Answer
At a depth of 31 meters, the water pressure is 4.0 atm
Work Step by Step
We can find the required gauge pressure:
$P_{abs} = P_{atm}+P_g$
$P_g = P_{abs} - P_{atm}$
$P_g = 4.0~atm - 1.0~atm$
$P_g = 3.0~atm$
We can convert the gauge pressure to units of $N/m^2$:
$3.0~atm \times \frac{1.01\times 10^5~N/m^2}{1~atm} = 3.03\times 10^5~N/m^2$
We need to find the depth $h$ below the surface with this gauge pressure:
$\rho~gh = 3.03\times 10^5~N/m^2$
$h = \frac{3.03\times 10^5~N/m^2}{\rho~g}$
$h = \frac{3.03\times 10^5~N/m^2}{(1.0\times 10^3~kg/m^3)(9.80~m/s^2)}$
$h = 31~m$
At a depth of 31 meters, the water pressure is 4.0 atm.
