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Introduction to Marine Engineering

Subsubsection Manometers

Manometers.

A manometer is another pressure measuring instrument. Unlike a barometer, which measures atmospheric pressure, a manometer is used to measure the pressure above or below atmospheric, or the pressure difference between two points.
The manometer consists of a U-shaped tube filled with liquid, usually mercury or water.
When the pressures on both sides of the manometer are equal, the fluid levels will equalize, but if two different pressures are applied , the levels will adjust until the pressures are balanced by the weight of liquid in the higher leg. The height difference (\(h\)) between the twp surfaces corresponds to the pressure difference.
When one leg is open to the atmosphere, the pressure difference represents a gauge pressure.
Figure 2.7.11. U-tube manometer
For a U-tube manometer the pressure difference \(\Delta p\) is calculated using the formula:
\begin{equation} \Delta p = \rho g h\tag{2.7.2} \end{equation}
where \(\rho\) is the density of the liquid in the manometer, \(g\) is the acceleration due to gravity, and \(h\) is the height difference between the liquid columns.

Example 2.7.12. Manometer Example.

If the height difference measured by a mercury manometer is 25 cm, determine the pressure difference .
Answer.
\begin{equation*} \Delta p = \kPa{33.3} \end{equation*}
Solution.
Recall these facts:
\begin{align*} g \amp= \aSI{9.8}\\ \N{1} \amp = \kg{1}\aSI{}\\ \Pa{1} \amp = \N{1}/\m{}^2\\ \kPa{1} \amp = \Pa{1000} \end{align*}
Apply equation (2.7.2) using the density of mercury \(\rho_{\text{Hg}} = 13.6 \mathrm{\ grams}/\mathrm{cm}^3\text{.}\)
\begin{align*} \Delta p \amp = \rho g h\\ \amp= \left( 13.6 {\mathrm{\ grams}}/{\mathrm{cm}^3} \times \left[\frac{\kg{1}}{1000 \mathrm{\ grams}}\right]\right)\left(\aSI{9.8}\right)\left(\cm{25}\right)\\ \amp = 3.33 \frac{\kg{} \m{}}{\sec{}^2 \cm{}^2} = 3.33 \frac{\N{}}{\cm{}^2}\\ \amp= 3.33 \frac{\N{}}{\cm{}^2}\times\left[\frac{\cm{100}}{\m{1}}\right]^2\\ \amp= 33300 \frac{\N{}}{\m{}^2} = \kPa{33.3} \end{align*}