Wave Structures on A Jet Entering the Bulk Liquid. He Yijun; Li Youxi: Zhu Zijia; Lin Liang; Corkill Ashley Christine
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1 Wave Structures on A Jet Entering the Bulk Liquid He Yijun; Li Youxi: Zhu Zijia; Lin Liang; Corkill Ashley Christine
2 Introduction The formation of capillary waves on fluid pipes Our goal is to describe the formation of stationary fields of capillary waves on a fluid jet entering a bulk liquid. The waves are affected by the velocity of the jet, the height of the jet,the size of the stream, and the surface tensions of the fluids.
3 Picture of the jets with capillary waves
4 Cases-there are four primary cases to consider 1. A fluid jets enters a reservoir containing the same fluid. 2. A fluid jets enters a reservoir containing a fluid with a smaller surface tension. 3. A fluid jets enters a reservoir containing a fluid with a greater surface tension. 4. A fluid jet meets a fluid(air) with no surface tension.
5 Past research There is a paper about fluid pipes by Maattew J. Hancock and John W. M.Bush. Show lots of information about capillary waves. So we will be comparing our results to those paper.
6 Derivation of formulas Simple formula Fourier transform formula
7 ω is angular frequency σ is surface tension number is density of the water ρ1 is density of the air, in this formula, it is nearly equal zero K is wavenumber and it is equal
8 Simple formula
9 Fourier transform formula
10
11 The procedure about this experiment
12 Equipment for this experiment 1. cup with volume 2. stopwatch to measure time 3. rule to measure the length of waves 4. camera to get pictures.
13 Procedures of the experiemnt: 1.we need to measure out the volume of the cup, so we can find out the capacity of the water. 2. use the stop-watch to measurement the time. 3. after we record the time about the flux, we need to move the cup until we can see the waves clearly. 4. put the ruler on the side, and the use camera to take pictures. 5. repeat those steps more times and take pictures for different length of waves.
14 Procedure to measure wave length and cross sectional area. 1. use ruler to find out the waves length in pictures. 2. use ruler to get the proportion about the ruler in pictures. 3. use proportion to find out the real length about the waves. 4. repeat those steps and find out the radius about the cross sectional in different high. 5. After all those steps,we will use the measurements to do following test.
15 result of experiment 1. time 2. cup volume: 497 cm^3 v = ((diameter/2)^2) * pi * height of cup 3.wave 4.k: water wave cross section area 03/11/14
16 get the value of flow flow = volume of cup / time 03/11/14
17 get the value of velocity velocity = flow / k 03/11/14
18 the realtionship between velocity and wave 03/11/14
19 the graph of wave v.s velocity 03/11/14
20 calculate the value of a 03/11/14
21 use the function of experiment 03/11/14
22 the result of a from the function of experiment, we can get the result of a have a range. from to /11/14
23 use the function of experiment velocity = a / (wave)^0.5 get the average value of a, a = So: surface tension = density of water * a^2 / 2 pi And the surface tension is about 72 mn/m. 03/11/14
24 experiment error personal error(photo, feeling and reflect, calculation) temperature lighting 03/11/14
25 More about Surface Tension
26 The Relationship between Temperature and Surface Tension Surface tension Contraction force caused by the imbalance of molecular attraction in liquid surface layer. When the liquid temperature increases, the molecular motion will be enhanced.
27 The Relationship between Temperature and Surface Tension Then the average distance between liquid molecules will be increased The attraction between liquid molecules decreases. Major Assumption: Surface tension is inverse proportional to temperature.
28 Future Work Capillary Rise Method: - Using a circular capillary to dip into water - water wets the walls and rises in the capillary to get a balance level - The surface is a hemispherical concave.
29 Future Work - On the surface, there is an equilibrium with gravity force and surface tension - To derive the equation of surface tension from these balance forces - Compare the result of experiment to verify the relationship between temperature and surface tension
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