**Manometers**

The manometer is a wet meter which means that
the fluid whose pressure is being measured is brought in contact with another
fluid, for example mercury, which is displaced to indicate the pressure. Mercury can be used because it has a high
density and so the manometer size is minimised. From the conversion table above 1 bar corresponds to 0.75m of Hg
whereas from the example above, a column of water 10m is high is equal to 1
bar. Compared to water, a much smaller
column of mercury is needed to measure pressure.

The common types of manometer are the **U-tube**,
the **Well** and the **Inclined** manometer. Signal conditioning on a manometer consists of marking
graduations on the glass column corresponding to calibrated pressure
readings. With mercury manometers a
range of 1mbar to 1.5bar can be easily achieved.

This manometer is very easily
constructed. It consists of a tube of
glass bent into a U shape. It is then
filled with a fluid. The density of the
fluid dictates the range of pressures that can be measured. Both ends of the tube are pressure
ports. If one port is left open to the
atmosphere and the other port is connected to the pressure to be measured, the
device acts as a gauge pressure meter.
If both ports are connected to two different unknown pressures, the
instrument acts as a differential pressure gauge.

The U-tube manometer is shown opposite. The difference in the height of the two
columns is due to the fact that p1 is greater than p2. For equilibrium at the datum point at the
bottom of the tube the total pressure in each limb must be equal. The pressure in the left limb is due to (a)
the column of measuring fluid (e.g. mercury) of height h_{1} (b) the
column of measurand fluid (e.g. air) of height h and (c) the pressure p_{1}. The pressure in the right limb is due to (a)
the column of measuring fluid (e.g. mercury) of height h_{2} and (b)
the pressure p_{2}. Therefore
we have as follows:

_{}

where r_{1} is the density
of the measurand fluid and r is the density
of the fluid in the manometer.
(Measurand fluid = fluid whose pressure you are measuring). If the measurand fluid is air then the
pressure due to it can be ignored as the term will be very small compared to
the other terms. If the measurand fluid
is a liquid or some other fluid of significantly high density then it cannot be
ignored in the equation. Assuming that
we have air as the measurand fluid the equation above becomes:

_{}

Since g is the acceleration due to gravity
and is a constant and the fluid density is a constant, the difference in
pressure is directly proportional to the difference in the heights of the
columns. With some experimental work
graduations could be marked on the glass to give a direct pressure reading.

Rearranging the above equation gives:

_{}

If p_{2} is atmospheric pressure then
the result for p_{1} is an absolute pressure measurement. If a gauge pressure measurement is
sufficient then we can use the following equation:

_{}

Example.
A mercury filled U-tube manometer is used to measure the flowrate of air
in a pipe. One leg of the manometer is
connected to the upstream side of an orifice plate and the other leg is
connected to the downstream side. The
pressure on the upstream side is higher causing a difference in height of the
two columns of 8mm. What is the
differential pressure across the orifice plate? What is the pressure of the air
in the pipe? The density of mercury is
13.56x10^{3}kg/m^{3}.

Answer.
We use the equation from above:

_{}

A difference in height of 8mm of mercury
indicates a difference in pressure of just over 1kPa.

We cannot say what the air pressure is
because neither tapping is open to the atmosphere. We can only determine the differential pressure but not the absolute
or gauge pressure.

Suppose water was flowing through the pipe
instead of air and the same reading was obtained. Does this mean that the same pressure difference exists?

Since water has a significant density of
1000kg/m3 it must be taken into account so we use, from above:

_{}

This time the differential pressure is just
under 1kPa.

If the fluid whose pressure is being measured
is not air but has a significant density then the r_{1}gh term above
cannot be ignored.

Other types of manometer exist such as the
well type and the inclined tube. The
idea behind the well type is that if you made the left hand side of the U-tube
to be a really large diameter compared to the right hand side, then you don't
notice the level changes in the left hand side but see them as normal in the
right hand side. In a well manometer
the cross sectional area of one side is so large that changes in its height can
be ignored.

The inclined tube manometer has a large diameter well on one side of the U and an inclined or angled leg on the other side. The incline allows for a smaller resolution. The height of the inclined leg is equal to Lsina where L is the length of measuring fluid in the incline and a is the angle.

Here’s a picture of an inclined manometer
that I got from the Dwyer instrumentation website - http://www.dwyer-inst.com/htdocs/PRESSURE/qsmodel250-451.cfm

These devices are cheap (€100) and are typically
used for pressure drop in airflow. For
example, one of these could be installed and the two tappings connected to
either side of an air filter (upstream and downstream sides). When the filter is clean, the pressure drop
is small. When the filter gets dirty
the pressure drop goes up.