Answer :
Final answer:
The depth at which the pressure in a lake is 197 lb/in², when calculated using principles of fluid mechanics, is approximately 138 meters.
Explanation:
The problem given can be solved using the concepts of fluid mechanics which is part of physics.
When a body submerged in a fluid, there will be a pressure exerted on it by the fluid. This pressure increases with the depth and is given by the equation: P = ρgh, where P is the pressure, ρ is the fluid density (for water it's typically aprox. 1000 kg/m³), g is the acceleration due to gravity (approx. 9.8 m/s² on Earth) and h is the depth.
In your question, the pressure P is 197 lb/in². To make this compatible with our equation, we need to convert this to Pascals (Pa). This comes to approximately 1357903.8 Pa.
Substituting the values for ρ and g we get: 1357903.8 = 1000*9.8*h, solving we find approximately 138 m for h, the depth in the lake.
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