Final answer:
The absolute pressure at the deepest part of the lake is 472136.05 Pa, and the gage pressure, which is relative to atmospheric pressure, is 392400 Pa.
Step-by-step explanation:
To solve for the absolute and gage pressure at the deepest part of a lake, we need to consider the water depth and the atmospheric pressure above the lake. First, we convert the atmospheric pressure from mm of Hg to pascals:
- 1 atm = 760 mm Hg
- 1 atm = 101325 Pa
- Thus, 598 mm Hg = (598/760) × 101325 Pa = 79736.05 Pa
Next, we calculate the pressure due to the water at the lake's deepest point using the formula P = ρgh, where:
- ρ (rho) is the density of water, approximately 1000 kg/m3
- g is the acceleration due to gravity, which is about 9.81 m/s2
- h is the maximum depth of the lake, 40 m in this case
The pressure due to water at the bottom is:
P = 1000 kg/m3 × 9.81 m/s2 × 40 m = 392400 Pa
The absolute pressure at the bottom of the lake, which includes the atmospheric pressure above the lake, is:
Absolute Pressure = Atmospheric Pressure + Pressure due to Water
Absolute Pressure = 79736.05 Pa + 392400 Pa = 472136.05 Pa
The gage pressure, which is the pressure relative to atmospheric pressure, is simply the pressure due to the water:
Gage Pressure = 392400 Pa