Fundamentals of Momentum, Heat and Mass Transfer, 6th Edition International Student Version - Chapter 7

7.1 For a two-dimensional, incompressible flow with velocity υx = υx(y), sketch a three-dimensional fluid element and illustrate the magnitude, direction, and surface of action of each stress component.
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7.2 Using a cylindrical element, show that Stokes’s viscosity relation yields the following shear stress components:...
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7.3 Estimate the viscosity of nitrogen at 175 K using equation (7-10).
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7.4 At what temperature is the kinematic viscosity of glycerin the same as the kinematic viscosity of helium?
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7.5 According to the Hagen–Poiseuille laminar flow model, the volumetric flow rate is inversely proportional to the viscosity. What percentage change in volumetric flow rate occurs in a laminar flow as the water temperature changes from near freez- ing to 140°F?
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7.6 An automobile crankshaft is 3.175 cm in diameter. A bearing on the shaft is 3.183 cm in diameter and 2.8 cm long. The bearing is lubricated with SAE 30 oil at a temperature of 365 K. Assuming that the shaft is centrally located in the bearing, determine how much heat must be removed to maintain the bearing at constant temperature. The shaft is rotating at 1700 rpm, and the viscosity of the oil is 0.01 Pa.s.
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7.7 An auto lift consists of 36.02-cm-diameter ram that slides in a 36.04-cm-diameter cylinder. The annular region is filled with oil having a kinematic viscosity of 0.00037 m2/s and a specific gravity of 0.85. If the rate of travel of the ram is 0.15 m/s, estimate the frictional resistance when 3.14 m of the ram is engaged in the cylinder.
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7.8 The conical pivot shown in the figure has angular velocity w and rests on an oil film of uniform thickness h. Determine the frictional moment as a function of the angle a, the viscosity, the angular velocity, the gap distance, and the shaft diameter....
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7.9 For water flowing in a 0.1-in.-diameter tube, the velocity distribution is parabolic (see Example 4.2). If the average velocity is 2 fps, determine the magnitude of the shear stress at the tube wall.Example 4.2Let us consider the case of an incompressible flow, for which the flow area is circular and the velocity profile is parabolic (seeFigure 4.3), varying according to the expression...where vmax is the maximum velocity, which exists at the center of the circular passage (i.e., at r=0), and R is the radial distance to the inside surface of the circular area considered....Figure 4.3 A parabolic velocity profile in a circular flow passage.The above velocity-profile expression may be obtained experimentally. It will also be derived theoretically in Chapter 8 for the case of laminar flow in a circular conduit. This expression represents the velocity at a radial distance, r, from the center of the flow section. As the average velocity is of particular interest in engineering problems, we will now consider the means of obtaining the average velocity from this expression.At the station where this velocity profile exists, the mass rate of flow is...For the present case of incompressible flow, the density is constant. Solving for the average velocity, we have...
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7.10 A Newtonian oil with a density of 60 lbm/ft3, viscosity of 0.206 103 lbm/ft-s and kinematic viscosity of 0.342 × 105 ft2/s undergoes steady shear between a horizontal fixed lower plate and a moving horizontal upper plate. The upper plate is moving with a velocity of 3 ft/s. The distance between the plates is 0.03 in., and the area of the upper plate in contact with the fluid is 0.1 ft2. Assume incompressible, isothermal, inviscid, frictionless flow....
a. What is shear stress exerted on the fluid under these conditions?
b. What is the force of the upper plate on the fluid?

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7.11 The figure below shows the geometry of a rheological experiment. A fluid lies between R0 and Ri, where Ri = 16.00 mm and R0 = 17:00 mm. The gap between the two cylinders can be modeled as two parallel plates separated by a fluid. The inner cylinder is rotated at 6000 rpm, and the torque is measured to be 0.03 Nm. The length of the inner cylinder is 33.4 mm. Determine the viscosity of the fluid. We can assume that the inner cylinder is completely submerged in the fluid, that the fluid is Newtonian, and that the viscous end effects of the two ends of the inner cylinder are negligible....
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