#### Pressure, Physics tutorial

Pressure in Fluids:

Pressure is the measurement of the force per unit area. Fluid pressure can be caused by gravity, acceleration, or forces in the closed container. As a fluid has no definite shape, its pressure exerts in all directions. Fluid pressure can also be amplified by hydraulic mechanisms and changes with velocity of fluid.

The fluid applies the pressure on all bodies immersed in it. For the fluid at rest the difference in pressure between two points in it relies only upon the density of the fluid and the difference in depth between the two points. For example, a swimmer diving down in a lake can easily observe an increase in pressure with depth. For each meter (foot) increase in depth, the swimmer is subjected to an increase in pressure of 9,810 N per sq m (62.4 lb per sq ft), because water weighs 9,810 N per cu m (62.4 lb per cu ft). Since a liquid is nearly incompressible, its density does not change significantly with increasing depth. Therefore, the increase in pressure is caused solely by the increase in depth.

Pressure Due to Weight of a Liquid Column:

The atoms or molecules of which the liquid is made up of are attracted to earth appropriate to Newton's law of universal gravitation. Therefore, liquids gather at the bottom of containers and upper layers apply forces on those underneath.

Pressure at the given depth in the static liquid is the result the weight of liquid acting on the unit area at that depth with any pressure acting on surface of liquid.

P = Patm + ρgh

Pressure because of liquid alone (that is gauge pressure) at the given depth relies only on density of liquid ρ and distance below the surface of liquid h.

P = ρgh

Pressure is not actually a vector although it looks like it in sketches. Arrows point out direction of force which pressure would apply on the surface it is contact with.

Atmosphere Pressure:

Just like liquids apply pressure, gases also apply pressure. Pressure because of air around us is explained as atmospheric pressure. Small particles of gases which make up atmosphere of earth have weight and thus apply pressure on all objects on earth. Pressure because of air column is provided as

P = hρg

Air pressure differed thus with altitude. The higher we go, the lower the pressure. Air pressure is highest at sea level. Value of atmospheric pressure on surface of earth at sea level is almost 1013 x 105Pa. Air pressure - atmospheric pressure is generally denoted as Po or ho, where ho is barometric height. That is the height of mercury, which air pressure can maintain in the tube filled with mercury. Thus, when the diver or any object is at depth h below sea level, total pressure on such a diver or object is composed of

• Atmospheric pressure Po or ho and
• Pressure because of liquid itself P1 or h1
• Therefore, total pressure P on object is given as

P = Po + P1 Note that Po or ho is always given in reference to height of mercury, thus units of pressure should be same.

Transmission of Pressure in Fluids:

The forces of pressure are transmitted in the liquid in all directions. Forces of pressure are applied by the liquid not only on bottom and on piston but also on the vessels walls.

This is why, when membranes are utilized to cover holes in wall of vessel there are visible bulges at side of wall because of forces of pressure applied by water.

Pascal's Principle:

Pascal's Principle has got to do with transmission of pressure in fluids. Pascal's Principle defines that pressure applied to any point to the fluid in the closed vessel is transmitted evenly to every other point in fluid. Another way to state principle is: the pressure applied by surface forces is transmitted without loss to any point of the liquid. This is the principle utilized in construction of hydraulic press in engineering.

Applications of Pascal's Principle:

Pascal's Principle is applied in the given machines,

• The hydraulic press
• The hydraulic jack
• The hydraulic brakes

Measuring Pressure:

Medical doctor utilizes instrument known as sphygmomanometer (Sphyg) to compute human blood pressure. Several methods have been developed for measurement of pressure and vacuum. Instruments utilized to estimate pressure are known as pressure gauges or vacuum gauges.

The manometer is the instrument which utilizes the column of liquid to estimate pressure, though term is frequently utilized nowadays to mean pressure measuring instrument.

The Simple/Mercury Barometer:

Mercury barometer is utilized to compute atmospheric pressure. It is composed of straight glass tube, sealed at one end of approx one meter long. It is filled with mercury after it has been cleaned and dried. Tube filled with mercury is turned numerous times to make sure that no air bubbles exist in tube. When mercury is filled correctly to the end of tube, thumb is then placed over it. This end is then inverted in the vessel of mercury. Thumb is then removed. Observe that mercury drops, leaving the space at top. Space is known as Torricellian vacuum. Height AB is column of mercury supported by pressure of atmosphere on the free surface of the mercury in vessel. This is generally 76cm of mercury.

Many laboratories now have Fortin barometers placed there to compute atmospheric pressure. A Fortin barometer is just like structure with simple barometer. It has the fixed scale from which barometric height of mercury column can be read simply.

The Hare's Apparatus:

The apparatus for comparing densities of liquids in two separate vessels using their rise in two graduated vertical tubes immersed at their lower ends in liquids and connected at the top by the third tube to which suction is applied.

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