A submarine called the DeepView 66 is currently being built to take tourists on undersea tours along tropical coral reefs. According to the guidelines of the American Society of Mechanical Engineers, to be safe for human occupancy the submarine must be able to withstand a pressure of 1.0 × 106 Pa from the water. To what depth can the submarine safely descend in seawater? Take the density of seawater to be 1030 kg/m3.
To determine the depth to which the submarine can safely descend in seawater, we can use the concept of hydrostatic pressure. The hydrostatic pressure at a certain depth in a fluid is given by the equation:
P = ρgh
Where:
P is the pressure
ρ (rho) is the density of the fluid
g is the acceleration due to gravity
h is the height (or depth) of the fluid column
In this case, we want to find the depth at which the pressure is 1.0 × 10^6 Pa, and the density of seawater (ρ) is 1030 kg/m^3.
Rearranging the equation, we have:
h = P / (ρg)
Substituting the given values, we get:
h = (1.0 × 10^6 Pa) / (1030 kg/m^3 × 9.8 m/s^2)
Simplifying the expression, we have:
h ≈ 98 meters
Therefore, the submarine can safely descend to a depth of approximately 98 meters in seawater while withstanding a pressure of 1.0 × 10^6 Pa.