The yellow submarine in which we all live is at rest s km below the surface of the ocean (ρ = 1030 kg/ms), what pressure does the water exert on the outside surface of the submarine if the pressure at the surface is 1 atm (101 kPa)?
Please help!!!! show all work
1 atm + rho g h
To calculate the pressure exerted by the water on the outside surface of the submarine, we can use the concept of hydrostatic pressure. The hydrostatic pressure is determined by the weight of the fluid above a specific point.
The formula to calculate hydrostatic pressure is:
P = ρgh
Where:
P is the pressure
ρ is the density of the fluid
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height or depth of the fluid column
In this case, the density of seawater (ρ) is given as 1030 kg/m^3, the height or depth (h) is s km below the surface, and the pressure at the surface is 1 atm, which is equivalent to 101 kPa.
To start, we need to convert s km to meters since the other values are given in SI units:
1 km = 1000 meters
So, the distance in meters would be:
s km = s * 1000 m
Next, we can substitute the given values into the formula and calculate the pressure:
P = (ρ)(g)(h)
P = (1030 kg/m^3)(9.8 m/s^2)(s * 1000 m)
As we want the pressure in kilopascals (kPa), we need to convert the result from the SI unit of pascals (Pa) to kPa:
1 kPa = 1000 Pa
Therefore, the pressure in kilopascals can be calculated as:
P (kPa) = (P (Pa)) / 1000
Once you substitute the values provided into the formula and perform the necessary calculations, you will obtain the pressure in kilopascals that the water exerts on the outside surface of the submarine.
Note: Make sure to use consistent units throughout the calculation to avoid errors.