課程名稱︰流體力學
課程性質︰必修
課程教師︰丁肇隆
開課學院：工學院
開課系所︰工程科學與海洋工程學系
考試日期（年月日）︰2007/07/11
考試時限（分鐘）：14:20-16:00
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Fluid Mechanics Midterm Exam I
1. A thin 20-cm*20-cm flat plate is pulled at 1m/s horizontally through
a 3.6-mm-thick oil layer sandwiched between two plates, one stationary
and the other moving at a velocity of 0.3m/s. The dynamic viscosity of oil
is 0.027 Pa*s. Assume the velocity in each oil layer to vary linearly,
(a)plot the velocity profile and find the location where the oil velocity
is zero and (b) determine the force that needs to be applied on the plate
to maintain this motion. 20%
=================================================
↑
1 mm
------------------------------------------------- → 1 m/s
2.6 mm
↓
================================================= ← 0.3 m/s
2. A 1.9-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度. Determine th surface of the liquid.
10%
3. Two water tanks are connected to each other through a mercury manometer
with included tubes. If the pressure difference between the two tanks is
20 kPa, calculate A and θ 15%
┌─┐
│ │ ───
└─ ＼ a ┌─┐
＼＼ ── │ │
＼＼ 2a ╱ ─┘
＼＼ ╱╱
＼＼─ ╱╱
＼＼╱╱
＼╱ θ
4. A 1-m diameter, 2 m high vertical cylinder is completely filled with
gasoline whose density is 740 kg/m^3. the tank is now rotated about
its vertical axis at a rate of 90 rpm, while being accelerated
upward at 5 m/s^2. Determine (a) the difference between the pressure
at the centers of the bottom and top surfaces and (b) the difference
between the pressures at the center and the edge of the bottom surface.
20%
5. A general equation for a two-dimensional velocity field that is linear
in both spatial direction (x and y) is
V=(u,v)=(U+a1x+b1y) i +(V+a2x+b2y) j
where U and V and the coefficients are constants.
(a) Is the flow field steady?why? 3%
(b) At what condition, the flow is incompressible? 5%
(c) Calculate the x-and y-components of the acceleration field? 10%
(d) Calculate the shear strain rate in the xy-plane. 7%
6. Please give the definitions of streamlines, pathlines, streaklines,
incompressible flow and irrotaional flow. 15%
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