Difference between revisions of "Liquid Pressure Variation with Depth"

From wwwelab
Jump to navigation Jump to search
(Versão inicial)
 
m (Text replacement - "\[" to "<math>")
 
(24 intermediate revisions by 4 users not shown)
Line 1: Line 1:
===Description of the Experiment===
+
=Description of the Experiment=
In this experiment, we determine the density of four different liquids through the way pressure varies with depth.
+
In this experiment, we study the density of four different liquids by taking into account that pressure variation with depth depends on it.
  
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
+
 
===Experimental Apparatus=== <!-- Secção colapsável -->
+
<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
 +
'''Links'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
In this experiment there are four acrylic tubes with a diameter of thirty millimiters and a meter in length. Each tube is filled with a diferent liquid: distilled water, salt water, glycerin and vegetable oil. Inside each of these tubes there is a bell with air that allows pressure to be sensed through a flexible hose, which is attached to a pressure sensor located on the outside of the tube.
 
  
[fig.1]
+
*Video: rtsp://elabmc.ist.utl.pt/scuba.sdp
 +
*Laboratory: Basic in e-lab.ist.eu[http://e-lab.ist.eu]
 +
*Control room: scuba
 +
*Grade: **
 +
 
 +
</div>
 +
</div>
 +
 
 +
 
 +
<swf height="550" width="480">http://www.elab.tecnico.ulisboa.pt/anexos/descricoes-flash/Scuba.swf</swf>
 +
 
 +
 
 +
=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 \( 2 cm^3 \) and the hose has a cross-section of \(1 mm\) and a length of \(1 mm\), but it can be ignored.
+
The change in volume can be estimated considering that each bell has a volume of approximately \( 2 cm^3 \). The hose has a cross-section of <math>1 mm</math> and a length of \(1 m\), but it can easily be ignored.  
 +
<!-- (why?)(because the hose's volume doesn't change significantly with the change in pressure?). -->
  
The tubes are mounted vertically, and the four probes move simultaneously as established by the programming. The latter pause for a second at each measuring point to allow the pressure to stabilize before measuring. This will make the experiment run longer if the user requests many points.</div>
+
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.
</div>
 
  
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
 
===Protocol=== <!-- Secção colapsável -->
 
<div class="mw-collapsible-content">
 
The user must define the following parameters: maximum and minimum height, and the number of samples to take.
 
  
The user can choose the initial and final depth for the probe's motion and obtain the data (for each liquid) on the variation of the pressure as the depth changes.
+
=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.
 
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 accepted values for the four liquid's density.
+
The following table shows the four liquid's density accepted values.
  
[tabela]
+
{| border="1"
 +
|-
 +
! Material
 +
! Accepted density (\( \frac{kg}{m^3} \))
 +
|-
 +
| Water       
 +
| \( 1,00 \times 10 ^3 \)
 +
|-
 +
| Glycerine
 +
| \( 1,26 \times 10 ^3 \)
 +
|-
 +
| Salty water
 +
| \( 1,03 \times 10 ^3 \)
 +
|-
 +
| Vegetable oil
 +
| \( 0,92 \times 10 ^3 \)
 +
|}
  
</div>
 
</div>
 
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
 
===Advanced Protocol=== <!-- Secção colapsável -->
 
<div class="mw-collapsible-content">
 
Under construction.</div>
 
</div>
 
  
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
+
=Theoretical Principles=
===Data Analysis===
+
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:
<div class="mw-collapsible-content">
 
Under construction.</div>
 
</div>
 
  
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
+
<math>  
===Theoretical Principles=== <!-- Secção colapsável -->
 
<div class="mw-collapsible-content">
 
The pressure exerted by a liquid is proportional to the weight of the pillar of that liquid, which means that of depends not only on depth, but also on density. This can be determined through the relation between pressure and depth. The mathematical law the rules this relation is
 
 
 
\[
 
 
p = p_0 + \rho g h  
 
p = p_0 + \rho g h  
\]
+
</math>
  
where \( \p_0 \) represents the pressure at the liquid's surface and \( \rho \) it's density \((^m/_V)\), g is the standard gravity and h the depth.
+
where \( p_0 \) represents the pressure at the liquid's surface and \( \rho = m/V\) it's density, being <i>g</i> the local gravity acceleration and <i>h</i> the depth.
By Pascal's Principle, \( \p_0 \) is evenly distributed through the whole liquid.</div>
+
Recalling Pascal's principle note that \( p_0 \) is evenly distributed through the whole liquid.
</div>
 
  
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
 
===Historical Elements=== <!-- Secção colapsável -->
 
<div class="mw-collapsible-content">
 
Under construction.</div>
 
</div>
 
  
===Bibliography===
+
=Links=
Under construction.
+
*[[Variação da Pressão num Líquido com a Profundidade |Portuguese Version (Versão em Português)]]

Latest revision as of 20:10, 24 May 2015

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

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 \( 2 cm^3 \). The hose has a cross-section of [math]1 mm[/math] and a length of \(1 m\), but it can easily be ignored.

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.

[math] 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.

The following table shows the four liquid's density accepted values.

Material Accepted density (\( \frac{kg}{m^3} \))
Water \( 1,00 \times 10 ^3 \)
Glycerine \( 1,26 \times 10 ^3 \)
Salty water \( 1,03 \times 10 ^3 \)
Vegetable oil \( 0,92 \times 10 ^3 \)


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:

[math] p = p_0 + \rho g h [/math]

where \( p_0 \) represents the pressure at the liquid's surface and \( \rho = m/V\) it's density, being g the local gravity acceleration and h the depth. Recalling Pascal's principle note that \( p_0 \) is evenly distributed through the whole liquid.


Links