Next: Buoyant Forces Up: Solids and Fluids Previous: Variation of Pressure with

Pressure Measurements

Idea: It is possible to measure pressure by relating pressure differences to the variation in the height of a column of liquid. Two devices for measuring pressure are:

1. Open-tube manometer

**Figure 9.5:** Open tube manometer
$\begin{figure} \begin{center} \leavevmode \epsfxsize=2 in \epsfbox{fig9-3.eps}\end{center}\end{figure}$

The pressure P of the gas in the closed cylinder on the left in fig.9.5 is related to atmospheric pressure P₀ (exerted on the top of the column of liquid on the right) by:

P - P₀ = $\displaystyle\rho$ gh (11)

where $\rho$ is the density of the fluid in the closed tube. The pressure P of the gas is called the Absolute Pressure, to distinguish it from what is directly measured from the height of the column, namely the Gauge Pressure. Thus:

P_absolute = P_gauge + P₀.

2. Mercury Barometer

**Figure 9.6:** Mercury barometer
$\begin{figure} \begin{center} \leavevmode \epsfxsize= 3cm \epsfbox{fig9-4.eps}\end{center}\end{figure}$

Atmospheric pressure is measured by ensuring that the pressure at the closed end of the barometer tube in Fig.9.6 is zero (i.e. it is vacuum). Thus

P₀ = $\displaystyle\rho$ gh (12)

where $\rho$ is the density of the mercury.

It turns out that the pressure of 1 atmosphere (1 atm), is equivalent to a column of mercury exactly 0.76 m high at a temperature of 0^o C with g = 9.80665 m/s ² and $\rho_{\:\rm mercury}^{}$ = 13.595 x 10³ kg/m ³. From this information, we conclude that

1 atm = 1.013 x 10⁵ Pa = 101.3 kPa. (13)

Next: Buoyant Forces Up: Solids and Fluids Previous: Variation of Pressure with

www-admin@theory.uwinnipeg.ca
10/9/1997