eFunda Introduction to U Tubes




eFunda: Introduction to U Tubes








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U Tubes: Introduction


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Overview






The U Tube contains water or
mercury in a U-shaped tube, and is usually used to measure gas
pressure. One end of the U tube is exposed to the unknown pressure
field and the other end is connected to a reference pressure source
(usually atmospheric pressure), shown in the schematic below.



Typical U Tube

By comparing the level of the liquid on both sides of the U tube,
the unknown pressure can be obtained from fluid statics,


If fluid C is the atmosphere, fluid B is the liquid
in the U tube (e.g. water or mercury), and fluid A is a gas,
then we can assume that rB
rA, rC. The pressure contributed by the
weight of gas within the U tube can therefore be neglected.
The gage pressure of the gas can be approximated by,






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Further
Information






To automate the pressure measurement in a mercury-filled U tube,
a Wheatstone
Bridge can be fabricated by connecting two external resistance
to a high-resistance wire threading the interior of the U tube, as
shown in the schematic below.



U Tube Pressure Sensor

The resistance of the U tube wire is proportional to its
current-carrying length. The two parts of the wire external to the
mercury will carry current and therefore will impart resistances to
the circuit. However, the immersed portion of the wire carries no
current, since the current will instead travel through the
highly-conductive mercury. The U tube wire is effectively separated
into two separate resistances, each resistance dependent upon the
wire length above the mercury. As a result, the difference in the
resistance of these two wire segments will be proportional to the
pressure difference across the U tube,


where c and k = cRw are factors that can
be obtained during calibration.
For an initially
balanced Wheatstone Bridge, the voltage output is given by,


where r = Rw / RRef is the
efficiency of the bridge circuit.
Thus, the unknown gas pressure (with respect to the reference
pressure) is proportional to the output voltage,






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Pros and Cons










  •
Pros:

 
-
Low cost

 
-
Simple and reliable



  •
Cons:

 
-
Low dynamic response rate.
Requires time to damp out oscillations.

 
-
Measurement accuracy dependent
on precise leveling of U tube.

 
-
Cannot be used in weightless (0
g) environments.

 
-
The liquid in the U tube must
NOT interact with measured fluid (be it gas or liquid).

 
-
Mercury or water vapor
contamination can occur, especially in low pressure
measurements.
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