# fluids hw7 - CK Water may be considered to ﬂow without...

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Unformatted text preview: CK Water may be considered to ﬂow without friction through-the siphon. The water ﬂow rate is 0.03 m3fsec, its temperature is 20 C, and the pipe diameter is 75 mm. Compute the maximum allowable height, h, so that the pressure at pomt A is above the vapor pressure of the water. An open-circuit wind tunnel draws in air from the atmosphere through a. well- contoured nozzle. In the test section, where the ﬂow is straight and nearly uniform, a static pressure tap is drilled into the tunnel wall. A manometer connected to the tap shows that static pressure within the tunnel is 45 mm of water below atmos henc. Assume that the an IS incompresmble, and at 25 C, 100 kPa (abs). Calculate the air speed in the wind—tunnel test section. a A rectangular microcircuit “chip” ﬂoats on a thin layer of air, It : 0.5 mm thick, above a porous surface. The chip width is b = 20 mm, as shown. Its length, L, is very long in the direction perpendicular to the diagram. There is no flow in the z direction. Assume ﬂow in the x direction in the gap under the chip is uniform. Flow is incompressible and frictional effects may be neglected. Use a suitany chosen control volume to show that U (x) = qx/h in the gap. Find a genera] expression for the acceleration of a ﬂuid particle in the gap. Evaluate the maximum acceleration. Obtain an expression for the pressure gradient, tip/5x, and sketch the pressure distribution under the chip. Show palm on your sketch. Is the net pressure force on the chip directed upward or downward? Explain. For the conditions shown, with q = 0.06 m3/sec/m, estimate the mass per unit length of the chip. k __ Porous surface Consider the ﬂow ﬁeld represented by the stream function (,0 = ley +17. Is this a possible two-dimensional, incompressible ﬂow? A velocity ﬁeld is represented by the expression 1} = (Ax ~B)i+Cyf+Dtk. where A = 2 sec", B = 4 m-sec", D = 5 m-sec'z, and the coordinates are measured in meters. Determine the proper value for C if the ﬂow ﬁeld is to be incompressible. Calculate the aceeleration of a fluid particle located at point (x y) = (3, 2). Sketch --..-u- An aircraft ﬂies due North at 300 mph ground speed. Its rate of climb is 3003 fti'rnin. The vertical temperature gradient is —3 F per 1000 ft of altitude. The groun temperature varies with position through a cold front, falling at the rate of 1 F per mile. Compute the rate of temperature change shown by a recorder on board the aircraft. Which of the following sets of equations represent possible three-dimensional in- compressible ﬂow cases? (a) u =x+y+z2; v =x—y+z; w=2xy+y2+4 (b) u = xyzr; v = -xyzr2; w = (zzﬂxxt2 - yr) (:3) u = y2 +2xz; v :--2yz +x2yz; w = %1222+x3y4 Incompressible ﬂow around a circular cylinder of radius a is represented by the stream function [it =-Ur sine + U a2 sin 8/ r. where U represents the freestream ve- locity; Obtain an expression for the velocity ﬁeld. Show that it; = 0 along the circle - r = a. Locate the points along :- = a where M = U. Consider a ﬂow with velocity components at = 0, v =—y3 * 4z, and w = 3ylz. (a) Is this a one—, two—, or three~dimensional flow? (b) Demonstrate whether this is an incompressible or compressible ﬂow. (c) If possible, derive a stream functidn for this flow. ...
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## This note was uploaded on 02/27/2010 for the course ASE 320 taught by Professor Raman during the Fall '08 term at University of Texas at Austin.

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fluids hw7 - CK Water may be considered to ﬂow without...

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