Table of Contents
Pressure, Density and Specific Gravity
1. Introduction
Pressure, density and specific gravity are fundamental physical quantities used to describe how matter behaves under different conditions. They are particularly important in fluid mechanics, engineering, meteorology, hydraulics, atmospheric science and everyday applications.
Pressure describes the force acting per unit area, density describes the mass contained in a unit volume, and specific gravity compares the density of a substance with the density of a reference substance.
2. Pressure
2.1 Definition of Pressure
Pressure is the normal force acting per unit area of a surface.
[
P=\frac{F}{A}
]
Where:
- (P) = pressure
- (F) = perpendicular force
- (A) = area over which the force acts
The SI unit of pressure is the pascal (Pa).
[
1,Pa=1,N/m^2
]
One pascal is the pressure produced by a force of one newton acting normally on an area of one square metre.
2.2 Factors Affecting Pressure
Pressure depends on two principal factors:
- Applied force: pressure increases when the force increases, provided the area remains constant.
- Area: pressure decreases when the area increases, provided the force remains constant.
For example, a sharp knife cuts more effectively than a blunt knife because its thin edge produces greater pressure for the same applied force.
Similarly, snowshoes distribute a person’s weight over a larger area, reducing pressure on the snow.
2.3 Types of Pressure
Atmospheric Pressure
Atmospheric pressure is the pressure exerted by the weight of the air surrounding the Earth.
At sea level, standard atmospheric pressure is approximately:
[
1,atm=101,325,Pa
]
It is also approximately equal to:
- 760 millimetres of mercury (mmHg)
- 760 torr
- 1.01325 bar
Atmospheric pressure decreases with increasing altitude because the height and weight of the air column above a location decrease.
Absolute Pressure
Absolute pressure is measured relative to a perfect vacuum.
Gauge Pressure
Gauge pressure is measured relative to the surrounding atmospheric pressure.
[
P_{gauge}=P_{absolute}-P_{atmospheric}
]
Therefore:
[
P_{absolute}=P_{atmospheric}+P_{gauge}
]
A tyre pressure gauge normally displays gauge pressure rather than absolute pressure.
Vacuum Pressure
Vacuum pressure describes pressure below atmospheric pressure. It may be expressed as the difference between atmospheric pressure and absolute pressure.
2.4 Pressure in Liquids
The pressure exerted by a liquid at a particular depth is known as hydrostatic pressure.
[
P=\rho gh
]
Where:
- (\rho) = density of the liquid
- (g) = acceleration due to gravity
- (h) = depth below the liquid surface
Hydrostatic pressure increases with depth and liquid density.
Important characteristics include:
- Pressure increases with depth.
- Pressure is greater in denser liquids at the same depth.
- At the same depth in a stationary connected liquid, pressure is equal.
- Hydrostatic pressure does not directly depend on the shape or total volume of the container.
- Pressure at a point in a stationary fluid acts equally in all directions.
If atmospheric pressure is also included, the absolute pressure at depth is:
[
P_{absolute}=P_{atmospheric}+\rho gh
]
2.5 Pascal’s Principle
Pascal’s principle states that pressure applied to an enclosed fluid is transmitted equally and undiminished throughout the fluid and to the walls of its container.
This principle forms the basis of hydraulic machines.
[
\frac{F_1}{A_1}=\frac{F_2}{A_2}
]
Where:
- (F_1) = input force
- (A_1) = area of the smaller piston
- (F_2) = output force
- (A_2) = area of the larger piston
A small force applied to a small piston can produce a much larger force on a larger piston.
Applications:
- Hydraulic presses
- Hydraulic lifts
- Hydraulic brakes
- Hydraulic jacks
- Heavy machinery
A hydraulic machine multiplies force but does not create energy. Ideally, the output piston moves a shorter distance than the input piston.
3. Density
3.1 Definition
Density is the mass contained in a unit volume of a substance.
[
\rho=\frac{m}{V}
]
Where:
- (\rho) = density
- (m) = mass
- (V) = volume
The SI unit of density is kilogram per cubic metre (kg/m³).
Another commonly used unit is gram per cubic centimetre (g/cm³).
[
1,g/cm^3=1000,kg/m^3
]
Density is an intensive property, meaning it does not normally depend on the total quantity of a uniform substance.
3.2 Factors Affecting Density
Density is influenced by:
- Nature and composition of the substance
- Temperature
- Pressure
- Physical state
For most substances, density decreases when temperature increases because thermal expansion increases volume while mass remains constant.
For gases, pressure and temperature can significantly affect density.
3.3 Density of Common Substances
Approximate densities under ordinary conditions:
| Substance | Approximate density |
|---|---|
| Water | 1000 kg/m³ |
| Ice | 917 kg/m³ |
| Mercury | 13,600 kg/m³ |
| Aluminium | 2700 kg/m³ |
| Iron | 7870 kg/m³ |
| Copper | 8960 kg/m³ |
| Air | 1.2 kg/m³ |
Actual values depend on temperature, pressure and material composition.
3.4 Relative Density and Density Comparison
Density comparison helps explain why certain objects float while others sink.
An object generally floats in a liquid when its average density is lower than the liquid’s density. It generally sinks when its average density is greater.
For example, ice floats on water because its density is lower than that of liquid water.
3.5 Anomalous Expansion of Water
Water behaves unusually between 0°C and 4°C.
- Water has its maximum density at approximately 4°C.
- When water is cooled from 4°C to 0°C, it expands.
- When water freezes, its volume increases.
- Ice is therefore less dense than liquid water and floats on it.
This property helps aquatic life survive in cold climates because ice forms at the surface, while deeper water can remain liquid.
4. Specific Gravity
4.1 Definition
Specific gravity, also called relative density, is the ratio of the density of a substance to the density of a reference substance.
For solids and liquids, the reference substance is usually water at a specified temperature.
[
SG=\frac{\text{Density of substance}}{\text{Density of water}}
]
Specific gravity is dimensionless because it is a ratio of two quantities with the same units.
For gases, the reference substance is commonly air under specified conditions.
4.2 Interpretation of Specific Gravity
- SG greater than 1: the substance is denser than water.
- SG less than 1: the substance is less dense than water.
- SG equal to 1: the substance has the same density as the reference water.
For example, a liquid with a specific gravity of 0.8 has approximately 80% of the density of water under the stated reference conditions.
4.3 Specific Gravity and Floating
Specific gravity helps predict whether a substance will float or sink in water.
- A substance with SG less than 1 generally floats.
- A substance with SG greater than 1 generally sinks.
- A substance with SG equal to 1 is neutrally buoyant under ideal conditions.
The actual behaviour of an object also depends on its shape, trapped air and average density.
4.4 Applications of Specific Gravity
Specific gravity is used in:
- Measuring the concentration of certain solutions
- Testing petroleum products
- Checking battery electrolyte
- Identifying minerals
- Quality control in food and chemical industries
- Assessing the density of construction materials
A hydrometer is an instrument used to measure the specific gravity of liquids.
5. Measurement of Pressure and Density
5.1 Barometer
A barometer measures atmospheric pressure.
The mercury barometer was developed by Evangelista Torricelli.
A standard mercury barometer shows a column approximately 760 mm high at standard sea-level atmospheric pressure.
5.2 Manometer
A manometer measures pressure or pressure differences, commonly in gases and liquids.
A simple U-tube manometer uses the difference in liquid levels to determine pressure difference.
5.3 Pressure Gauge
A pressure gauge measures the pressure of a gas or liquid in a system, such as a boiler, gas cylinder or vehicle tyre.
5.4 Hydrometer
A hydrometer measures the specific gravity or relative density of liquids.
It floats at different levels depending on the liquid’s density.
5.5 Measuring Density
Density can be determined by measuring the mass and volume of a substance.
- Balance: measures mass.
- Graduated cylinder: measures liquid volume.
- Displacement method: determines the volume of an irregular solid.
- Density meter: measures density directly in suitable applications.
6. Worked Examples
Example 1: Calculating Pressure
A force of 500 N acts normally on an area of 0.25 m². Calculate the pressure.
[
P=\frac{F}{A}
]
[
P=\frac{500}{0.25}=2000,Pa
]
Answer: 2000 Pa.
Example 2: Calculating Density
A metal block has a mass of 600 g and a volume of 200 cm³. Calculate its density.
[
\rho=\frac{m}{V}
]
[
\rho=\frac{600}{200}=3,g/cm^3
]
Answer: 3 g/cm³ or 3000 kg/m³.
Example 3: Hydrostatic Pressure
Calculate the pressure due to water at a depth of 5 m. Take water density as 1000 kg/m³ and (g=9.8,m/s^2).
[
P=\rho gh
]
[
P=1000\times9.8\times5
]
[
P=49,000,Pa
]
Answer: 49,000 Pa or 49 kPa gauge pressure.
Example 4: Specific Gravity
A liquid has a density of 800 kg/m³. Calculate its specific gravity relative to water.
[
SG=\frac{800}{1000}=0.8
]
Answer: 0.8.
Example 5: Hydraulic Force
A hydraulic press has an input piston area of 0.02 m² and an output piston area of 0.5 m². If the input force is 100 N, calculate the ideal output force.
[
\frac{F_1}{A_1}=\frac{F_2}{A_2}
]
[
F_2=\frac{100\times0.5}{0.02}
]
[
F_2=2500,N
]
Answer: 2500 N.
7. Practical Applications
Pressure, density and specific gravity have extensive applications in everyday life and engineering.
- Dams are constructed thicker at the bottom because water pressure increases with depth.
- Hydraulic brakes use Pascal’s principle to transmit pressure.
- Ships are designed to displace sufficient water to support their weight.
- Hot-air balloons rise because heated air is less dense than surrounding air.
- Hydrometers test the relative density of liquids.
- Atmospheric pressure measurements help in weather forecasting.
- Pressure gauges monitor industrial systems.
- Density measurements assist in identifying materials and controlling product quality.
8. Important Examination Distinctions
| Concept | Meaning | SI unit |
|---|---|---|
| Pressure | Force per unit area | Pascal |
| Density | Mass per unit volume | kg/m³ |
| Specific gravity | Ratio of two densities | Dimensionless |
| Atmospheric pressure | Pressure exerted by the atmosphere | Pascal |
| Gauge pressure | Pressure relative to atmosphere | Pascal |
| Absolute pressure | Pressure relative to vacuum | Pascal |
| Hydrostatic pressure | Pressure due to a fluid at rest | Pascal |
9. 36 Key Takeaways for Exams
- Pressure is the normal force acting per unit area.
- The SI unit of pressure is the pascal.
- One pascal equals one newton per square metre.
- Pressure increases with force when area remains constant.
- Pressure decreases when the area increases for the same force.
- Atmospheric pressure is caused by the weight of the atmosphere.
- Standard atmospheric pressure is 101,325 Pa.
- Standard atmospheric pressure is approximately 760 mmHg.
- Atmospheric pressure generally decreases with altitude.
- Absolute pressure is measured relative to a perfect vacuum.
- Gauge pressure is measured relative to atmospheric pressure.
- Absolute pressure equals atmospheric pressure plus gauge pressure.
- Hydrostatic pressure increases with depth.
- Hydrostatic pressure is calculated using (P=\rho gh).
- Hydrostatic pressure depends on fluid density, gravity and depth.
- Pascal’s principle states that pressure applied to an enclosed fluid is transmitted throughout it.
- Hydraulic machines operate on Pascal’s principle.
- Hydraulic machines multiply force but do not create energy.
- Density is mass per unit volume.
- The SI unit of density is kg/m³.
- Density is calculated using (\rho=m/V).
- One g/cm³ equals 1000 kg/m³.
- Density depends on the nature and physical conditions of a substance.
- Most substances expand and become less dense when heated.
- Water has maximum density at approximately 4°C.
- Ice is less dense than liquid water.
- Ice floats because its density is lower than that of water.
- Specific gravity is the ratio of a substance’s density to a reference density.
- Specific gravity has no unit.
- Water is the usual reference substance for solids and liquids.
- A substance with SG below 1 is generally less dense than water.
- A substance with SG above 1 is generally denser than water.
- A barometer measures atmospheric pressure.
- A manometer measures pressure or pressure difference.
- A hydrometer measures the relative density of liquids.
- Pressure, density and specific gravity are important in hydraulics, meteorology, engineering and material testing.