 3 - The distance between the centers of the two arms...Ch. 3 - A 1.2-m-diameter, 3-m-high scaled vertical...Ch. 3 - A15-ft-long, 6-ft-high rectangular tank open to...Ch. 3 - An 8-ft-long tank open to the atmosphere initially...Ch. 3 - A 3-m-diameter, 7-m-long cylindrical tank is...Ch. 3 - Prob. 131PCh. 3 - Prob. 132PCh. 3 - Prob. 133PCh. 3 - Prob. 134PCh. 3 - An air-conditioning system requires a 34-m-long...Ch. 3 - Prob. 136PCh. 3 - If the rate of rotational speed of the 3-tube...Ch. 3 - A 30-cm-diameter vertical cylindrical vessel is...Ch. 3 - Prob. 139PCh. 3 - Prob. 141PCh. 3 - Prob. 142EPCh. 3 - The basic barometer can be used as an...Ch. 3 - The lower half of a 12-m-high cylindrical...Ch. 3 - A vertical, frictionless pistoncylinder device...Ch. 3 - A pressure cooker cooks a lot faster than an...Ch. 3 - Prob. 147PCh. 3 - The average atmospheric pressure on earth is...Ch. 3 - When measuring small pressure differences with a...Ch. 3 - Prob. 150EPCh. 3 - Prob. 151PCh. 3 - A gasoline line is connected to a pressure gage...Ch. 3 - Prob. 154PCh. 3 - Prob. 155EPCh. 3 - The pressure of water flowing through a pipe is...Ch. 3 - Consider a U-tube filled with mercury as shown in...Ch. 3 - Prob. 158PCh. 3 - The variation of pressure with density in a thick...Ch. 3 - A 3-m-high. 5-m-wide rectangular gale is hinged al...Ch. 3 - Prob. 161PCh. 3 - A semicircular 40-ft-diameter tunnel is to be...Ch. 3 - A 30-ton. 4-m-diameter hemispherical dome on a...Ch. 3 - The water in a 25-m-deep reservoir is kept inside...Ch. 3 - Prob. 165PCh. 3 - A 1-m-diameter, 2-m-high vertical cylinder is...Ch. 3 - A 5-m-long, 4-m-high tank contains 2.5-m-deep...Ch. 3 - Prob. 169PCh. 3 - Prob. 170PCh. 3 - The density of a floating body can be determined...Ch. 3 - The 280-ke, 6-m-wide rectangular gate shown in Fig...Ch. 3 - Prob. 173PCh. 3 - Prob. 174PCh. 3 - Prob. 175PCh. 3 - The gage pressure in a pipe is measured by a...Ch. 3 - Prob. 177PCh. 3 - Prob. 178PCh. 3 - Prob. 179PCh. 3 - Consider the vertical rectangular wall of a water...Ch. 3 - Prob. 181PCh. 3 - Prob. 182PCh. 3 - Prob. 183PCh. 3 - Prob. 184PCh. 3 - Prob. 185PCh. 3 - Consider a 6-m-diameter spherical sate holding a...Ch. 3 - Prob. 188PCh. 3 - Prob. 189PCh. 3 - Prob. 190PCh. 3 - Prob. 191PCh. 3 - Prob. 192PCh. 3 - A 15-cm-diameter, 40-cm-high vertical cylindrical...Ch. 3 - Prob. 194PCh. 3 - Prob. 195PCh. 3 - Shoes are to be designed to enable people of up to...Ch. 3 - The volume of a rock is to be determined without...Ch. 3 - The density of stainless steel is about 8000 kg/m3...
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- 30 mm D = 40 MPa -30 mm B C 80 MPa PROBLEM 2.69 A 30-mm square was scribed on the side of a large steel pressure vessel. After pressurization, the biaxial stress condition at the square is as shown. For E = 200 GPa and v=0.30, determine the change in length of (a) side AB, (b) side BC, (c) diagnonal AC.arrow_forwardPlease solve in detail this problem thank youarrow_forward0,5 mm 450 mm 350 mm Bronze A = 1500 mm² E = 105 GPa प 21.6 × 10-PC Aluminum A = 1800 mm² £ = 73 GPa = a 23.2 × 10-PC PROBLEM 2.58 Knowing that a 0.5-mm gap exists when the temperature is 24°C, determine (a) the temperature at which the normal stress in the aluminum bar will be equal to -75 MPa, (b) the corresponding exact length of the aluminum bar.arrow_forward
- 0.5 mm 450 mm -350 mm Bronze Aluminum A 1500 mm² A 1800 mm² E 105 GPa E 73 GPa K = 21.6 X 10 G < = 23.2 × 10-G PROBLEM 2.59 Determine (a) the compressive force in the bars shown after a temperature rise of 82°C, (b) the corresponding change in length of the bronze bar.arrow_forwardThe truss shown below sits on a roller at A and a pin at E. Determine the magnitudes of the forces in truss members GH, GB, BC and GC. State whether they are in tension or compression or are zero force members.arrow_forwardA weight (W) hangs from a pulley at B that is part of a support frame. Calculate the maximum possible mass of the weight if the maximum permissible moment reaction at the fixed support is 100 Nm. Note that a frictionless pin in a slot is located at C.arrow_forward
- It is the middle of a winter snowstorm. Sally and Jin take shelter under an overhang. The loading of the snow on top of the overhang is shown in the figure below. The overhang is attached to the wall at points A and B with pin supports. Another pin is at C. Determine the reactions of the pin supports at A and B. Express them in Cartesian vector form.arrow_forwardRecall that the CWH equation involves two important assumptions. Let us investigate how these assumptions affect the accuracy of state trajectories under the control inputs optimized in (a) and (b). (c.1): Discuss the assumptions about the chief and deputy orbits that are necessary for deriving CWH.arrow_forwardPROBLEM 2.50 1.8 m The concrete post (E-25 GPa and a = 9.9 x 10°/°C) is reinforced with six steel bars, each of 22-mm diameter (E, = 200 GPa and a, = 11.7 x 10°/°C). Determine the normal stresses induced in the steel and in the concrete by a temperature rise of 35°C. 6c " 0.391 MPa 240 mm 240 mm 6₁ = -9.47 MPaarrow_forward
- For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with time according to a(t) = a(0) exp(-4) (15.10) where σ(t) and o(0) represent the time-dependent and initial (i.e., time = 0) stresses, respectively, and t and T denote elapsed time and the relaxation time, respectively; T is a time-independent constant characteristic of the material. A specimen of a viscoelastic polymer whose stress relaxation obeys Equation 15.10 was suddenly pulled in tension to a measured strain of 0.5; the stress necessary to maintain this constant strain was measured as a function of time. Determine E (10) for this material if the initial stress level was 3.5 MPa (500 psi), which dropped to 0.5 MPa (70 psi) after 30 s.arrow_forwardFor the flows in Examples 11.1 and 11.2, calculate the magnitudes of the Δ V2 / 2 terms omitted in B.E., and compare these with the magnitude of the ℱ terms.arrow_forwardCalculate ℛP.M. in Example 11.2.arrow_forward
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