the deepest part of the ocean is 10,900 meters deep.
a) calculate the absolute pressure at that depth in units N/m^2. Use the mass density of sea water, 1030 kg/m^3. see part b for more info
b) one atmosphere of pressure is about 1.013 X 10^5 N.m^2. How many atmospheres is the pressure of part a?
p = Patmosphere + rho g h
= 1.013*10^5 + 1030*9.81*10900
for part b divide that by 1.013*10^5
To calculate the absolute pressure at a given depth in a fluid, we can use the hydrostatic pressure formula:
P = ρgh
Where:
P is the pressure
ρ is the density of the fluid
g is the acceleration due to gravity
h is the height or depth of the fluid
a) To calculate the absolute pressure at 10,900 meters depth, we need to determine the density of seawater, which is given as 1030 kg/m^3. Assuming the acceleration due to gravity to be approximately 9.8 m/s^2, we can plug in the values into the formula:
P = (1030 kg/m^3) * (9.8 m/s²) * (10,900 m)
Calculating this gives us:
P = 111,784,400 N/m^2
Therefore, the absolute pressure at a depth of 10,900 meters is 111,784,400 N/m^2.
b) To calculate the pressure in atmospheres, we divide the absolute pressure by the atmospheric pressure. Given that one atmosphere of pressure is approximately 1.013 x 10^5 N/m^2, we can divide the absolute pressure (111,784,400 N/m^2) by this value:
Pressure in atmospheres = (111,784,400 N/m^2) / (1.013 x 10^5 N/m^2)
Calculating this gives us:
Pressure in atmospheres ≈ 1103.13 atmospheres
Therefore, the pressure at that depth is approximately 1103.13 atmospheres.