What is the specific weight (unit weight) of water in SI units, to the nearest standard value?

Introduction:
Specific weight (unit weight) is weight per unit volume. For water at standard conditions, engineers commonly use a convenient rounded value for design and quick checks.

Given Data / Assumptions:

• Standard reference conditions near 4°C to 20°C.
• Acceleration due to gravity g ≈ 9.81 m/s^2.

Concept / Approach:
Specific weight gamma = rho * g. For water, rho ≈ 1000 kg/m^3. Therefore gamma ≈ 1000 * 9.81 N/m^3 = 9810 N/m^3 = 9.81 kN/m^3. This is the widely accepted design value in SI.

Step-by-Step Solution:
1) Take rho_w ≈ 1000 kg/m^3.2) Multiply by g: 1000 * 9.81 = 9810 N/m^3.3) Convert to kN: 9810 N/m^3 = 9.81 kN/m^3.

Verification / Alternative check:
Using more precise densities changes only the third decimal place of gamma, not the standard rounded 9.81 kN/m^3 used for hand calculations.

Why Other Options Are Wrong:

• 981 kN/m^3: Off by a factor of 100; implies rho ≈ 100,000 kg/m^3.
• 9.81 N/m^3: Off by a factor of 1000; would imply extremely low density.
• 9810 kN/m^3: Off by a factor of 1000; numerically equals 9.81 MN/m^3, not water.

Common Pitfalls:

• Mixing N/m^3 and kN/m^3 units.
• Using mass density (kg/m^3) directly as specific weight without multiplying by g.

Final Answer:
9.81 kN/m^3