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8.2 A common type of viscosimeter for liquids consists of a relatively large reservoir with a very slender outlet tube, the rate of outflow being determined by timing the fall in the surface level. If oil of constant density flows out of the viscosimeter shown at the rate of 0.273 cm3/s, what is the kinematic viscosity of the fluid? The tube diameter is...
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8.3 A thin rod of diameter d is pulled at constant velocity through a pipe of diameter D. If the wire is at the center of the pipe, find the drag per unit length of wire. The fluid filling the space between the rod and the inner pipe wall has density r and viscosity μ.
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8.4 Two immiscible fluids of different density and viscosity are flowing between two parallel plates. Express the boundary conditions at the interface between the two fluids.
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8.5 Fluid flows between two parallel plates, a distance h apart. The upper plate moves at velocity, v0; the lower plate is stationary. For what value of pressure gradient will the shear stress at the lower wall be zero?
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8.6 A continuous belt passes upward through a chemical bath at velocity v0 and picks up a film of liquid of thickness h, density, ρ, and viscosity μ. Gravity tends to make the liquid drain down, but the movement of the belt keeps the fluid from running off completely. Assume that the flow is a welldeveloped laminar flow with zero pressure gradient, and that the atmosphere produces no shear at the outer surface of the film.
a. State clearly the boundary conditions at y = 0 and y = h to be satisfied by the velocity.
b. Calculate the velocity profile.
c. Determine the rate at which fluid is being dragged up with the belt in terms of μ, ρ, h, v0.
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8.7 Oil is supplied at the center of two long plates. The volumetric flow rate per unit length is Q and the plates remain a constant distance, b, apart. Determine the vertical force per unit length as a function of the Q, μ, L, and b.
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8.8 A viscous film drains uniformly down the side of a vertical rod of radius R. At some distance down the rod, the film approaches a terminal or fully developed flow such that the film thickness, h, is constant and vz = f (r). Neglecting the shear resistance due to the atmosphere, determine the velocity distribution in the film.
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8.9 A Newtonian fluid in continuous, incompressible laminar flow is moving steadily through a very long 700-m, horizontal pipe. The inside radius is 0.25 m for the entire length, and the pressure drop across the pipe is 1000 Pa. The average velocity of the fluid is 0.5 m/s. What is the viscosity of this fluid?
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8.10 You have been asked to calculate the density of an incompressible Newtonian fluid in steady flow that is flowing continuously at 250°F along a 2500-ft pipe with a constant diameter of 4 in. and a volumetric flow rate of 2.5 ft3/s. The only fluid properties known are the kinematic viscosity, 7.14 10–6 ft2/sec, and surface tension 0.0435 N/m. Assuming that the flow is laminar and fully developed with a pressure drop of 256 lbf/ft2, calculate the density of this fluid if the no-slip boundary condition applies.
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