Question

In a vertical cylindrical vessel of base area $A=80c{m}^2,$ water is filled to a height h = 30 cm. If density and bulk modulus of water be $\rho =1000kg{m}^{-3}$ and $B=2\times {10}^{9}N{m}^{-2}$. The elastic deformation energy of water in the vessel is $P\times 9\times {10}^{-7}$ Joule. Find the value of P. (Take g = 10 $m/s^2)$___

Answer 1

Energy density $=\frac{p^2}{2B}$
Volume of a layer of water of thickness = Ady
dy at a depthe y is
Energy stored in this layer = dU = $\frac{P^2}{2B}$ Ady
$dU=\frac{{\rho }^2{g}^{2}A}{2B}{y}^2$ dy
Total strain energy stored in the water of vessel
$U=\frac{{\rho }^2{g}^{2}A}{2B}{\int }_0^h{y}^{2}dyU=\frac{{\rho }^2{g}^{2}A{h}^3}{6B}=1.8\times {10}^{-6}JouleU=2\times 9\times {10}^{-7}JouleP=2$