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P4.1 An idealized velocity field is given by the formula
Is this flow field steady or unsteady? Is it two- or three-dimensional? At the point (x, y, z) = (?1, +1, 0), compute (a) the acceleration vector and (b) any unit vector normal to the acceleration. Solution: (a) The flow is unsteady beca
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5.1 For axial flow through a circular tube, the Reynolds number for transition to turbulence is approximately 2300 [see Eq. (6.2)], based upon the diameter and average velocity. If d = 5 cm and the fluid is kerosene at 20°C, find the volume flow rate in m3/h which causes transition.
Solution: For
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1.1 A gas at 20°C may be rarefied if it contains less than 1012 molecules per mm3. If Avogadro’s number is 6.023E23 molecules per mole, what air pressure does this represent? Solution: The mass of one molecule of air may be computed as
Then the density of air containing 1012 molecules per mm3 i
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P3.1 Discuss Newton’s second law (the linear momentum relation) in these three forms: ∑F=ma ∑F= d dt(mV) ∑F= d dt V ρ d υ system ∫ ? ? ? ? ? ? ? ?
Solution: These questions are just to get the students thinking about the basic laws of mechanics. They are valid and equivalent for constant-mass syst
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P7.1 An ideal gas, at 20°C and 1 atm, flows at 12 m/s past a thin flat plate. At a position 60 cm downstream of the leading edge, the boundary layer thickness is 5 mm. Which of the 13 gases in Table A.4 is this likely to be?
Solution: We are looking for the kinematic viscosity. For a gas at l
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P6.1 An engineer claims that flow of SAE 30W oil, at 20°C, through a 5-cm-diameter smooth pipe at 1 million N/h, is laminar. Do you agree? A million newtons is a lot, so this sounds like an awfully high flow rate. Solution: For SAE 30W oil at 20°C (Table A.3), take ρ = 891 kg/m3 and ? = 0.29 kg/m
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2.1 For the two-dimensional stress field in Fig. P2.1, let σ xx =150 kPa σ yy =100 kPa σ xy =25 kPa Find the shear and normal stresses on plane AA cutting through at 30°. Solution: Make cut “AA” so that it just hits the bottom right corner of the element. This gives the freebody shown at right. Now
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8.1 Prove that the streamlines ψ (r, θ ) in polar coordinates, from Eq. (8.10), are orthogonal to the potential lines φ (r, θ ).
Solution: The streamline slope is represented by
Since the ψ ? slope = ?1/( φ ? slope), the two sets of lines are orthogonal. Ans.
8.2 The steady plane
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11.1 Describe the geometry and operation of a human peristaltic PDP which is cherished by every romantic person on earth. How do the two ventricles differ? Solution: Clearly we are speaking of the human heart, driven periodically by travelling compression of the heart walls. One ventricle serves the
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9.1 An ideal gas flows adiabatically through a duct. At section 1, p1 = 140 kPa, T1 = 260°C, and V1 = 75 m/s. Farther downstream, p2 = 30 kPa and T2 = 207°C. Calculate V2 in m/s and s2 ? s1 in J/(kg ? K) if the gas is (a) air, k = 1.4, and (b) argon, k = 1.67.
Fig. P9.1
Solution: (a) For
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