課程名稱︰流體力學
課程性質︰機械系大二必修
課程教師︰馬小康
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰105/3/29
考試時限（分鐘）：65 min
試題 :
(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