Question

Problem: Find the change in volume of 1m3 of water when subjected to pressure increase of 35MPa .the bulk modulus of elasticity of water is 2.2×109Pa. Also estimate the volume of water after the pressure is applied

Answer 1

Answer on Question #53005 - Physics - Mechanics - Kinematics - Dynamics

Find the change in volume of $V_0 = 1 \, \text{m}^3$ of water when subjected to pressure increase of $\Delta P = 35 \, \text{MPa}$. The bulk modulus of elasticity of water is $K = 2.2 \times 10^9 \, \text{Pa}$. Also estimate the volume of water after the pressure is applied.

Solution:

The bulk modulus of $K$ of the liquid is given by

$$K = - V _ {0} \frac {\Delta P}{\Delta V},$$

where $\Delta V$ – is the increase in the volume of the fluid. Since $V_{0} = 1 \, \text{m}^{3}$, $K = 2.2 \times 10^{9} \, \text{Pa}$, and $\Delta P = 35 \, \text{MPa}$, we obtain

$$\Delta V = - \frac {V _ {0} \cdot \Delta P}{K} = - \frac {1 \, \text{m}^3 \cdot 35 \, \text{MPa}}{2.2 \times 10^9 \, \text{Pa}} = - 15.9 \times 10^{-6} \, \text{m}^3$$

The final volume is

$$V _ {f} = V _ {0} + \Delta V = 1 \, \text{m}^3 - 15.9 \times 10^{-6} \, \text{m}^3 = 0.9999841 \, \text{m}^3$$

**Answer**: $\Delta V = -15.9 \times 10^{-6} \, \text{m}^3$, $V_f = 0.9999841 \, \text{m}^3$.

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