Question

Problem: Due to an increase in pressure of 10Pa in a liquid, the density increases by 0.02%. What is its bulk modulus of elasticity? In this case, use the formula for the bulk modulus of elasticity in terms of density change.

Answer 1

Answer on Question #53006 - Physics - Mechanics - Kinematics - Dynamics

Due to an increase in pressure of $\Delta P = 10$ Pa in a liquid, the density $\rho$ increases by $\frac{\Delta\rho}{\rho} = 0.02\%$ . What is its bulk modulus of elasticity $K$ ? In this case, use the formula for the bulk modulus of elasticity in terms of density change.

Solution:

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

$$K = \rho \frac {\Delta P}{\Delta \rho},$$

where $\Delta \rho$ – is the increase in the density of the fluid. Since $\Delta P = 10\mathrm{Pa}$ , and $\frac{\Delta\rho}{\rho} = 0.02\%$ , we obtain

$$K = \rho \frac {\Delta P}{\Delta \rho} = \frac {\Delta P}{\left(\frac {\Delta \rho}{\rho}\right)} = \frac {1 0 \mathrm {P a}}{2 \times 1 0 ^ {- 4}} = 5 \times 1 0 ^ {4} \mathrm {P a}$$

Answer: $5 \times 10^{4} \mathrm{~Pa}$ .

http://www.AssignmentExpert.com/