Difference between revisions of "Liquid Pressure Variation with Depth"

From wwwelab
Jump to navigation Jump to search
Line 51: Line 51:
 
===Theoretical Principles=== <!-- Secção colapsável -->
 
===Theoretical Principles=== <!-- Secção colapsável -->
 
<div class="mw-collapsible-content">
 
<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
+
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:
  
 
\[  
 
\[  
Line 57: Line 57:
 
\]  
 
\]  
  
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 acelaration 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>
  
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
 +
 
===Historical Elements=== <!-- Secção colapsável -->
 
===Historical Elements=== <!-- Secção colapsável -->
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">

Revision as of 16:14, 23 March 2012

Description of the Experiment

In this experiment, we determine the density of four different liquids through the way pressure varies with depth.

Experimental Apparatus

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, salty 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 tube, which is attached to a pressure sensor located on the outside of the liquid.

[fig.1]

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 tubes are mounted vertically, and the four probes move simultaneously as established by the configuration choosed. 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.

Protocol

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. Afterwards, the data can be fitted to the following equation, and from that, the density of the various liquids can be determined.

\[ p(h) = p_0 + \rho g h \]

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.

[tabela]

Advanced Protocol

Under construction.

Data Analysis

Under construction.

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:

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

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

Historical Elements

Under construction.

Bibliography

Under construction.