PRESSURE

(i)A person makes deeper marks while walking on a soft ground in very narrow and sharp-heeled shoes than when in ordinary shoes with flat heels.

(ii)It is easier to push a sharp pin through a cardboard than it is to push a blunt one through the same material using the same force ,see figure 4.1(a) and (b).

In (i) above,sharp pointed heels dig deeper on soft ground because the force applied acts on smaller area than when the blunt pin is used.

In all these cases , a force acting on a surface produces a penetration effect.This penetration effect is larger when the force acts on a small area than when the same force acts on a larger area.

Pressure is defined as force acting per unit area.

Units of pressure

The SI unit of pressure is thus Newton per Square metre (N/m2), which is also called the Pascal(Pa).1N/m2=1 PaOther units include mmHg,cmHg and atmosphere(atm).

Ex1:A man of mass 84 kg stands upright on a floor.If the area of contact of his shoes and flor is 420 cm2,determine the average pressure he exerts on the floor.(take g=10 N/kg)

Ex 2: A metallic block of mass 40 kg exerts a pressure of 20 N/m2 on aflat surface.Determine the area of contact between the block and the surface.(take g=10 N/kg)

Ex3: A rectangular aluminium solid block of density 2700 kg/m3 has dimensions of 40cmx12cmx6cm.The block rests on a horizontal flat surface.Calculate

a)the minimum pressure,

b)the maximum pressure it can exert.

Forces-in-Fluids-P7 - What is Pressure____2.flv

PRESSURE IN LIQUIDSExp 4.1: to show variation of pressure in liquid

Observation: the lower hole,A,throws water farthest,followed by B and lastly C.Conclusion : Pressure of water at A is greater than pressure at B and Pressure at B is bigger than at C.So,Pressure increases with depth.

Liquid levels

This show that the liquid flows to find its own level.

Pressure in liquid is equal at all points at the same level.

Liquid levels in a U-tube

When water is poured into a U-tube, it will flow into the other arm.The water will setle in the tube with the levels on both arms being the same,see in fig 4.5(a)

When one arm of the U tube is blown into with the mouth, the level moves downwards,while on the arm other arm it rises, see in figure 4.5(b). This caused by the pressure difference between the two arms.

Exp :4.2(a) to investigate the variation of liquid pressure with depth and density

1. Take a beaker filled with water. Insert the manometer at different levels. You will notice, as seen earlier, that greater the depth, higher is the pressure. 

2. Take two beakers, one filled with water and one filled with a salt solution. If you keep the manometer funnel at same depths in the two beakers, you will notice that pressure is dependent on the density of the liquid. Higher the density, higher the pressure.  

3. Take a beaker filled with water. Insert the manometer at a certain depth. Rotate the manometer mouth in all direction. You will notice that the pressure at a certain depth inside a liquid is equal in all directions.  

4. In a beaker filled with water, insert the manometer funnel at a fixed depth, move the funnel back and forth at the same depth. You will notice that the manometer pressure does not change. This means that the pressure inside a liquid is same at all places at the same depth.

In summary :

(i) pressure in a liquid increases with depth below its surface.

(ii) pressure in a liquid at a particular depth is the same in all directions.

(iii) pressure in a liquid increases with the density of the liquid.

Homework :Exercise 4.1

Fluid Pressure Formula

If A is the cross-section area of the column, h is the height of the column and p the density of the liquid, then;

Volume of the liquid=cross-section area x height

=A x h

Mass of the liquid=volume of the liquid x density

=Axhxp

So,weight of the liquid=mass of the liquid x gravity

=A x h x p x g

From the definition of pressure,

P=h x p x g

P=h x p x g

From the formula , it can be seen that the pressure due to a liquid column is directly proportional to:

(i) height h of the column.

(ii) the density p of the liquid.

Example 4: A diver is 10 m below the surface of water in a dam.If the density of water is 1000kg/m3,determine the pressure due to the water on the diver.(take g=10 N/kg)

Example5: The density of mercury is 13600 kg/m3.Determine the liquid pressure at a point 76 cm below the surface of mercury.(take g=10N/kg) .

 

ATMOSPHERIC PRESSURE

There is an envelope of air that surrounds the earth. We call it the atmosphere. The atmosphere is bound to the earth by the gravitational attraction of the earth.

This atmosphere of air around us produces pressure at ground level or other levels due to the weight of the air above that level.

Simple demonstrations of Air Pressure

Atmospheric pressure acts in all directions.

(a)Take a little water in a tin and boil the water to drive the air out of it. Cork the tin tightly and then cool it by pouring water on it. What happens?

When the air inside the tin is driven out,the atmospheric pressure outside is not counterbalanced by the pressure inside(when the steam cools , a partial vacuum is created inside). The tin collapses.

You can understand now why an open empty tin does not get squashed with the atmosphere pressing on the outside.

(b) Fill glass or lipless beaker with water to the brim and slide a paper card over the top.Take care not to leave any air bubble in water. Invert the glass. What happens?

The card is held in position by the atmospheric pressure pushing upwards on the card and the water does not fall out. The upward atmospheric pressure is greater than the downward force due to water.

A more convenient method is to use a glass tube sealed at one end ,as in fig 4.18(a)

İf mercury , which is much denser than water is used, the column supported is found to be much shorter,see figure 4.18(b). At sea level , the atmospheric pressure supports approximately 76 cm of mercury column or approximately 10 m of water column.

MEASUREMENT OF PRESSURE

U-tube Manometer

A manometer is an instrument that can measure fluid pressure. It consists of a U-tube filled with water or any other suitable liquid,see figure 4.19

Due to pressure of the gas Pg,

The water level in the aother limb rises to, say,Y.

This difference in water levels is the difference between gas pressure Pg and the atmospheric pressure Pa.

Since X and Z are at the same horizontal level ,pressure at X equals pressure at Z.Pressure at X is pressure of gas Pg.

Pressure at Z=atmospheric pressure+pressure due to the column of water

Therefore ,Pg=Pa+hpg

Example:

Mercury Barometer

It has been shown that atmospheric pressure supports a liquid column in a tube. When this arrangement is used to measure pressure, it is called a barometer.

At sea level, acolumn of mercury and water supported by atmospheric pressure is approximately 76 cm.

The height h of the column is a measure of the atmospheric pressure. At sea level , h=76cmHg.

Since density p of mercury is 13600 kg/m3;

 

This is the Standard atmospheric pressure , and is sometimes referred to as one atmosphere.

Testing the vacuum in a BarometerIf the barometer has air at the top, it will be faulty.

If the mercury column is tilted, the mercury from the dish flows to the tube and completely fills it.

If there was air,the mercury would not fill the tube completely. This shows that space above the mercury in the tube is a vacuum.

The space above the mercury in the tube when upright is called Toricellian vacuum and contains a little mercury vapour.

Fortin Barometer

The simple mercury barometer cannot be used for accurate measurements of atmospheric pressure. An improved version called the Fortin barometer is used where high precision is required.

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Aneroid Barometer

The mercury barometer is the most reliable type of barometer, but is not readily portable. The aneroid barometer is a portable type of barometer consisting of asealed,corrugated metal box,see figure 4.22.

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Pressure Gauges

Pressure gauges are portable anda re used mostly for measuring gas pressure,tyre pressure,pressure of compressed air in compressors and steam pressure.

TRANSMISSION OF PRESSURE IN LIQUIDSWhen the plunger is pushed in,the liquid squirts out the holes with equal force. If the plunger exerts a force F and the piston area is A,then the pressure P developed is F/A. This pressure is transmitted equally to all parts of liquid.

EXP 4.3:To investigate how pressure is transmitted in liquids(Using Identical Syringes)

Procedure :

Place a mass m on one of the plungers and observe what happens.

When the first mass is placed on the plunger, the plunger moves downwards and the second plunger moves up.

Place an identical mass on the other plunger and observe what happens.

When an identical mass is placed on the second plunger, the first plunger with the mass on it moves upwards and stops when their levels are the same.

The pressure in two syringes is the same. This is because the masses and diameters of the syringes are the same.

Using different Syringes

At balance , the pressure due to the mass in P is equal to the pressure due to the other mass in Q.

Pressure applied at one part in a liquid is transmitted equally to all other parts of the enclosed liquid. This is called the Principle of Transmission of Pressure in Liquids(Pascal’s Principle).

Note: gases may transmit pressure in a similar way when they are confined and incompressible.

Hydraulic Machines

Pascal’s Principle enables a small force to be multiplied into a large force. This principle of transmission of pressure in liquids is made use of in hydraulic machines.

Hydraulic Lift

When a force is applied on piston S,the pressure exerted by the force is transmitted throughout the liquid to piston L,see figure 4.12.

The pressure P1 exerted on the liquid by the piston S due to F1 is given by;

This pressure will be transmitted by the liquid to the larger piston L.

So, the force F2 produced on the large piston is given by;

Note:Hydraulic lifts are used for hoisting cars in garages.

Example : in figure 4.12 ,a force of 100 N acts on the smaller piston of area 2 cm2. Calculate the upward force acting on the larger piston of area 900 cm2.

Example: figure 4.13 shows two masses placed on light pistons.The pistons are held stationary by the liquid, whose density is 0.8 g/cm3.Determine the value of the force.

Hydraulic Brake SystemThe force applied on the foot pedal exerts pressure on

the master cylinder. The pressure is transmitted by the brake fluid to the slave cylinder. This causes the pistons of the slave cylinder to open the brake shoe and hence the brake lining presses the drum. The rotation of the Wheel is thus resisted.

When the force on the foot pedal is withdrawn, the return spring pulls back the brake shoe which then pushes the slave cylinder piston back.

The advantage of this system is that the pressure exerted in master cylinder is transmitted equally to all the four Wheel cylinders. So the braking force obtained is uniform.

Brake fluid should have the following properties:

•Be incompressible

•Have low freezing point and high boiling point

•Should not corrode the parts of the brake system

homeworkExercise : 4.2

APPLICATIONS OF PRESSURE IN GASES AND LIQUIDSTHE BICYCLE PUMP

It consist of a hollow metal cylinder C with a lid at the top and a smallhole at the bottom.

The piston rod passes through the lid.

The upper end of P has a handle while at its lower end, a cup-shaped leather washer W. The washer touches the sides of the cylinder tightly.

(i)when the psiton is withdrawn , the air in section A of the cylinder expands. Hence the pressure inA is less than the atmospheric pressure .So air can pass the washer into A.

(ii)when the piston is lowered , the air inA is compressed. The pressure exerted by the compressed air presses the leather washer tightly against the walls of the cylinder and does not allow the air to escapeoutside. When the pressure in A exceeds that in the tyre, the valve in the tyre opens and more air enters the tyre.

The lift Pump

A lift pump is used to raise water from wells. İt consists of a cylindrical meatal barel with a side tube. İt has two valves ,P and Q, as shown in figure 4.25.

UpstrokeWhen the plunger moves up during the upstroke , valve P

closes due to its weight and pressure of water above it. At the same time , air above valve expands and its pressure reduces below atmospheric pressure.

The atmospheric pressure on the water in the well below thus pushes water up past valve Q into barrel, as shown fig.4.25(a)

The plunger is moved up and down until the space between P and Q is filled with water.

Downstroke

During downstroke , valve Q closes due to its weight and pressure of water above the piston,see fig 4.25(b)

Limitations of this pump

The atmospheric pressure can only support a column of water of about 10 m.

In practice , the possible height of water that can be raised by this pump is less than 10 m because of:

(a) low atmospheric pressure in places high above sea level.

(b)leakages at the valves and pistons.

The force Pump

This pump can be used to raise water to heights of more than 10 m.

In this case the valve V2 is not in the piston, but in the side delivery tube which is near the bottom of the cylinder. Valve V1 must be about 7-8 m from the surface of water. This pump can force water to great heights as the water is forced out due to the pressure applied at the piston. Thus , water is raised from the well into the pump under atmospheric pressure , but it is forced into the tank under the pressure applied by the piston. Fire- Brigade pumps are of this type.

Siphon

Tanks are difficult to empty out simply by pouring out their contents. To make easier , we use a siphon.

Aflexible pipe filled with the liquid is fitted as shown below. One end is outside (below the surface of the tank) and the other is in the tank (insiude the liquid). The liquid pours out of the pipe at the lower end.

The water pours out due to the pressure between A and B:pg(h2-h1). End B is at a higher pressure than end A due to the difference ib heights: h=h2-h1.

Note : if the pipe is initially empty, the siphon would not work. The air needs to be sucked out of the pipe fort he liquid tor ise and pour out.

HOMEWORK:REVISION EXERCISE