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）︰2007/12/19
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 II
1.Water enters a tank of diamater Dr steadily at a mass flow rate of min.
An orifice at the bottom with diameter Do allows water to eacape. The
orifice has a rounded eterance, so the frictional losses are negligable.
If the tank is initially empty,(a)(8)determine the maximum height that the
water wull reach in the tank and (b)(12)obtain a relation for water height
z as a function of time.
╴╴
∥m﹋
￣￣ ﹋ ╱￣￣￣╲
╲╴╴╴╱
｜ ｜
｜﹉Dr﹉﹉｜
｜ ∣
╱￣Do￣╲
╲╴╴╴╱
︴︴
2.(10)(a)(8) Difine static,dynamic,hydrostatic pressure.Under what condition
is their sum constant in a flow stream?(b)(2)Difine stagnation pressure?
3.(15)A 60-kg ice skater is standing on ice eith ice skates(negligable
friction).She is holding a flexiible hose (essentially weightless)that
directs a 2-cm-diameter stream of watter horizontally parallel to her skates.
The water velocity at the hose outlet is 10 m/s.If she is initially standing
still, determine the velocity of the skater and the distance she travels in
5s.
4.(25)Alarge lawn spinkler with four indentical arms is to be converted into
a turbine to generate electric power by attaching a generator to its
rotating head.Water enters the sprinkler from the base alomg the axis of
rotation at a rate of 20L/s and leaves the nozzles in the tangential
direction the sprinkler rotates at a rate of 300 rpm in a horizontally plane.
The diameter of each jet is 1 cm,and the normal distance between the axis
of rotation and the center of each nozzle is 0.6 m.(a)(15)Estimate
the eletcric powew produced.(b)(10)At what rotational rate, a maximum power
can be generated by the generator?
5.(20)Consider steady,laminar,fully developed,two dimensional Poiseuille
flow-flow between two infinite parallel plate seperated by distance h,
with both the top plane and bottom plane stationary,and a forced pressure
gradient dP/dx driving the flow as illustracted in Fig,(dP/dx is constant
and negative.)The flow is steady,incompressible,and two-dimensional in the
xy-plane.The flow is also fully developed,meaning that the velocity profile
does not change with downstream distanse x.Because of the fully developed
nature of the flow,there are no inertial effects and density does not enter
the problem.It turns out that u ,the velocity component in the x-direction,
is a function of distance h,pressure grafiebt dP/dx,fluid viscosity μ
and vertical coordinate y.Perform a dimensional analysis(showing all your
works),and generate a dimensionless relatioship between the given varuables.
╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴
↑￣￣￣￣￣ .
｜→ . u(y)
μ ｜ → .
h ｜ → . umax y
｜ → . ↑
↓╴╴╴╴╴｜ →.╴╴╴╴╴╴╴╴╴｜╴╴x╴╴╴╴╴╴╴╴╴╴╴
6.(15)Consider the steady,laminar,fully developed, two dimensional Poiseuille
flow of Prob(5).The maximum velocity umax occurs at the center of the
channel.(a)Generate a dimensionless relationship for umax as a function of
distance between plates h,pressure gradient dP/dx, and fluid viscosity μ
(b)If the plate seperation distance h is doubled,all else beig equal,by
what factor will umax change?(d)How many experiments are required to
describe the complete relationship between umax and the other parameters
in the problem?
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那假設有一件事情維持現狀只會更慘，可是你又不知道該怎麼改善它時，你會怎樣做？
什麼事呀，是指日本的經濟嗎？
無視我的詢問，朝倉依舊笑著繼續說
難道你不會想說先不管結果如何，一切做了再說嗎？反正再繼續下去也不會有任何變化。
恩，說不定會吧！
就是阿！ 涼宮春日的憂鬱 政治魔人請勿亂入
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