低雷諾數圓形及多邊形水躍的研究
打開水龍頭，水鉛直落到正下方的水平板時形成圓形水躍。我們實驗研究20＜Nr＜150 的低雷諾數圓形水躍的變因，探討圓形水躍半徑和流量、出水口高度、以及液體黏滯係數間的關係。改用高黏滯係數的液體（4：1 的乙二醇水溶液），鉛直落入板上方深h 的相同液體時，先形成圓形，h 漸大時形成環形圓紋曲面，再加大h，形成多邊形水躍，內外圍同方向旋轉，轉速ω；液中加水，黏滯係數高於及低於某定值，多邊形都消失，側面觀察，外圍液體作鉛直面旋轉。將水平板改置於旋轉盤上方，使高黏滯係數（4：1）的乙二醇水溶液鉛直落入板上方形成多邊水躍，逐漸加快旋轉盤的轉速至 ω 時，多邊形都消失；逐漸減少乙二醇的濃度，至完全用水實驗，亦有多邊形出現，我們認為；平板上方的液體的轉動是非圓形水躍的成因。When a jet of water falls vertically on to a horizontal plate, it spreads out rapidly in a thin layer until it reaches a critical radius at which the layer depth increases abruptly. This phenomenon commonly called the circular hydraulic jump. We study the variations of the circular hydraulic jump radius, as a function of volume flow rate of the jet, the drop height, and the viscosity of the fluid at low Reynold numbers (20＜Nr＜150). When a jet of ethylene-glycol mixed with water (the kinetic viscosity is 10 times of water) falls on to a horizontal plate which is immersed in the same liquid with height h. We find the circular state frequently undergoes spontaneous breaking at its axial symmetry into a stationary polygonal shape. Rather than displaying the weak angular deformation generally seen in fluids, the jump forms clear corners and edges that are often straight. Several of these polygon formations show consistency in height h. And we find the polygon structure rotates in a horizontal motion. When a jet of water falls on to a horizontal plate, and the plate is rotated by a motor ,we find the axial symmetry of the free surface of circular hydraulic jump is spontaneously broken a various number of cornered polygonal shapes. We study the number of corners as a result of the volume flow rate of the jet, the drop height and the viscosity of the fluid in the experiment. And the frequency of rotation of the plate is taking into consideration.
橡膠鍵鏈結構與自由能的關係
受應力拉伸時，橡膠溫度明顯上升；縮放回原長，橡膠溫度驟降。由文獻得知橡膠內部具有特殊的鍵鍊結構，在一般的情況下，交鏈分子糾結成一團，狀態複雜；受外力拉伸時，交鏈分子依橡膠長度之增加而伸展，排列較為整齊，狀態之複雜度減小。根據熱力學第一定律，當內能變化為零，則外力作功會造成能量變化。在定溫之下，橡膠內能變化為零，當其受應力拉伸，使其內部交鏈分子排列複雜度降低，造成橡膠熵值減小，而有能量（dQ=TdS）的釋出。測量此一能量dQ 變化，即可計算出熵與狀態數之變化The temperature of rubber rises as it is stretched, its temperature comes back again while it restores to its original length. It is known that the rubber is consisted of long-chain molecules, the long-chain molecules strangle each other at normal state, however, they become more order when the rubber is stretched. Based on the 1st law of thermodynamics dU=dQ+dW, The deformation caused by applied force supplies energy to the rubber and reduce its entropy, the heat dQ (=TΔS) released by the reduction of entropy causes the temperature rise of rubber as dU=0. We report the study on the correlation of thermal properties and the molecular network in rubber, from the measurements of temperature change, the changes of entropy and the changes of states’ number were estimated.
培地茅根系碎形維度及抗拉力
本研究首先確認培地茅根系具有碎形之基本特性，再進一步以方格覆蓋法計算之碎形維度來分析培地茅根系在不同時間及環境因素下的生長。主要探討碎形維度與抓地力之關係，並設計以實際根系模型來加以模擬，並發展出一可描述抓地力與碎形維度及深度關係的方程式。我們的結論為：（1） 經由方格覆蓋法之計算，培地茅此種植物，不管是整個根系或單枝根，均具有碎形基本特性，適合進一步實驗研究。（2） 碎形維度會隨著培地茅生長時間增長而增加，並且在自然光照及30℃左右會有較大值，而種植於土壤中根系發展較廣，其碎形維度比種植於沙耕中來的高。（3） 實驗結果顯示，抓地力受碎形維度及根系深度兩因素影響，而培地茅根系對土壤有較強的抓地力，推測是因為兩者根系皆又深又長，土中培地茅根碎形維度較大，接觸面積較廣，而又進一步以矽膠模型做實驗驗證。（4） 矽膠模型之目的在於減少難控制之自然變因，實驗之前，測量了根系模型與洋菜凍之基本性質，實驗結果顯示抓地力與碎形維度及根系深度皆呈正向關係，可用數學方程式加以描述。This project is mainly a research into the fractal dimension of the vetiver root system. First, we confirm the vetiver root system has the basic fractal structure by checking its self-similarity, then using box-counting method to calculate fractal dimension. We begin with a fundamental investigation into the relation between different time and environmental factors and fractal dimension. Then we move to our main point: the relation between fractal dimension and its pull-out resistance. In the next step, we make a fundamental silicon model, simulating the vetiver root system, to continue our experiments. In the end, we develop a formula that can describe the relation between its pull-out resistance, roots depth and fractal dimension. Here are our conclusions: （1） After using box-counting method to calculate fractal dimension, we discover that not only the whole vetiver root system but also a single vetiver root has the basic fractal structure. （2） Fractal dimension increases when time goes on. Also the value of fractal dimension is larger in natural sunlight and the temperature at about 30℃.The vetiver root system grows more widely in soil than those in sand. That’s why it has larger fractal dimension. （3） Data shows that its pull-out resistance is influenced by both fractal dimension and the depth of the roots. The vetiver roots, in the meantime, show greater pull-out resistance than some other plants. Thus we draw the assumption that the vetiver root system grows deep and wide, and in natural soil its fractural dimension is greater and reaches greater area. Therefore, a silicon model is constructed to further confirm the findings of the experiment.（4） The design of the silicon model is to reduce the uncontrollable variables in nature. Before starting the experiment, we measured some basic characteristics of the silicon model, including density and angle of repose. Furthermore, the experiment demonstrates that pull-out resistance and fractural dimension have a commensurate mutual relation: the stronger the pull-out resistance, the wider the fractural dimension and the deeper the root system. Thus we derive a math formula to describe this relation.
全民攻笛
本實驗主要是研究閉管駐波的發聲原理。何謂「閉管駐波」？就是一個管子在相同長度下，用不同的力道吹，會有不同音高的聲音產生，這些音被稱為「諧音」。原管長所能發出的最低頻率稱作「第一諧音」，第二低的聲音稱作「第三諧音」，依此類推。在簫的演奏上，只要按住同樣的孔，用較大的力量吹，也同樣會發出較高的音；同樣地，在曲笛的演奏技巧上，有平吹、急吹等分別。為什麼吹越用力，音就越高呢？如果現在拿一個大吸管吹（要裝活塞），你會發現，只有在特定的位置（角度）下，才能吹出聲音。那麼，角度對於聲音也有影囉？這些現象的幕後黑手，就是在管口產生的「渦流」，渦流頻率也會隨著風速而增加；而且，渦流的頻率在特定風速下，會有特定的範圍。經由實驗可以大略歸納出，影響閉管駐波的三個主要變因，分別是「風速」、「風吹角度」、及「吹口至管口的距離」。吹得越急，風速就越快，渦流頻率越高，越易使諧音躍遷；吹的角度越小，越易產生渦流，亦易引發聲音；吹的距離越小，渦流越不?定，越易產生其他的擾動。以上就是本實驗的概略。This project is aimed to fine out how the closed tube can produce a sound. We know what harmonics are. When we hold a big straw and blow with increasing strength (the bottom should be in water), it will generate a higher sound. The high sound is called “harmonic”. The lowest sound it can make is “the first harmonic”, the second lowest sound is “the third harmonic”, and so forth. Likewise, when we press the same key on vertical bamboo flute with increasing strength, it’ll also produce a higher sound. But why do we use the strong air stream to blow the tube to cause the tone to transfer? Now let’s blow a straw flute. You will find that you need to blow in the particular position, and then the sound will be produced. So, is there any relationship between the blowing angle and the frequency? Actually, all these sound are produced by “vortex in the mouthpiece.” The frequency of vortex will increase with the wind speed. Moreover, the frequency of vortex has a range. In sum, the higher the wind speed is , the higher the frequency of the vortex is , and leads to the higher frequency of the sound. The smaller the blowing angle is, the easier the vortex will be produced; the easier the frequency will be made. The smaller the distance between the blowing angle and the frequency is, the more unstable the frequency will be. The above is the most important research in this project.
Comfortable Equipment for Pedestrians
The phenomenon of pedestrians nowadays is still found. Due to frequent walking, sometimes our legs feel tired and hard to move. This is become the basis for developing tools that are convenient for pedestrians. An easy tool for humans is needed for our activities, especially walking. The Synergy between our hands and feet provides a big and significant contribution to the appliance. Normally, the movement of our hand gets along with its motion with a different side of the foot. When the right foot step, then the left hand is swung forward, and vice versa. The tools can be developed by utilizing a variety of systems. The system includes the tools concentric wheel and axles system, spring system, and pulley system. The concentric wheel and axles system is useful in controlling the rope. Movement on the rope could activate the entire system on the appliance. Wheel that related with the hand is three times bigger than wheel that related with pulley that is applied on foot. Spring system is able to lighten the pressure of the foot with a given upward force, and able to provide downward force when the spring returned to its original position. While the pulley system on the tool used to provide mechanical advantage two times is also useful to lighten the pressure of the foot when walking. The tools can be designed with simple, and able to provide benefits to users. By trial and error, it shows that the tool is able to lighten human’s activity when they walk. The tool can be able to lighten the leg’s load by utilizing arm muscles work. Utilization of the arm muscles which helps to ease the pressure of the foot can provide more benefits. One of them is that it can strengthen the arm strength, so the tool can be used as sport equipment. Utilization of the tool can also be reserved for special people who have difficulty in walking due to an accident or birth with leg defect.