6. (Extra Credit) Solar ponds are small artificial lakes 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 Figure 3, and the density

can be expressed as

P = Po√√1+tan² (77)

where po is the density on the water surface, z is the vertical distance measured down-

ward from the top of the gradient zone, and H is the thickness of the gradient zone.

For H = 4 m, po = 1040 kg/m³, and a thickness of 0.8 m for the surface zone, calculate

the gage pressure at the bottom of the gradient zone.