Problem Statement
If the bulk modulus of elasticity of water is 2.2 GPa (GN/m²), what pressure is required to reduce a volume by 0.8%?
Given Data
- Bulk modulus of elasticity (K) = 2.2 GPa = 2.2 × 10⁹ Pa
- Reduction in volume (ΔV/V) = -0.8% = -0.008
- Required: Pressure (P)
Solution
1. Recall the Bulk Modulus Formula
K = -P / (ΔV/V)
2. Rearrange Formula to Solve for Pressure
P = -K × (ΔV/V)
3. Substitute Values and Calculate
P = -(2.2 × 10⁹) × (-0.008)
P = 17.6 × 10⁶ Pa = 17.6 MPa
Required Pressure = 17.6 MPa
Explanation
The bulk modulus formula relates pressure changes to fractional volume changes. When arranging the formula to solve for pressure, we multiply the bulk modulus by the fractional change in volume.
The negative sign in the formula accounts for the inverse relationship between pressure and volume – as pressure increases, volume decreases. The volume reduction of 0.8% is expressed as -0.008 in decimal form.
The final result of 17.6 MPa represents the pressure required to achieve a 0.8% reduction in the water’s volume, demonstrating water’s significant resistance to compression.
🔍 Discover More About Similar Topic
