Pressure Definition 1. It is the effect of force on an area. 2. It is force per unit area.
Formula:
=
F = force (N)
unit of Pressure: N/m2 or Pascal (Pa)
A = area (m2)
1 N/m2 = 1 Pascal (Pa)
Pressure is directly proportional to force. If the force applied at a point is doubled, the pressure acting at that point also doubles. Pressure is inversely proportional to area of contact. A knife cutting an apple exerts more pressure than an elephant standing on ground because the area in contact of the knife is much smaller thus increasing the pressure. Some common examples of
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1. Thumb pin
2. Bare foot on beach
3. Car travelling on sand
4. Lying on a bed of nails
5. A block lying on foam
Liquid Pressure Pressure in a liquid depends on its depth, its density and the gravitational field strength.
Formula:
=
= density of the liquid (kg/m3) = gravitational field strength (10N/kg) = depth (height in m)
Properties of liquid pressure 1. Pressure increases with depth
2. Pressure is same at same depths (at equal heights)
The shape and width of the container does not matter.
3. Pressure acts equally in all directions 4. Pressure is transmitted equally throughout a liquid
Hydraulic systems (see animation on http://www.physics.com.pk/)
Example:
Assuming Fx = 10 N, Ax = 1 m2, AY = 10 m2 , we can find Fy.
Pressure exerted by piston 1 =
Pressure exerted by piston 2 =
As pressure is same at same depth, pressure exerted by piston 1 at X is equal to pressure exerted by piston 2 at Y. y
=
so Fy = 10 x 10 = 100 N
Atmospheric pressure The atmosphere exerts a pressure on the surface of every object on earth. The particles of air bombard and exert a force on per unit area of the object thus resulting in a pressure being exerted on it. Remember pressure is force per unit area. The atmospheric pressure at sea level is approximately 101 000 Pascals. This value changes as you go upward away from the earth’s surface. On top of a mountain it will be very less because the air particles are fewer and so exert less pressure. We take the value of atmospheric pressure as 100 000 Pa for calculations. Remember to take the value that is given in your paper. 1 atmospheric pressure (1 atm.) = 100 KPa = 100 000 Pa. NOTE: When calculating total liquid pressure you must add the atmospheric pressure to the liquid pressure. Example:
100 000 Pa (atm. pressure) Liquid pressure = = 1000 x 10 x 10 = 100 000 Pa.
h = 10 m
Total pressure = 100 000 + 100 000 Pa = 200 000 Pa.
Barometer A barometer measures atmospheric pressure.
The height h represents atmospheric pressure (also known as the barometric height). At normal air pressure it has a value of 75 cm. If the outside pressure increases this barometric height increases. REASON: the outside air pressure pushes on the surface of the container which pushes the mercury level higher up into the tube. When the outside pressure decreases (on top of a mountain) the barometric height decreases. 1 atm. = 75 cm Hg (750 mm Hg) Converting 75 cm Hg to Pascals. Remember to always convert the height into metres (m).
= = 13600 x 10 x 0.75 = 102 000 Pa. So a barometric height of 75 cm represents 102 000 Pa of atmospheric pressure.
Manometer
This U-shaped instrument is used for two purposes: 1. Comparing and measuring gas pressure, 2. Comparing and measuring densities of liquids.
Comparing and measuring gas pressure The pressure is same at both ends of the manometer so the levels of the liquid are same. The pressure exerted on both sides is equal to outside atmospheric pressure.
Case 1
The pressure at B is greater than the pressure at A. The difference A
B
in pressure is given by ∆h. if ∆h = 3 cm then the pressure at B is greater than pressure at A by 3 cm Hg. Pressure at B is higher than the outside atmospheric pressure.
Mercury (Hg)
Let’s assume a gas supply is attached to side B. The gas pressure is obviously more than the outside air pressure. To find the gas pressure follow the steps below. Air pressure outside at A = 100 000 Pa. Total Gas Pressure = ρgh + 100 000 = 13600 x 10 x .03 + 100 000
(g = 10 N/kg)
= 4080 + 100 000 = 104080 Pa
(see the gas pressure is more than the air pressure)
Case 2
The pressure at A is now greater than the pressure at B. A
B
if ∆h = 3 cm then the pressure at A is greater than pressure at B by 3 cm Hg. Pressure of gas at B is lower than the outside atmospheric pressure.
Air pressure outside at A = 100 000 Pa. Total Gas Pressure = 100 000 - ρgh = 100 000 - 13600 x 10 x .03 = 100 000 – 4080 = 95920 Pa.
(see the gas pressure is less than the air pressure)
Looking at the above two examples we can see that if a gas supply is attached to one side of a manometer we can calculate the difference in pressure of the gas and the atmospheric pressure. We can then calculate the value of the gas pressure.
REMEMBER: if the gas pressure is
more than the air pressure then ADD the two together.
If the gas pressure is less than the air pressure then SUBTRACT the two.
Comparing and measuring densities.
oil
the density of oil is less than water because it is floating on top of it.
Calculating the density of oil 4 cm
P = ρgh so if the depth of oil is twice then it must have half the density i.e. 500 kg/m3. Oil and water both exert same pressure at
2 cm
same level. water (1000 kg/m3)
P=ρgh OR We can calculate the pressure at same level. Pressure of water = pressure of oil (at same level) 1000 x 10 x .02 = ρ x 10 x 0.04 ρ = 500 kg/m3
Boyle’s Law It states that pressure of a fixed mass of gas is inversely proportional to its volume at constant temperature. P1V1 = P2V2 REMEMBER: always use this equation when calculating the gas pressures of the same gas.
Weather Charts On weather charts we see lines that represent the isobars. ISOBAR: it is the line joining points of equal pressure.
Isobar
On weather charts pressure is measured in millibars, mb. 1 bar = 1000 mb On weather charts the place where the isobars are closest represents the place of high wind or storm.
By Shafaq Hafeez shafaq@physics.com.pk