Calculate the pressure on the top lid of a chest buried under 4.30 meters of mud with density 1.75 103 kg/m3 at the bottom of a 12.5-m-deep lake

To calculate the pressure on the top lid of a chest buried under mud at the bottom of a lake, we need to consider two factors: the depth of the mud and the density of the mud.

Here's how you can calculate it step by step:

1. First, calculate the pressure due to the water column above the mud. The pressure in a fluid due to the weight of the fluid column is given by the formula:

Pressure = Density * Gravity * Depth

In this case, the density of water is approximately 1000 kg/m^3, and the acceleration due to gravity is 9.8 m/s^2. The depth of the lake is given as 12.5 meters. So, the pressure due to the water column is:

Pressure_water = Density_water * Gravity * Depth_water
= (1000 kg/m^3) * (9.8 m/s^2) * (12.5 m)
= 122,500 Pascal (Pa)

2. Next, we need to calculate the pressure due to the mud column above the top lid of the chest. The pressure in the mud is calculated using the same formula as above, but this time, we use the density of the mud (1.75 * 10^3 kg/m^3) and the depth through the mud (4.30 meters). So, the pressure due to the mud column is:

Pressure_mud = Density_mud * Gravity * Depth_mud
= (1.75 * 10^3 kg/m^3) * (9.8 m/s^2) * (4.30 m)
= 74,319 Pascal (Pa)

3. Finally, we add the pressure due to the water column and the pressure due to the mud column to get the total pressure on the top lid of the chest:

Total pressure = Pressure_water + Pressure_mud
= 122,500 Pa + 74,319 Pa
= 196,819 Pascal (Pa)

So, the pressure on the top lid of the chest buried under 4.30 meters of mud at the bottom of a 12.5-meter deep lake is approximately 196,819 Pascal.