Hydrostatic Pressure in a Solar Pond with Variable Density
Solar ponds are small artificial lakes of a few meters deep that are used to store solar energy. The rise of heated (and thus less dense) water to the surface is prevented by adding salt at the pond bottom. In a typical salt gradient solar pond, the density of water increases in the gradient zone, as shown in Fig. 1–55, and the density can be expressed as
\rho=\rho_{0} \sqrt{1+\tan ^{2}\left(\frac{\pi}{4} \frac{z}{H}\right)}
where \rho_{0} is the density on the water surface, z is the vertical distance measured downward from the top of the gradient zone, and H is the thickness of the gradient zone. For H=4 m , \rho_{0}=1040 kg / m ^{3} , and a thickness of 0.8 m for the surface zone, calculate the gage pressure at the bottom of the gradient zone.
