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# Download ME 750A: Spring 2005 HW Due on Wednesday, March 9

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Transcript

ME 750A: Spring 2005 HW Due on Wednesday, March 9 1. It has been suggested that the velocity field near the core of a tornado may be approximated by V = – er (q/r) + e (K/r). Does this represent incompressible flow? Is this an irrotational flow? [FM 5.16, 5.78] 2. An incompressible fluid of negligible viscosity is being pumped through two tiny holes at the centers of two parallel discs into the narrow gap (= h) between the disks. The fluid has only a radial velocity component. The pressure at the edge of the gap (at r = R) is 1 atm. For a total flow-rate of Q m3/s, plot the variation in pressure (p) in the gap as a function of r. [FM 6.10] R r h p= 1 atm Q m3/s 3. Consider the flow-field obtained by combining a doublet and a uniform flow in class. Choosing an appropriate free stream velocity and a cylinder radius, plot the stream function and potential function around the cylinder with “line-contours” using a software such as MATLAB (available in most computers in our labs). 4. Consider a long section of a large pipe half buried into the ground. The radius of the pipe is 3 m. A wind of 100 km/hr is blowing perpendicular to the axis of the pipe, and the static pressure and temperature of the air are 100 kPa and 290 K, respectively. Assuming a steady, inviscid, and incompressible flow, estimate the force (per unit length) tending to lift the pipe off the ground. [FM 6.66] 5. A flow field is represented by the stream function = x2 – y2. Find the corresponding velocity field (express the vector V, or its components u and v, as a function of x & y). Show that this flow field is irrotational and obtain the corresponding potential function. [FM 6.83]