Short Answer:

The fundamental dimensions are the basic physical quantities that are independent of each other and are used to express all other physical quantities in mechanics and engineering. The most commonly used fundamental dimensions are mass (M), length (L), time (T), temperature (θ), electric current (I), luminous intensity (J), and amount of substance (N).

In simple words, fundamental dimensions are the building blocks of all physical measurements. Every derived physical quantity, like velocity, force, or pressure, can be expressed in terms of these basic dimensions. They provide a consistent framework for defining and comparing all measurable quantities in science and engineering.

Detailed Explanation:

Fundamental Dimensions

In engineering and physics, all physical quantities can be classified into two types — fundamental quantities and derived quantities.

• Fundamental quantities are those that cannot be expressed in terms of any other quantities.
• Derived quantities are those that can be expressed as a combination of fundamental quantities.

The fundamental dimensions correspond to these fundamental quantities and form the basis of the dimensional system used in mechanics and other fields.

The use of dimensions allows engineers and scientists to establish relationships between various physical quantities and check the correctness of equations by ensuring that they are dimensionally consistent.

1. Meaning of Fundamental Dimensions

The term fundamental dimension refers to the basic measurable quantities that define all other physical quantities. These dimensions are independent of each other, which means that one cannot be derived from another.

For example:

• The dimension of velocity can be expressed in terms of length (L) and time (T) as [L T⁻¹].
• Similarly, force is derived from mass (M), length (L), and time (T) as [M L T⁻²].

However, the quantities mass, length, and time themselves cannot be expressed in terms of any other quantities — hence, they are called fundamental dimensions.

2. Fundamental Dimensions Used in Mechanics

In mechanical engineering and fluid mechanics, only three fundamental dimensions are most commonly used:

1. Mass (M)
2. Length (L)
3. Time (T)

All mechanical quantities such as force, pressure, energy, and power can be derived from these three. This system is therefore known as the M-L-T system.

However, in general physics, additional fundamental dimensions are also considered, depending on the physical phenomenon being studied.

3. Complete List of Fundamental Dimensions

The internationally accepted SI system (Systeme International d’Unités) recognizes seven fundamental dimensions, which are as follows:

1. Length (L):
   • It represents the measurement of distance or space occupied.
   • Example: meter (m).
   • Used in defining velocity, area, volume, etc.
2. Mass (M):
   • It represents the amount of matter contained in a body.
   • Example: kilogram (kg).
   • Used in defining momentum, force, energy, etc.
3. Time (T):
   • It measures the duration of an event or process.
   • Example: second (s).
   • Used in defining velocity, acceleration, frequency, etc.
4. Temperature (θ):
   • It represents the degree of hotness or coldness of a body.
   • Example: kelvin (K).
   • Used in defining heat transfer, thermal energy, and entropy.
5. Electric Current (I):
   • It represents the rate of flow of electric charge.
   • Example: ampere (A).
   • Used in defining electrical quantities such as voltage, resistance, and power.
6. Luminous Intensity (J):
   • It represents the brightness or intensity of light emitted by a source.
   • Example: candela (cd).
   • Used in defining luminous flux and illumination.
7. Amount of Substance (N):
   • It measures the number of atoms, molecules, or particles in a substance.
   • Example: mole (mol).
   • Used in chemical calculations and thermodynamic processes.

These seven dimensions are universally accepted for representing all measurable quantities across different branches of science and engineering.

4. Importance of Fundamental Dimensions

The concept of fundamental dimensions is extremely important in engineering and scientific analysis. It provides a foundation for dimensional equations and unit systems. The major advantages are:

1. Helps in Dimensional Analysis:
   • Fundamental dimensions are used to express derived quantities and simplify complex relationships.
2. Ensures Equation Correctness:
   • Dimensional homogeneity requires that all terms in an equation must have the same dimensions, ensuring that the equation is physically meaningful.
3. Useful in Unit Conversion:
   • Dimensions provide a way to convert quantities from one unit system (such as CGS) to another (such as SI).
4. Simplifies Model Studies:
   • In fluid mechanics, fundamental dimensions help establish similarity laws between models and prototypes (for example, using dimensionless numbers like Reynolds and Froude numbers).
5. Foundation of Derived Quantities:
   • Quantities like force, energy, and power are derived directly from fundamental dimensions. For instance:
     • Force = [M L T⁻²]
     • Energy = [M L² T⁻²]
     • Pressure = [M L⁻¹ T⁻²]

5. Systems of Fundamental Dimensions

Different systems of fundamental dimensions exist, depending on the type of measurements used. The four major systems are:

1. MKS System (Meter–Kilogram–Second):
   • Based on mass, length, and time.
   • It forms the basis of the modern SI system.
2. CGS System (Centimeter–Gram–Second):
   • Older system used for small-scale measurements.
3. FPS System (Foot–Pound–Second):
   • Used mainly in the British engineering system.
4. SI System (Systeme International):
   • The modern and universally accepted system that includes seven fundamental dimensions.

Each system maintains consistency by using the same basic dimensions but with different units.

6. Example of Derived Quantities from Fundamental Dimensions

Every derived quantity can be expressed using fundamental dimensions.
For example:

• Velocity: [L T⁻¹]
• Acceleration: [L T⁻²]
• Force: [M L T⁻²]
• Work or Energy: [M L² T⁻²]
• Pressure: [M L⁻¹ T⁻²]

This shows that all physical quantities are dependent on a few fundamental dimensions.

Conclusion

In conclusion, the fundamental dimensions are the essential and independent physical quantities that form the foundation of all scientific and engineering measurements. Every other quantity, known as a derived quantity, can be expressed using these basic dimensions. The seven recognized fundamental dimensions in the SI system are length, mass, time, temperature, electric current, luminous intensity, and amount of substance. They play a vital role in ensuring dimensional consistency, performing dimensional analysis, converting units, and deriving relationships among physical quantities. Understanding fundamental dimensions is therefore essential in the study and application of fluid mechanics, thermodynamics, and all fields of engineering.