Determine the absolute pressure at the bottom of a lake that is 66.1 m deep. Write your answer correct to two decimal paces let Patm = 101,300 Pa
rho g h + Pa
1000 kg/m^3 * 9.81 * 66.1 + 101,300
648,441 + 101,300 = 749,741 Pascals
7.50 * 10^5 Pascals
two decimal places here only makes sense if using scientific notation
To determine the absolute pressure at the bottom of the lake, we can use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid due to the weight of the fluid above it.
The formula to calculate hydrostatic pressure is:
P = P₀ + ρgh
Where:
P is the absolute pressure at a certain depth,
P₀ is the atmospheric pressure (Patm in this case),
ρ is the density of the fluid (water in this case),
g is the acceleration due to gravity, and
h is the depth of the fluid.
Given:
P₀ = 101,300 Pa (atmospheric pressure)
h = 66.1 m (depth of the lake)
To calculate the absolute pressure, we need to find the density of water. The density of water is approximately 1000 kg/m³.
Now, we can substitute the values into the formula:
P = 101,300 + (1000 kg/m³) * (9.8 m/s²) * (66.1 m)
P = 101,300 + 646,180 N/m²
P = 747,480 N/m²
Finally, to convert the pressure from N/m² to Pascals (Pa), we divide by 1 N/m² = 1 Pa:
P = 747,480 Pa
Therefore, the absolute pressure at the bottom of the lake is 747,480 Pa (correct to two decimal places).