Meen 344- HW 1

Meen 344- HW 1 - 4. A flow is described by the velocity...

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MEEN 344: HW Problem Set #1 1. Very small particles moving in fluids are known to experience a drag force proportional to speed. Consider a particle of net weight W dropped in a fluid. The particle experiences a drag force, kV F D = , where V is the particles speed. Express the distance required for the particle to accelerate from rest to 95 percent of its terminal speed in terms of g , k and W . 2. Derive the following conversion factors: (a) Convert a pressure of 1 psi to kPa. (b) Convert a volume of 1 liter to gallons. (c) Convert a viscosity of 1 lbf•s/ft 2 to N•s/m 2 . 3. A velocity field is specified as, j bxy i ax V ˆ ˆ 2 + = G , where a = 1 m -1 s -1 , b= -5 m -1 s -1 , and the coordinates are measured in meters. Is the flow field one-, two-, or three-dimensional? Why? Calculate the velocity components at the point (2, ½). Develop an equation for the streamline passing through this point. Plot several streamlines in the first quadrant including the one that passes through the point (2, ½).
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Unformatted text preview: 4. A flow is described by the velocity field, j b i at V + = G , where a = 0.3 m/s 2 and b = 2.2 m/s. At t = 2s, what are the coordinates of the particle that passed through point (2, 1) at t = 0? At t = 3 s, what are the coordinates of the particle that passed through point (2, 1) at t = 2 s? Plot the pathline and streakline through point (2, 1) and compare with the streamlines through the same point at the instants t = 0, 1, and 2 s. 5. A concentric cylinder viscometer may be formed by rotating the inner member of a pair of closely fitted cylinders (see Fig. below). The annular gap is small so that a linear velocity profile will exist in the liquid sample. Consider a viscometer with an inner cylinder of 4 in. diameter and 8 in. height, and a clearance gap width of 0.001 in., filled with water at 90 o F. Determine the torque required to turn the inner cylinder at 400 rpm....
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