Given: sigma is the compressibility of water, | vedclass

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(A) The pressure at a depth $h$ in a lake is given by the hydrostatic pressure formula: $P = h\rho g$.This pressure acts as the stress on the water.Th

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$\frac{1}{2}\sigma (h\rho g)^2$

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(A) The pressure at a depth $h$ in a lake is given by the hydrostatic pressure formula: $P = hho g$.This pressure acts as the stress on the water.The energy density $u$ stored in a material under stress is given by the formula: $u = \frac{1}{2} 	imes 	ext{stress} 	imes 	ext{strain}$.Since the bulk modulus $K = \frac{	ext{stress}}{	ext{strain}}$,we have $	ext{strain} = \frac{	ext{stress}}{K}$.Substituting this into the energy density formula: $u = \frac{1}{2} 	imes 	ext{stress} 	imes \frac{	ext{stress}}{K} = \frac{1}{2} \frac{(	ext{stress})^2}{K}$.Given that compressibility $\sigma = \frac{1}{K}$,we can rewrite the expression as: $u = \frac{1}{2} \sigma (	ext{stress})^2$.Substituting the stress $P = hho g$,we get: $u = \frac{1}{2} \sigma (hho g)^2$.

Given: $\sigma$ is the compressibility of water,$\rho$ is the density of water,and $K$ is the bulk modulus of water. What is the energy density of water at the bottom of a lake $h$ metre deep?

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