PRESSURE.

In physics, the term pressure is defined as force acting normally per unit area of the surface.

If F, is the force and A is the surface area over which F acts, then pressure P is given by P = F

Thus when the surface area reduces, then pressure increases.

Example.

nail

needle

When the same force F is applied at the ends of the needle and a nail, one tends to fill more pain from the needle. This is because the tip of the needle has a very small surface area.

The Unit of pressure is Newton per square metre (Nm^-2) or Pascal (Pa).

1N m^-2 = 1 Pa.

Example.

The diamentions of a cuboid are 5cm X 10cm X 20cm and the weight of a cuboid is 60N. Calculate the maximum pressure the cuboid exerts.

Solution:

P = F

P_max = height of Cuboid .

Minimum surface area

= 60 N .

0.05X0.1

= 12000 Nm^-2.

Pressure in liquids.

B A C

Consider a column of liquid h above the level BC in the cylinder. Pressure on surface A is due to the weight W of the liquid above it.

W = Volume of liquid X density X g in column h

= A h r g

Thus P = W = Ahrg = hrg.

A A

Generally, we talk of pressure at a point in a liquid and from the formula above, we can conclude that, the pressure at a point in a liquid is the same in all directions and depends on:

Ø The depth h below the surface of the liquid.

Ø The density of the liquid.

Ø The pressure exerted on the surface of the liquid above.

The pressure in a liquid is independent of croo sectional area and shape of the vessel containing the liquid. This can be illustrated by use of the communicationg tubes.

When a liquid is poured in to the tubes, it moves until the levels are the same. This is because pressure depends on height and is the same at the bottom. The pressure acting above the liquid is atmospheric pressure and is constant.

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Communicating tubes.

The liquid stands at the same level in each tube showing that pressure at the same level is the same and independent of cross sectional area and the shapes of the vessel. Increase in pressure at a point in a liquid can be illustrated by punching three holes at the sides of a can.

When water is poured in to the can, water from hole 1 travels furthest followed by that from hole 2. Water from hole 3 travels the shortest distance. This means that pressure increases with depth below the surface of the liquid.

Example 1.

Find the pressure at a depth of 10m in a liquid of density 13600 Kgm^-3.

P = hr g

Example 2.

----------------------

B 3m

The tank above contains mercury and water. The density of mercury is 13600 Kgm^-3 and the density of water is 1000 Kgm^-3. Find the pressure at B.

Solution:

P = h₁r₁g + h₂r₂g.

ATMOSPHERIC PRESSURE.

This is the pressure exerted by the weight of air surrounding the earth on all objects. The density of air above the earth decreases as the altitude increases. Hence atmospheric pressure decreases as you go higher. At sea level, the air is most dense and the magnitude of Atmospheric pressure there is about 10⁵ Pa.

We are not conscious of atmospheric pressure because: -

Our blood pressure is slighly greater than atmospheric pressure.
Atmospheric pressure acts equally in all directions.

Experiment to demonstrate Existance of atmospheric pressure:

Take a beaker or glass and fill it with water to the brim. Slide a paper card over the top so that no air is trapped between the card and water. Place your hand over the card firmly and invert the beaker. Remove your hand carefully.

- - - - - - - - - - - - - - water

- - - - - - - - - - - - - -

- - - - - - - - - - - - - - beaker

- - - - - - - - - - - - -

- - - - - - - - - - - - - water pressure

- - - - - - - - - - - - - - -

Cardboard Atmospheric pressure

Observation:

Water does not pour out.

Since no air was trapped inside the glass, there is no air pressure from inside. On the outside, however, the atmosphere exerts pressure. The force due to this pressure keeps the card in place against the weight of water inside.

The collapsing can experiment.

Obtain a sheet metal can with a light – fitting stopper. Remove stopper and pour a little water in the can. Boil the water for several minutes. Stop heating and immediately replace the stopper tightly. Pour cold water on the can.

Observation:

When you boil the water, the steam drives out most of the air from the can. When you close the can, the steam pressure inside balances the atmospheric pressure outside. However, on pouring cold water on the can, the steam condeses causing the pressure inside to fall, as a result, the atmospheric pressure becomes greater than the pressure inside the can and so the can collapses.

steam stopper

Steam

pressure

_ _ _ _ _ _ _ _ -_ _ _ _ _ _ _ _ -_

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ water boiling _ _ _ _ _ _ _ _

heat

atmospheric

pressure

_ _ _ _ _ _ _ _ _ _

_ _ __ _ _ _ _ _ _ _

U – TUBE MANOMETER.

If a transparent tube were bent in to a U – shape and a liquid put into it, we would expect the levels of the liquid in the two arms to be the same. Such a tube is usefull for measuring pressure differences and is called a U tube manometer.

If the pressure in one arm is changed for example by blowing in to it, the levels would become different. The difference in the level is proportional to the pressure difference in the two arms.

a.t.p blow

P₂

P₁ - - - -

h - - - -

- - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - -

- - - - - - i) - - - - - - - - - - - - - - - - ii)

- - - - - - - - - - - - -

Blow in to one arm of the manometer as hard as you can while some body else measures the difference in levels.

In (ii), P₁> P_2.

Atmospheric pressure P₁ = P₂ + hrg.

P₁ – P₂ = hrg

If P₂ is atmospheric pressure, then P₁ = atmospheric pressure + hrg.

· Used to measure lung pressure.

The difference is the difference between your lung pressure P₁ and atmospheric pressure P_o. If the difference is h, then lung pressure can be calculated.

P₁ = P_o+ hrg.

Problem: A woman blows in to one end of a water u – tube manometer until the levels differ by 40.0cm. If the atmospheric pressure is 1.01X10⁵ Nm^-2 and the density of water is 1000 kgm^-3, Calculate her lung pressure.

P₁ = Atmospheric pressure + hrg

MEASURING PRESSURE

i) Simple mercury barometer

If pressure in one arm of a U – tube manometer was reduced to zero while that in the other arm was left at atmospheric level, the difference in levels could be used to calculate atmospheric pressure.

Constructing a simple mercury barometer.

Obtain a thick-walled glass tube about one metre in length and closed at one end. Fix a funnel to this tube and fill it with mercury almost to the top. Remove the funnel and place one fingure tightly on the open end and invert the tube several times until all the bubbles of air clinging to the sides disappear. Then replace the funnel and fill the tube completely with mercury. Now, with your fingure on the open end, invert the tube into the dish filled with mercury. Remove the fingure when the open end is under the mercury in the dish. The column of mercury drops. Arrange the apparatus as below.

Tarricellian vacuum

Stand

h glass tube

dish

= = = = mercury

The height (h) from the mercury surface in the dish to the top of the column of mercury in the tube is a measure of the atmospheric pressure. The space above the mercury column is called Tarricellian vacuum.

If this experiment is done at sea level, the height (h) would be found to be 760mm.

Therefore from P = hrg

r = 1.36 X 10⁴ kgm^-3 and

g = 9.81 Nkg^-1

h = 0.76m

P = 1.014 X 10⁵ Pa. (Standard atmospheric pressure)

~ 1 bar (one atmosphere).

FORTIN BAROMETER.

A more accurate mercury barometer is the Fortin barometer.

Scale

vernier Screw to adjust vernier

Protecting brass tube

Barometer tube

Ivory pointer

screw to adjust mercury = Leather bag

Before reaching this Barometer, the screw for adjusting the level of mercury is turned until the ivory pointer just tourches the mercury level in the leather bag. The vernier scale makes the reading on this barometer quite accurate.

Problem. The height of the column in a mercury barometer is found to be 67.0 cm at a certain place. What would be the height of a water barometer at the same place?

Density of mercury 1.36 X 10⁴ kgm^-3

Water 1.0 X 10³ kgm^-3

h₁r₁g = hrg

h₁ = 9.11 m

APPLICATION OF PRESSURE IN GASES AND LIQUIDS.

Rubber sucker.

This is a circular shallow rubber cap. Before it is used, it is moisturised to get a good air seal and then pressed firmly against a smooth flat surface so that air inside is pushed out. The atmospheric pressure will then hold it firmly against the surface.

Smooth surface

. vaccum

a.t.p

rubber sucker

- useful in industry for lifting metal sheets or glass filates

-some printing machines use them for lifting the paper to be fed into the printer

-useful in the kitchen for clearing blocked swicks and such other drainage systems

DRINKING STRAW.

When you drink a soda or any other drink using a straw, you suck in the straw so that some of the air in the straw goes into your lungs. This leaves the space in the straw partially evacuated (partial vaccum). The atmospheric pressure pushing down on the liquid in the container becomes greater than the pressure of air in the straw and so it forces the liquid up in to your mouth (same for pipete).

APPLIANCES USING ATMOSPHERIC PRESSURE:

1) The Syringe.

Handle

Plunger

Burrel

= = = = = = = = = = Nozzle

When the tight-fitting plunger is raised, a partial vacuum is formed in the barrel. A.t.p pushes water through the nozzle up in to the burrel. When the handle is pushed down, water is squirted out.

REVISION QUESTIONS

1.a) Define pressure and state its SI units.

b) Draw a diagram to show that the pressure in liquid increases with depth.

c) If the density of sea water is 1150kg/m3, calculate the pressure at 40m when atmospheric pressure acting on the surface of the sea is 100kpa.(Assume g = 10N/kg)

2.a) State the pressure law.

b) Air of volume 0.4m3 is under pressure of 240Pa. What pressure will be needed to reduce the volume to 0.3m3 at constant temperature.

3. A U-shaped water manometer, open at both ends, was connected to a gas supply in the physics laboratory. The difference in the water levels in the two arms was 25cm. The mercury barometer at the time gave a reading of 750mm of mercury. The density of mercury is 13,600kgm-3;

i) Explain why water and not mercury is used as the manometer liquid.

ii) Determine the gas pressure in Nm-2.

4.ai) Define pressure and define its standard units.

ii) Describe an experiment to show the existence of atmospheric pressure.

iii) Find the length of the mercury column in a simple barometer when the barometer is raised from sea level to a height of 2.3Km given that the average density of air is 1.25Kgm-3 and the density of mercury is 1.36 x 10/4Kgm-3.

Atmospheric pressure at sea level is 76cm of mercury

b) A tin containing 6,000cm3 of paint has a mass of 8.5kg. The mass of the empty tin is 700g.

i) Calculate the density of the paint.

ii)If the tin is made of a metal which has a density of 7,200kg/m3, find the volume of the metal used to make the tin.

5.ai) Define pressure.

ii) Find the length of the mercury column in a simple barometer when the barometer is raised from sea level to a height of 2.5km given that the average density of air is 1.2kg/m3 and the density of mercury is 1.36 x 10(4)kg/m3. Atmospheric pressure at sea level is 76cm of mercury.

b) If the pressure at the base of a water tank is 5 x 103Nm-2, calculate the weight of the water acting on 1.0cm2 of the tank bottom.

200mm

to gas

cylinder 750mm

Fig. (ii)

Fig. (i)

a) Name the apparatus in:-

i) fig (I)

ii) fig (ii)

b) What are the uses of two apparatus named in (a) above?

c) Name the parts marked:-

i) X

ii) Y

d) Calculate the gas pressure in N/m2 using the diagrams above.

7.ai) Define pressure.

ii) Describe an experiment which can be carried out to demonstrate the variation of pressure with depth in a liquid.

iii) A mercury barometer gave a reading of 74cm at the bottom of a mountain and 50cm at the top. If the average density of air is 1.25kg/m3 and the density of mercury is 1.36 x 10(4)kg/m3, calculate the height of the mountain.

b) A uniform meter rule of weight 0.8N is suspended horizontally by two spring balances P and Q at marks 5cm and 95cm respectively. An object X of weight 0.4N is suspended at mark 27.5cm.

i) Draw a neat diagram showing the forces on the ruler.

ii) Calculate the readings on the spring balances P and Q.

8.a) Define pressure and give its standard units.

12cm

The diagram shows a mercury manometer connected to a gas supply. If the atmospheric pressure is 750mm Hg, what is the pressure of the gas in N/m2?

Density of mercury = 13,600kg/m3.

9. Fig. 1

Ram

Lever V₃

Pump V₂

Fluid reservior

V₁

Figure 1 shows the diagram of the hydraulic jack:-

i) What fluid is used in it?

ii) What happens to V₁ and V₂ when the lever is pulled out?

iii) What happens to V₁ and V₂ when the lever is pushed towards the pump?

iv) What is the purpose of V₃?

v) State the physics concerning pressure in fluids which enables the jack to work.

10.a) Define pressure and give its SI units.

b) A U-tube contains a column of water balanced by a column of paraffin. The top of the water column is 0.40m above the common level and the top of the paraffin column is 0.50m above the common level. Find the density of the paraffin given that the density of water is 1000kg/m3.

11.ai) What is meant by pressure? Explain the fact that when someone uses his thumb to push a drawing pin into a block of wood the pressure on the wood is greater than the pressure on the thumb.

ii) Calculate the pressure on the thumb when force exerted is 20N, the top of the pin is square and the length of each side being 10mm.

b) X

M 0.5m

Piston Y

liquid

If the density of the liquid is 800kgm^-3 and a mass of 1kg has a weight of 10N, calculate the pressure at Y in Nm^-2 due to the column XY.

c.i) What is the pressure and the force on the lower surface piston if its area is 0..1m²?

ii) Calculate the value of M.

d) Would the value of M be increased, decreased or stay the same if;

i) The tube XY were wider but with the same height of liquid?

ii) Water of density 1000kgm^-3 replaced the liquid?

12.a) Draw a clearly labelled diagram of a simple barometer.

b) Explain how the barometer is used to measure atmospheric pressure.

c) Calculate the atmospheric pressure in N/cm if the barometric height is 74cm of mercury and the density of mercury is 13.6g/cm³.

13.a.i) Define pressure and state its units.

ii) Describe an experiment to show that atmospheric pressure exerts pressure.

iii) Find the pressure at a depth of 62m below the surface of sea water given that atmospheric pressure is 760mm Hg.

b) The air pressure at the base of the mountain is 75.0cm of mercury and at the top it is 60.0cm of mercury. Given that the average density of air is 1.25kg/m³, calculate the height of the mountain.

c) An alloy of copper and tin has a volume of 100cm³. The density of copper is 8.90g/cm³ and of tin is 7.30g/cm³. How much volume of each metal must be used if the alloy is to have a density of 7.62g/cm³?

14.a.i) Define pressure and state its standard units.

ii) Describe an experiment to show the existence of atmospheric pressure.

iii) Find the length of the mercury column in a simple barometer when the barometer is raised from sea level to a height of 2.5km given that the average density of air is 1.2kgm^-3 and the density of mercury is 1.36 x 10(4)kgm^-3.

Atmospheric pressure at sea level is 76cm of mercury.

b) A tin containing 5,000cm³ of paint has a mass of 7.0kg.

i) If the mass of the empty tin, plus the lid is 0.5kg, calculate the density of the paint.

ii) If the tin is made of a metal which has a density of 7,800kg/m³, calculate the volume of the metal used to make the tin and lid.