What would the gauge pressure be on a diver in atmospheres if she could dive to a depth of one km in sea water? One atmosphere is 1.01 X 10^5 N/m2. The density of sea water is 1.03 X 10^3 kg/m3.
To find the gauge pressure on a diver one kilometer deep in sea water, we can make use of the hydrostatic pressure formula. The hydrostatic pressure is given by:
P = ρgh
Where:
P is the pressure,
ρ is the density of the fluid (sea water),
g is the acceleration due to gravity,
h is the depth.
Given:
- Density of sea water (ρ) = 1.03 x 10^3 kg/m^3.
- Depth (h) = 1 km = 1000 m.
First, we need to find the value of g. The acceleration due to gravity is approximately 9.81 m/s^2 on Earth. Now we can calculate the gauge pressure using the formula mentioned earlier.
P = (1.03 x 10^3 kg/m^3) x (9.81 m/s^2) x (1000 m)
P = 1.0113 x 10^7 N/m^2
Since 1 atmosphere is equal to 1.01 x 10^5 N/m^2, we can convert the gauge pressure to atmospheres by dividing it by the atmospheric pressure.
Gauge Pressure (in atmospheres) = (1.0113 x 10^7 N/m^2) / (1.01 x 10^5 N/m^2)
Gauge Pressure (in atmospheres) ≈ 100.23 atmospheres
Therefore, if the diver could dive to a depth of one kilometer in sea water, the gauge pressure would be approximately 100.23 atmospheres.