Difference between revisions of "Liquid Pressure Variation with Depth"
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| − | + | =Description of the Experiment= | |
| − | In this experiment, we | + | In this experiment, we study the density of four different liquids by taking into account that pressure variation with depth depends on it. |
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| − | + | <div class="toccolours mw-collapsible mw-collapsed" style="width:420px"> | |
| − | <div class="toccolours mw-collapsible mw-collapsed" style="width: | ||
'''Links''' | '''Links''' | ||
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
*Video: rtsp://elabmc.ist.utl.pt/scuba.sdp | *Video: rtsp://elabmc.ist.utl.pt/scuba.sdp | ||
| − | *Laboratory: | + | *Laboratory: Basic in e-lab.ist.eu[http://e-lab.ist.eu] |
*Control room: scuba | *Control room: scuba | ||
*Grade: ** | *Grade: ** | ||
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</div> | </div> | ||
</div> | </div> | ||
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| + | |||
| + | <swf height="550" width="480">http://www.elab.tecnico.ulisboa.pt/anexos/descricoes-flash/Scuba.swf</swf> | ||
| + | |||
=Experimental Apparatus= | =Experimental Apparatus= | ||
| − | + | [[File:Hidroestatica-montagem.jpg|thumb|Photo of the four tubes used in this experiment.]] | |
| − | + | In this experiment, there are four acrylic tubes with a diameter of thirty millimiters and one meter long. Each tube is filled with a different liquid: distilled water, salt water, glycerin and vegetable oil. Inside each tube there is a bell with an air bubble that allows pressure to be measured through a flexible tube, which is attached to a pressure sensor located outside the liquid. | |
| + | |||
| + | The change in volume can be estimated considering that each bell has a volume of approximately 2cm3. The hose has a cross-section of <math>1 mm</math> and a length of 1m, but it can easily be ignored. | ||
| + | <!-- (why?)(because the hose's volume doesn't change significantly with the change in pressure?). --> | ||
| − | The | + | The tubes are mounted vertically, and the four probes move simultaneously as established by the configuration chosen. The latter pauses for a second at each measuring point to allow the pressure to stabilize before measuring. The experiment will take longer if the user requests many points. |
| − | |||
=Protocol= | =Protocol= | ||
| − | The user must define the | + | The user must define the maximum and minimum height, as well as the number of samples to take across the path. This means that he can choose the initial and final depth of the probe's motion and obtain the data (each liquid's) on the variation of the pressure as depth changes. |
Afterwards, the data can be fitted to the following equation, and from that, the density of the various liquids can be determined. | Afterwards, the data can be fitted to the following equation, and from that, the density of the various liquids can be determined. | ||
| − | + | <math> | |
p(h) = p_0 + \rho g h | p(h) = p_0 + \rho g h | ||
| − | + | </math> | |
If multiple runs are made (with different starting and ending points), the experimental error will be lower. | If multiple runs are made (with different starting and ending points), the experimental error will be lower. | ||
| − | The following table shows | + | The following table shows the four liquid's density accepted values. |
{| border="1" | {| border="1" | ||
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| 0,92×103 | | 0,92×103 | ||
|} | |} | ||
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=Theoretical Principles= | =Theoretical Principles= | ||
The pressure exerted by a liquid is proportional to the weight of the fluid column, meaning that it depends not only on depth but also on density. This can be determined through the relation between pressure and depth. This relation can be expressed mathematically by: | The pressure exerted by a liquid is proportional to the weight of the fluid column, meaning that it depends not only on depth but also on density. This can be determined through the relation between pressure and depth. This relation can be expressed mathematically by: | ||
| − | + | <math> | |
p = p_0 + \rho g h | p = p_0 + \rho g h | ||
| − | + | </math> | |
| − | where p0 represents the pressure at the liquid's surface and ρ=m/V it's density, being <i>g</i> the local gravity | + | where p0 represents the pressure at the liquid's surface and ρ=m/V it's density, being <i>g</i> the local gravity acceleration and <i>h</i> the depth. |
Recalling Pascal's principle note that p0 is evenly distributed through the whole liquid. | Recalling Pascal's principle note that p0 is evenly distributed through the whole liquid. | ||
| + | |||
| + | |||
| + | =Links= | ||
| + | *[[Variação da Pressão num Líquido com a Profundidade |Portuguese Version (Versão em Português)]] | ||
Latest revision as of 21:10, 24 May 2015
Contents
Description of the Experiment
In this experiment, we study the density of four different liquids by taking into account that pressure variation with depth depends on it.
Links
- Video: rtsp://elabmc.ist.utl.pt/scuba.sdp
- Laboratory: Basic in e-lab.ist.eu[1]
- Control room: scuba
- Grade: **
<swf height="550" width="480">http://www.elab.tecnico.ulisboa.pt/anexos/descricoes-flash/Scuba.swf</swf>
Experimental Apparatus
In this experiment, there are four acrylic tubes with a diameter of thirty millimiters and one meter long. Each tube is filled with a different liquid: distilled water, salt water, glycerin and vegetable oil. Inside each tube there is a bell with an air bubble that allows pressure to be measured through a flexible tube, which is attached to a pressure sensor located outside the liquid.
The change in volume can be estimated considering that each bell has a volume of approximately 2cm3. The hose has a cross-section of 1mm
The tubes are mounted vertically, and the four probes move simultaneously as established by the configuration chosen. The latter pauses for a second at each measuring point to allow the pressure to stabilize before measuring. The experiment will take longer if the user requests many points.
Protocol
The user must define the maximum and minimum height, as well as the number of samples to take across the path. This means that he can choose the initial and final depth of the probe's motion and obtain the data (each liquid's) on the variation of the pressure as depth changes. Afterwards, the data can be fitted to the following equation, and from that, the density of the various liquids can be determined.
p(h)=p0+ρgh
If multiple runs are made (with different starting and ending points), the experimental error will be lower.
The following table shows the four liquid's density accepted values.
| Material | Accepted density (kgm3) |
|---|---|
| Water | 1,00×103 |
| Glycerine | 1,26×103 |
| Salty water | 1,03×103 |
| Vegetable oil | 0,92×103 |
Theoretical Principles
The pressure exerted by a liquid is proportional to the weight of the fluid column, meaning that it depends not only on depth but also on density. This can be determined through the relation between pressure and depth. This relation can be expressed mathematically by:
p=p0+ρgh
where p0 represents the pressure at the liquid's surface and ρ=m/V it's density, being g the local gravity acceleration and h the depth. Recalling Pascal's principle note that p0 is evenly distributed through the whole liquid.
