Short Answer:

Specific weight is defined as the weight of a fluid per unit volume. It tells us how much weight a certain volume of fluid has. The specific weight depends on both the density of the fluid and the acceleration due to gravity (g). It is denoted by the symbol w (sometimes γ) and is measured in newtons per cubic meter (N/m³).

The formula for specific weight is:

where ρ = density of the fluid (kg/m³), and g = acceleration due to gravity (9.81 m/s²). For example, the specific weight of water is approximately 9810 N/m³.

Detailed Explanation :

Specific Weight

Specific weight is an important physical property of fluids that represents the weight per unit volume of a substance. It shows how heavy a given volume of fluid is under the influence of gravity. In simple terms, specific weight describes how much force due to gravity acts on a certain volume of fluid.

Mathematically, it is expressed as:

where,

• w = Specific weight (N/m³)
• ρ = Density of the fluid (kg/m³)
• g = Acceleration due to gravity (9.81 m/s²)

Since weight is the product of mass and gravitational acceleration, the specific weight directly relates to density. The higher the density of a fluid, the greater its specific weight.

Concept of Specific Weight

The concept of specific weight helps in understanding how fluids behave under the influence of gravity. For example, two fluids with the same volume but different densities will have different specific weights. A denser fluid like mercury will have a much higher specific weight than water because its particles are more closely packed and it contains more mass per unit volume.

Specific weight is a force property, not just a mass property, because it depends on the gravitational pull. This means the specific weight of a fluid can slightly change with location—since gravity (g) varies slightly from place to place on Earth.

For instance, gravity is a bit stronger near the poles than at the equator, so the specific weight of water will be slightly higher near the poles.

Units of Specific Weight

In the SI system, the specific weight is expressed in newton per cubic meter (N/m³).

• 1 N = 1 kg·m/s²
  Hence,

In the CGS system, it is expressed in dyne/cm³.
However, in engineering practice, the SI unit (N/m³) is widely used because it directly relates to gravitational force.

Example:
If the density of water is 1000 kg/m³ and g = 9.81 m/s², then

This means every cubic meter of water weighs 9810 newtons.

Relation Between Density and Specific Weight

Specific weight and density are closely related but not the same.

• Density (ρ) is the mass per unit volume.
• Specific weight (w) is the weight per unit volume.

The relationship is given by:

So, for a constant gravitational acceleration, specific weight is directly proportional to density. When density increases, specific weight also increases.

Example:

• For oil (ρ = 850 kg/m³):

• For mercury (ρ = 13,600 kg/m³):

This shows that mercury has a much higher specific weight compared to water or oil.

Importance of Specific Weight in Engineering

Specific weight plays a major role in mechanical and civil engineering calculations involving fluids, materials, and energy. It helps in determining fluid pressures, forces on submerged surfaces, and flow behavior in pipes and channels. Some key applications include:

1. Hydrostatic Pressure Calculation:
   The pressure in a fluid at rest depends on its specific weight. The hydrostatic pressure at a depth   is given by

Thus, the greater the specific weight, the higher the pressure at a given depth.

1. Design of Dams and Reservoirs:
   Engineers use specific weight to calculate the total water pressure on the dam surface. This helps in designing strong and stable dam structures.
2. Hydraulic Machines:
   The performance and power output of pumps, turbines, and other hydraulic systems depend on the specific weight of the working fluid.
3. Buoyancy and Floating Bodies:
   The buoyant force acting on a submerged object equals the weight of the displaced fluid, which is determined using the specific weight.
4. Material Selection:
   In mechanical and structural design, the specific weight helps in selecting materials that meet strength and weight requirements.

Specific Weight of Common Substances

Approximate values of specific weight for some common fluids at standard conditions are:

• Water = 9810 N/m³
• Sea water = 10250 N/m³
• Mercury = 133,000 N/m³
• Air = 12 N/m³
• Oil = 8300 to 8800 N/m³

These values help engineers and scientists perform practical calculations in hydraulics, aerodynamics, and thermal systems.

Variation with Temperature and Pressure

The specific weight of a fluid changes with temperature and pressure because these factors affect its density.

• With temperature rise: Fluids expand, density decreases, and specific weight reduces.
• With pressure increase: Fluids compress slightly, density increases, and specific weight increases.

However, for liquids, these variations are small, while for gases, they can be significant due to higher compressibility.

Conclusion

In conclusion, specific weight is defined as the weight per unit volume of a substance. It depends on the density of the fluid and the gravitational acceleration. Specific weight is an essential parameter in fluid mechanics and engineering calculations, as it helps determine pressure, buoyancy, and other fluid forces. Understanding specific weight allows engineers to design efficient hydraulic systems, dams, and fluid flow mechanisms, ensuring accuracy and safety in engineering applications.