The Concept of Pressure

Explain the concept of pressure

Pressure is defined as the force per unit area. OR Pressure is the force acting normally (perpendicularly) per unit surface area.

It is calculated by the formula:

Pressure = Force (f)/Area (A)

P = F/A

Where

• P – Pressure
• F – Force
• A – Area

The S.I Unit of Pressure

State the S.I unit of pressure

The SI unit of Pressure is Newton per square metre (N/M²). This unit is usually referred to as the Pascal (Pa).

1Pa = 1 N/M²

The other units of pressure are atmosphere, torr bar and mmHg.

• 1 atmosphere = 780mmHg
• 1 atmosphere = 1 10⁵ N/M² = 1bar (used by meteorologists)

Note: for a given amount of force, the smaller the area of application the greater the pressure exerted.

When a man lifts a bucket of water by its handle that is made with a thin metal, he would experience some discomfort but if the bucket was made with a thicker handle the discomfort will be much less if any.

This is because the area over which the force is applied is larger.

Pressure due to Solids

Dependence of Pressure on Surface of Contact

Explain dependence of pressure on surface of contact

The pressure in solid depends on the surface area of contact. A force (F) applied onto a small area exerts a higher pressure as compared to when it is applied onto a large surface.

Pressure in solid = Force applied/Area of contact.

Example 1

A block of wood that weighs 30N and measures 5m by 10m by 4m. If it was placed on a table with the largest possible area (5mx10m) in contact with table, exerts less pressure than it would when placed with its smallest possible area (5mx4m) in contact with table.

Solution

Data:

Force = 30N

Largest base area = ?

A_L = 10mx5m = 50m²

P = F/A = 30N = 0.6N/30m²

Pressure = 0.6N/m²

Force (F) = 30N.

Small base are = ?

As = 5mx4m

As = 20m²

P= F/A = 30N/20M² = 1.5 N/M²

Pressure = 1.5 N/M²

Example 2

A tip of needle has a cross- sectional area of 1×10⁶m². If doctor applies a force of 2N to a syringe that is connected to the needle, what is pressure is exerted at the tip of the needle?

Soln:

Data:

Area (A) = 1×10⁶m²

Force (F) = 20N

Pressure =?

P = F/A

P = 20 = 2.0×107 N/M²

The pressure extended by the needle lip is 2.0×10⁷N/m²

Example 3

A rectangle metal block with sides 105m by 1.0m by 1.2m rests on a horizontal surface. If the density of the metal is 7000kg/m3. Calculate the maximum and minimum pressure that the block can exerts on the surface.

(Take the weight of 1kg mass to be 10N)

Solution:

Data:

Dimension = 1.2m,1.5m,1.0m.

Density = 7000kg/m³

Maximum pressure (Pmx) = ?

Minimum pressure (Pmn) = ?

Volume = 1.2×1.5×1=18m³

Density = mass/ Volume

7000kg/m³ = mass/18

Mass = 7000×18 = 126000Kg

1kg = 10N

126000Kg = ?

F = 1260000 = 1.26 x 10⁶

Force of metal = 1.26 x 10⁶

A₁ = 1.2 x 1.5= 18m²

A₂= 1.2m²= 1.2mx1m=1.2m²

A₃= 1.5 x 1m= 1.5m²

A_mx = 18m²

A_min = 102m²

P_mn = F/A_mx =1.26 x 10⁶N/18M² = 1.26X10⁶/1.8 X10¹

Maximum pressure = 1.05×10⁶N/m²/maximum pressure= 0.7×10⁵N/m²

The Applications of Pressure due to Solids

Identify the applications of pressure due to solids

It is used to make different objects like screw, nails, pins, spears and arrows. This item is given sharp points to increase their penetrating power.

It helps some of living organisms for self-defence. A fish uses its sharp fins to protect itself.

When one walks on shoes with sharp pointed heels they exert greater pressure on the ground than when wearing flat shoes.

It helps in construction of railways. During the constructions of railways, wide wooden or concrete sleepers are placed below the railways tracks. This provides a larger surface area over which the weight of the train acts. This is a safety measure to train tracks.

Buildings are constructed with wide foundations to ensure that the weight of the building acts over the layer area.

pressure in Liquids

A liquid will exert pressure on an immersed object as well as on the walls of the container holding it. Note that the pressure exerted by liquids is due to the weight of the liquid. Also increase in water level in liquid cause increase in pressure.

The Characteristics of Pressure in Liquids

Describe the characteristics of pressure in liquids

Note: Pressure in liquids =Force/Area

But force= hApg/A

=Hsg

Hence pressure in liquids is given as hsg.

H= Height of the liquid column

A= Area of the base

The pressure at any point in a liquid at rest then depends

1. Depth
2. Density of liquid

Note: It does not defend on the area

Pressure in liquids is characterized using the following parameters

1. Pressure in a liquid increase with depth
2. Pressure in a liquid acts equally in all directors
3. Pressure in a liquid increases with increase in density of the liquid.

Mercury exerts more pressure than an equal volume of water. This because mercury is denser than water.

The Variation of Pressure with Depth in Liquids

Examine the variation of pressure with depth in liquids

Demonstration of water spurting from holes at different heights.

As pressure at point A is low due to small height of water above it but at point B the height increase and the distance of water increase while at point C the height is greatest therefore the level of water distance will be large distance.

Demonstration of pressure in a communicating vessel

The shape of vessel found in point A, B, C and D is different but the pressure is the same due to the equal height (L) of the liquid above the points.

Problems Involving Pressure in Liquids

Solve problems involving Pressure in Liquids

Example 4

A cube of side 2cm is completely submerged in water so that the bottom of the cube is at a depth of 10cm. use g=10m/s² and s=1000kg/m³

1. What is different between the pressure on the bottom of the cable and the pressure on its tap?
2. Determine the difference in the force on the top and bottom.
3. What is the weight of the water displaced by the cube?

Solution;

Data.

Depth = 10cm = 0.1m

s = 1000kg/m³

g = 10m/s

h= 8cm= 0.08

formular

p= sgh

p=1000kg/m³x10m/s²x0.1m=1000N/m²

At the h= 0.08m p= 1000x10x0.08= 800N/m²

Change in pressure = 1000N/m =200N/m²

So that different in pressure between the bottom the top is 200N/m²

Pressure = Force/Area = P= F/A

Area =L²= (10.02)²= 0.0004m²

Distance in water 200N/m²x0.0004m²

This is the upthrust acting on the cube

Water displaced by the cube in weight= volume of the cube

Volume = l3 (2cm) ³ = 8cm³

For water, 1cm³= 1g 50.8cm³ = 8g

Weight of displaced water

mass of displaced water/100=8g = 0.08N

Example 5

Calculate the pressure at the bottom of tank of water 15m deep due to the water above it is (s=1000kg/m³).

Solution:

Data:

Height =15m

S=1000kg/m³

g= 10m/s²

Formula

Pressure in liquid sgh

= 1000x10x15=150000N/M²

The Principle of a Hydraulic Pressure

Explain the principle of a hydraulic pressure

It state that “Any external pressure applied to the surface of an enclosed liquid will be transmitted equally throughout liquid.”

Illustration of Pascal’s Principle.

Note: in all side of vessel will experience equal pressure.

The hydraulic press works on Pascal’s principle, when using this principle a small force converted into a large force and vice versa.

From Pascal’s Principle

Note: The distance moved (d) is inversely proportional to the cross sectional area.

Example 6

The pistons of a hydraulic press have their areas given as 3.^0x10-4m2 and 2×10²m² respectively. If the smaller piston is pushed down with a force of 12N, what is the force required to push the larger piston?

Soln:

Data:

F₁ = 120N, A₂= 2X10²m²

A₂ = 3X10⁴m²

Application of Hydraulic Press

Measure pressure of a liquid

Hydraulic press is used in industries to express bulk items.

Hydraulic brake system

When pressure is applied to the brake pedal, it pushes the piston in the master cylinder forward creating a pressure in the brake fluid. This pressure is transferred to the slave cylinders where it is multiplied and pushes the brake shoes against the brake dram that is attached to the wheel of the vehicle.

It is used in industries in the forming of metals.

Since the hydraulic press act like a lift, it is used for lifting heavy loads.

Measuring the pressure of liquids using a manometer. Manometer is the device for measuring pressure (commonly gas).

Atmospheric Pressure

The Existence of Atmospheric Pressure

Describe the existence of atmospheric pressure

Atmospheric pressure is as a result of the weight of this layer of gases, the act at atmospheric pressure is surrounded the layer of air consisting of a mixture of gases.

Note. The atmospheric pressure on the earth’s surface and objects on the earth is a approximately 1.01×10⁵N/m^2.

The experiment which demonstrate the existence of atmospheric pressure.

Tumbler experiment

When you fill a glass timber with cord and gentle turned upside down. It will be seen that water will not poured down.

Plunger

Pulling the plunger is not easy. This is so because all the air is squeezed out from the table when the surrounding pressure being high the plunger sticks.

Crushed bottle

When putting hot water in, the bottle is cooled under cold water the steam condenses; leaving partial vacuum inside the bottle consequently the greater atmospheric pressure outside the bottle crushes it in wards.

Applications of Atmospheric Pressure

Identify the applications of atmospheric pressure

A siphon

A siphon is applied in areas and devices that we use everyday

1. It is used in the toilet flushing cisterns (chain and ball tank). The flush is triggered by a handle that operates a simple diaphragm like piston pump that lifts enough water.
2. It is used in special rain gauges called siphon rain gauge which are able to automatically drain out excess water.
3. A siphon cup is a reservoir attached to a gum.
4. It is used is some drainage systems to drain water to one point.

The lift pump

A lift pump is used to raise water from underground sources. This is a pump that is used to lift the liquid, rather than force liquid up.

A syringe is a simple piston pump that lifts a tube. The plunger that lifts can be pulled and pushed through inside a cylindrical tube or barrel. This enables the syringe to take in or expel fluid through the opening (nozzle) at the end of the tube.

Uses of syringe:

1. They can be fitted with hypodermic needles and used to administer injections.
2. They are used to measure liquids and gases in a laboratory.
3. They are used to apply certain compounds such as a glue or lubricant.

Bicycle pump

This is a type of force pump that consists of a hollow metal cylinder and a movable piston.

Measuring Atmospheric Pressure

Atmospheric pressure is measured by using barometer;

Types of barometer:

1. The simple barometer
2. Fortin barometer
3. Aneroid barometer

This is a type of force pump that consists of a hollow metal cylinder and a movable piston.

A simple barometer is the most fundamental of the other types of barometer. The barometric liquid used is mercury.

A simple barometer consists of a hard glass tube closed at one end.

Fortin barometer

A Fortin barometer is a modified simple barometer. It consists of an inverted tube closed at its upper end with the lower open end immersed in a reserve of mercury. The atmospheric pressure is measured in terms of the height of the column of mercury.

Disadvantages of Fortin barometer:

1. Mercury is very expensive to use and is very toxic. For these reasons, an aneroid barometer is usually preferred.
2. It is not portable as it is generally big and contains liquid.
3. It must be mounted in a vertical position.