課程名稱︰流體力學 課程性質︰必修 課程教師︰楊鏡堂 開課學院：工學院 開課系所︰機械系 考試日期（年月日）︰2011/04/14 考試時限（分鐘）：忘了0rz 是否需發放獎勵金：是，謝謝 （如未明確表示，則不予發放） 試題 : The First Midterm Examination of Fluid Mechanics 1.(10 points) (a) What is the physical meaning of the Newton's Law of Viscosity? (8 points) (b) How do the viscosity and the kinematic viscosity of fluid, respectively, vary with the fluid temperature? (7 points) 2.(10 points) The reservoir shown in the figure contains two immiscible liquids of specific weights γA and γB , respectively, one above the other. γA > γB . Which graph depicts the correct distribution of gage pressure along a vertical line through the liquids? Why? ├──────┤ │ Liquid B │ ├→ ├→ ├→ ├→ │ │ ├─→ ├ → ├─→ ├ → ├──────┤ ├───→ ├─→ ├──→ ├─→ │ Liquid A │ ├─── → ├──→ ├── → ├─ → │ │ ├────→ ├───→ ├───→ ├──→ └──────┘ └──── →└────→ └─── → └── → 3.(10 points) A water bug is suspended on the surface of a pond by surface tension (water does not wet the legs). The bug has six legs, and each leg is in contact with the water over a length of 5mm. Please derive a correlation th show what the maximum mass the bug is, if it is to avoid from sinking? 蟲 ＿╱ ╲＿ 5mm 5mm 4.(10 points) 2.102 (pp. 90) An inverted test tube partially filled with air floats in a plastic water-filled soft drink bottle as shown in the attached figure. The amount of air in the tube has been adjusted so that it just floats. The bottle cap is securely fastened. A slight squeezing of the plastic bottle will cause the test tube to sink to the bottom of the bottle. Explain this phenomenon. ╭╮ ├┤ ╭╯╰╮ │╭╮│ ├┤├┤ │├┤│ ││││←Plastic bottle Test tube─┼┤││ ││││ │╘╛│ Water┼→ │ ╰──╯ 5.(15 points) A crude accelerometer is made from a liquid-filled U-tube as shown. Derive an expression for the acceleration a, in terms of liquid level difference h, tube geometry, and fluid properties. ┌┐ ┌┐ ││ ↓ →││← d ├┤─── ││ Liquid ││ h ││ density,ρ ││ ││ y ││ ───├┤ ↑ ││ ↑ ││ → └→x ││ │├─→ a │╰─────╯│ ╰───────╯ │←─ L ─→│ 6.(15 points) A Pitot-static probe connected to a water manometer is used to measure the velocity of air. If the deflection (the vertical distance between the fluid levels in the two arms) is 10 cm, determine the air velocity. Take the density of air to be 1.20 kg/m^3. ┌──────────┐ │ │ │ ┌─────┐ │ └┬┬┘ │ │ ││ │ │ ┌┤├┐┌──┐ │ │ │││└┤ │ │ │ │││┌┤ │ │ │ ││││└┐ │ │ │ Pitot-static ││││ │ │ │ │ probe ──→││││ ├─┤┬│ │ Air ││││ │ │││ │10cm → ╭─ ──────┘│││ │ │┴├─┤ → └─────────┘││ │ ╰─╯ │ → ┌──────────┘│ │ │←Manometer → ╰─ ─────────┘ ╰─────╯ 7.(15 points) A 2-m-diameter open cylinder tank contains water and has a hemispherical bottom. Determine the magnitude, line of action, and direction of the force of the water on the curved bottom. 8.(15 points) Water flows into the sink as shown at a rate of 7.0L/min. If the drain is closed, the water will eventually flow through the overflow drain holes rather than over the edge of the sink. How many 1-cm-diameter drain holes are needed to ensure that the water does not overflow the sink? Neglect viscous effect. 這個圖好難畫不想畫XD 就一個洗手台底下是塞住的，旁邊直徑1公分的小孔距洗手台頂端2.5公分。 --

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