What is the unit weight of water in kg m3?
The Correct Answer and Explanation is :
The unit weight of water is approximately 1,000 kg/m³ at standard temperature and pressure conditions (specifically at 4 degrees Celsius). This value is crucial in various scientific and engineering applications, including fluid mechanics, civil engineering, and environmental science.
Explanation
Density and Unit Weight: The unit weight of a substance is closely related to its density. Density (( \rho )) is defined as mass (( m )) per unit volume (( V )), given by the formula:
[
\rho = \frac{m}{V}
]
For water, at its maximum density (4°C), the density is about 1,000 kg/m³, meaning one cubic meter of water has a mass of 1,000 kilograms. Unit weight (( \gamma )) is defined as the weight of a substance per unit volume. It can be calculated using the formula:
[
\gamma = \rho \cdot g
]
where ( g ) is the acceleration due to gravity (approximately 9.81 m/s²). When substituting the density of water, the unit weight of water becomes:
[
\gamma = 1,000 \text{ kg/m³} \times 9.81 \text{ m/s²} \approx 9,810 \text{ N/m³}
]
Importance in Applications: Understanding the unit weight of water is essential in many fields. In civil engineering, it helps in calculating the buoyant forces acting on submerged objects and determining the load-bearing capacity of soils. In environmental science, it assists in modeling the behavior of water in natural systems, including rivers and lakes.
Variations: The unit weight of water can vary slightly with changes in temperature and salinity. For example, seawater, which contains salts and other dissolved substances, has a higher density (around 1,025 kg/m³) than pure water, leading to a greater unit weight.
In summary, the unit weight of water at standard conditions is about 1,000 kg/m³, making it a fundamental value in physics and engineering.