Rotating Hydraulic Jump 轉動的水躍

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1 Rotating Hydraulic Jump 轉動的水躍
輔導教授：楊宗哲 指導老師：李文堂 學生：呂軒豪

2 Introduction 　 When a fluid jet falling vertically strikes a horizontal plate, fluid is expelled radially, and the layer generally thins until reaching a critical radius at which the layer depth increase abruptly. This phenomenon is called the Circular Hydraulic Jump .

3 1-2 Predictions for the jump radius based on inviscid theory were presented by Lord Rayleigh(1914). The dominant influence of fluid viscosity on the jump radius was elucidated by Watson(1964). Ellegaard(1998)identified that a striking in stability may transform the circular hydraulic jump into regular polygons.

4 1-3 We find when a fluid jet strikes to a container, at the moment when the flow over the container’s boundary the circular hydraulic jump transform into rotating polygons, this is referred to as Rotating Hydraulic Jump. 影片 影片(慢放)

5 Background Rayleigh regarded hydraulic jump as a discontinuity (shock). Close to the jet the fluid layer is thin and the motion is rapid, further away it is an order of magnitude thicker and moves correspondingly slower.

6 2-2 Rayleigh’s shock conditions imply that the fluid before and after jump are respectively “supercritical” and “subcritical” , which means the average velocity is respectively larger and smaller than the small amplitude wave

7 2-3 When a jet of viscous ethylene glycol strikes a container, a circular hydraulic jump is formed. As height of hext is increased, vertical rollers are formed surrounding the jump. The roller is formed owing to velocity gradient of the fluid layer. The vertical structure of flow now plays a crucial role, it produces multiple vortices around the jump. The vortex produces a horizontal pressure gradient : angular velocity of the roller. ; R= hext/2 , =density of the fluid .

8 2-4 液體旋轉示意圖： 上層液體向外流 下層液體向外流且受到較大的黏滯阻力

9 2-5 2/3秒後 2/3秒後 影片1 影片2

10 控制濃度固定(及黏滯係數固定)、流量固定，改變液深hext ，探討邊數和hext 關係。影片
2-6 控制濃度固定(及黏滯係數固定)、流量固定，改變液深hext ，探討邊數和hext 關係。影片 控制流量固定、液深固定，改變溶液濃度，探討邊數和黏滯係數的關係。 控制液深固定、濃度固定，探討邊數和流量的關係。

11 We measure the Reynold number of Rotating Hydraulic Jump.
2-7 We measure the Reynold number of Rotating Hydraulic Jump. We assume that N: the polygon number. : kinematical viscosity of fluid. Q: flow rate. We do experiment to find a,b,c. And know the dependence of number of polygon.

12 最近準備進行工作 用可以改變高度的容器，重做深度對邊數的實驗，在每一個穩定的多邊形旁放入膠片量出v，求出Vortex之 ，算出Vortex大小對邊數的關係。 架高盤子(透明盤)，液體中加入鋁粉(不起化學變化)由底端拍出較清晰的Vortex。 數據分析整理。

13 References 彭黃勝、范治明、蔡國棟和李志強：水牆，中華民國中小學科學展覽第二十一屆至三十屆優勝作品專輯　　　國立台灣科學教育館編印，頁 周雨剛等四人：利用因次分析法研究圓形水躍的變因，中華民國第四十六屆中小學科學展覽會作品說明書。 Clive Elligard, “Creating corners in kitchen sinks”, Nature, Vol.392, P , 1998. Thomas R. N. Jansson, “Polygons on a rotating fluid surface”, Physics Review Letters,174502, 2006(May)