四 ' Whal is the diffcrcncc between the Bernoulli equation and the Navicr-Stokcs Equations ? (10%)

(9) The drag force, F, on a smooth sphere depends on the relative velocity, V，the sphere diameter* D, the fluid density, p, and the fluid viscosity, Obtain a set of dimensionless groups that can be used to correlate the experimental data. (Note: dimensional analysis) (20 )

一、What is unifomi flow ? What is steady flow ? Given an example of non-uniform flow. (10%)

二、 What is laminar flow ? What is turbulent flow ? Why the Reynolds number can be used to tell the flow is laminar or lurbulcnt. (10%)

二、 What is inviscid flow ? Arc the flows naturally inviscid ? (5%)

【已刪除】五、 Water flows steadily past a porous flat plate. Constant suction is applied along the porous scction. The velocity profile at section cd is shown below. Evaluate the mass flow rate across scction be, (20%) 

六、 An airship is lo operate at 20 m/s in air at standard conditions (the pressure is 101 kpa). A model is constructed lo 1/20 scalc and tested in a wind tunnel at Ihc same air Icmpcralurc lo determine the drag. What criterion should be considered lo obtain dynamically similarity ? If the model is tested at 75 m/s, what pressure should be used in the wind tunnel ? If the model drag forcc is 250 N, what will be the drag of the prototype ? (25%)

【已刪除】七、 A metal container 0.6 m high, with an inside cross-sectional area of 0.09 m2, has a mass of 2.5 kg when empty. The container is placed on a scalc and water flows in llirough an opening in the top and out through the two equal area openings in ihc sides, as shown in the diagram. Under steady conditions, the height of Ihc water in llic tank is 0.57 m. Dclcrminc ihc reading on Ihc scalc. The density of water is 1000 kg/m3. (20%)

【已刪除】12.淡疆保險公司隨機抽出1200位大學生，並針對他們對人壽保險商品的偏好的做問卷調查，並得出如下的偏好列聯表  試在α = 0.05的顯著水準下，檢定大學生對人壽保險商品的偏好，是否存在性別差異? (11%)

【已刪除】1. Let A=  • Find det(A). (10 points) 

2. LetT: R3 → R2 be a linear transformation and T(l，0，0)=(l，-2)，T(l,l,0)=(l,3), T(0,0，l)=(2，-1). Find T(x，y，z). (10 points)