An eardrum can burst when the pressure exceeds one atmosphere and the pressure inside the ear fails to equalize. Determine the depth in seawater when this pressure would be reached.
(pressure of ocean = 1.03*10^3 kg/m^3)
Well, at the depth of seawater above weights enough to give a pressure of 101.3kpa
Water pressure= densityseawater*depth*9.8N/kg=101.3kPa
To determine the depth in seawater when the pressure exceeds one atmosphere, we need to use the concept of hydrostatic pressure.
The hydrostatic pressure at a certain depth in a fluid is given by the formula:
Pressure = density * acceleration due to gravity * depth.
In this case, the density of seawater is given as 1.03 x 10^3 kg/m^3.
The acceleration due to gravity is approximately 9.8 m/s^2.
We can rearrange the formula to solve for the depth:
Pressure = density * acceleration due to gravity * depth
depth = Pressure / (density * acceleration due to gravity)
Substituting the values into the formula, we have:
depth = (1 atm) / (1.03 x 10^3 kg/m^3 * 9.8 m/s^2)
Converting 1 atmosphere to pascals, we have:
depth = (101325 Pa) / (1.03 x 10^3 kg/m^3 * 9.8 m/s^2)
Evaluating the expression, we get:
depth ≈ 10.011 meters
Therefore, the depth in seawater when the pressure exceeds one atmosphere and the pressure inside the ear fails to equalize is approximately 10.011 meters.
To determine the depth in seawater when the pressure would exceed one atmosphere, we need to calculate the pressure at that depth.
First, let's assume that the pressure at the surface of the ocean is equal to one atmosphere, which is approximately 101,325 pascals (Pa).
As we go deeper into the seawater, the pressure increases due to the weight of the water above. The increase in pressure with depth in a fluid is given by the formula:
Pressure = Density * Gravity * Depth
Where:
- Pressure is the pressure at a given depth
- Density is the density of the fluid (seawater in this case)
- Gravity is the acceleration due to gravity (approximately 9.8 m/s^2)
- Depth is the depth below the surface
We are given the density of seawater as 1.03 * 10^3 kg/m^3.
Since we want to determine the depth at which the pressure exceeds one atmosphere, we can set up the following equation:
Pressure = 1 atm = 101,325 Pa
101,325 = (1.03 * 10^3) * 9.8 * Depth
Simplifying the equation, we can isolate the depth on one side:
Depth = 101,325 / [(1.03 * 10^3) * 9.8]
Evaluating this expression, we find:
Depth ≈ 104.11 meters
Therefore, the depth in seawater at which the pressure would exceed one atmosphere (and potentially cause an eardrum to burst if not equalized) is approximately 104.11 meters.