The density rho of a fluid changes proportionally with depth from the surface h according to the following formula: rho(h) = rho0 + ch. where rho0 is the density of the fluid at the surface (h = 0), and c is a constant.
(a) Write an expression for the gauge pressure p as a function of the depth. E
(b) A pressure gauge is placed at a depth of 5.3 m in a fluid with a density that varies with depth as described above. The constant c is 790 kg/m^4. The density of the fluid at h = 0 is 0 kg/m^4. What pressure, in pascals, would the gauge read?