Pressure in Properties of Matter is defined as the average force per unit area at the particular region of fluid (liquid or gas) i.e. P = F/A, where F is the normal force due to the liquid on the side of area A. At a given point in a liquid, the pressure can act in any direction i.e. pressure is a scalar quantity.
If the pressure in Properties of Matter were not same, there would be an unbalanced force on the fluid at that point and the fluid would move. The logical basis for the statement that pressure is exerted equally bin all directions, then, is simply that otherwise the parts of the fluid would not be in equilibrium. Also, pressure in Properties of Matter increases with depth, h below the liquid surface and with its density ρ so that;
P = hρg
SI Units of Pressure in Properties of Matter
When g is in ms-2, h is in meters and ρ is in kgm-3, then the pressure in Properties of Matter is in Newton per meter squared (Nm-2). The bar is a unit of pressure used in meteorology and by definition, 1bar = 105 Nm-2. The Pascal (Pa) is the name given to a pressure of 1Nm-2, thus 1bar = 105 Pa.
Pressure is often expressed in terms of that due to a height of mercury (Hg). One unit in Properties of Matter is the torr (after Torricelli);
1torr = 1mmHg = 133.3Nm-2
From P = hρg, it follows that the pressure in a liquid in Properties of Matter is the same at all points on the same horizontal level in it. Thus a liquid filling the vessel shown below rises to the same height in each of the sections.
A B C D
Atmospheric Pressure in Properties of Matter
A barometer when analyzing Properties of Matter is an instrument used for measuring the pressure of the atmosphere which is required in weather forecasting. It consists of a vertical tube about a meter long containing mercury with a vacuum at the closed top. The other end of the tube is below the surface of mercury contained in a vessel B.
‘’’’’’’’ ‘’’’’’’ ——
A A 760mm
The pressure on the surface of the mercury in B in Properties of Matter is atmospheric pressure A and since pressure is transmitted through the liquid, the atmospheric pressure supports the column of the mercury in the tube. Suppose the column is a vertical height H above the level of the mercury in B, then if h = 0.76m and ρ = 13600kgm-3, we have;
P = hρg = 0.76×13600×9.8 = 1.013×105 Nm-2
The pressure at the bottom of a column of mercury 760mm high for a particular density and value of g is known as standard pressure or one atmosphere in Properties of Matter. By definition, 1atmosphere = 1.01325×105 Nm-2
Standard temperature and pressure is 0oC and 760mm when dealing with Properties of Matter. It should be noted that the pressure P at a place x below the surface of a liquid when analyzing Properties of Matter in fluids is given by P = hρg where h is the vertical distance of x below the surface. In figure B above, a very long barometer tube is inclined at an angle of 60o to the vertical. The length of mercury along the slanted tube is say x mm. if the atmospheric pressure is the same as in A, then the vertical height to the mercury surface is still 760mm.
So: – xcos60o = 760 → x = 760/cos60o = 1520mm
Conclusion on Pressure in Properties of Matter
From the information above, it can be simply noted that pressure in Properties of Matter is independent of the cross section, and a simple mercury barometer gives an accurate measure of atmospheric pressure independent of the position on earth’s surface and thus a summary of pressure in Properties of Matter.