课程名称︰流体力学 课程性质︰机械系大二必修 课程教师︰马小康 开课学院：工学院 开课系所︰机械系 考试日期（年月日）︰105/3/29 考试时限（分钟）：65 min 试题 : (20%) (1) Please derive the rate of rotation vector http://i.imgur.com/e0mWjfA.jpg From the following figure. http://i.imgur.com/KQQ7JW2.jpg (15%) (2) A 30-ton, 4-m-diameter hemispherical dome on a level surface is filled with water, as shown in the rolling figure. Someone claims that he can lift this dome by making use of Pascal's law by attaching a long tube to the top and filling it with water.Determine the required height of water in the tube to lift the dome. Disregard the weight of the tube and the water in it. The density of water is 1000kg/m^3 throughout. http://i.imgur.com/wfPnxtL.jpg (20%) (3) A 3-m diameter, 7-m-long cylindrical tank is completely filled with water. The tank is pulled by a truck on a level road with the 7-m-long axis being horizontal. Determine the pressure difference between the front and back ends of the tank along a horizontal line when the truck (a) accelerates at 3 m/s^2 and (b) decelerates at 3 m/s^2. http://i.imgur.com/fDSq5qP.jpg (15%) (4) Consider fully developed Couette flow-flow between two finite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary. The flow is steady, incompressible, and two dimensional in the xy- plane. The velocity field is given by http://i.imgur.com/lghV0y7.jpg (a) Is this flow rotational or irrotational? (b) If it is rotational, calculate the vorticity component in the z-direction. (c) Do fluid particles in this flow rotate clockwise or counterclock wise? (10%) (5) Bsys is linear momentum mV of a system, please use the RTT to derive the equation of conservation of linear momentum for a control volume. (20%) (6) A 1.2-mm-diameter tube is inserted into an unknown liquid whose density is 960 kg/m^3, and it is observed that the liquid rises 5 mm in the tube making a contact angle of 15 degree. Determine the surface tension of the liquid. http://i.imgur.com/Wg2yyPj.jpg --

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