Calculate the pressure on the top lid of a chest buried under 4.30 meters of mud with density 1.75X 10^3 kg/m^3 at the bottom of a 12.5 m deep lake

Answer 1

To find the pressure on the top lid at the bottom of a lake, we need to calculate both water pressure and mud pressure.

First, let's calculate the water pressure.
The formula for the pressure at a depth h in a fluid is given by:
P = ρgh, where ρ is the density, g is the acceleration due to gravity, and h is the depth.

Given the depth of the lake h1 = 12.5 m and the density of water ρ1 = 1000 kg/m^3 (approximately, assuming fresh water), along with acceleration due to gravity g = 9.81 m/s^2, we can calculate the pressure due to the water:

P1 = ρ1 * g * h1
P1 = 1000 kg/m^3 * 9.81 m/s^2 * 12.5 m
P1 = 122625 Pa (Pascals)

Now let's calculate the pressure due to the mud.

Given, density of mud ρ2 = 1.75 * 10^3 kg/m^3 and depth of mud h2 = 4.30 m,

P2 = ρ2 * g * h2
P2 = 1.75 * 10^3 kg/m^3 * 9.81 m/s^2 * 4.30 m
P2 ≈ 73819.5 Pa

Now, to find the total pressure, add both the water pressure and the mud pressure:

P_total = P1 + P2
P_total = 122625 Pa + 73819.5 Pa
P_total ≈ 196444.5 Pa

So, the pressure on the top lid of the chest buried under the mud at the bottom of the lake is approximately 196444.5 Pascals.