Pressure on a Diver at 15 m Depth – Hydrostatic Pressure Calculation & Example | Query Point Official
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Determine the Pressure Exerted on a Diver at 15 m Below Sea Level
When an object is submerged in a fluid, the pressure acting on it increases with depth. This increase is due to the hydrostatic pressure exerted by the fluid above the object. The total pressure on a diver underwater is the sum of atmospheric pressure and water pressure.
Question
Determine the pressure exerted on a diver at a depth of 15 m below the free surface of the sea. Assume the atmospheric pressure is 101 kPa and the specific gravity of seawater is 1.03.
Given Data
- Atmospheric pressure, `\( P_{atm} = 101 \, \text{kPa} = 101000 \, \text{Pa} \)`
- Depth below surface, `\( h = 15 \, \text{m} \)`
- Specific gravity of seawater = 1.03
- Acceleration due to gravity, `\( g = 9.81 \, \text{m/s}^2 \)`
Density of seawater:
`\[` `\rho = 1.03 \times 1000 = 1030 \, \text{kg/m}^3` `\]`
Formula Used
`\[` `P = P_{atm} + \rho g h` `\]`
Solution
`\[` `P = 101000 + (1030 \times 9.81 \times 15)` `\]`
`\[` `P = 101000 + 151564` `\]`
`\[` `P = 252564 \, \text{Pa}` `\]`
Final Answer
Therefore, the pressure exerted on the diver at a depth of 15 m below the free surface of the sea is:
`\[` `\boxed{P = 2.53 \times 10^5 \, \text{Pa}}` `\]`
Frequently Asked Questions (FAQs)
1. Why is atmospheric pressure added in underwater pressure calculations?
Atmospheric pressure acts on the water surface and is transmitted through the fluid, so it must be included in the total pressure.
2. Why does seawater exert more pressure than freshwater?
Seawater has a higher density due to dissolved salts, which increases hydrostatic pressure.
3. What happens to pressure as depth increases?
Pressure increases linearly with depth because more fluid weight acts on the submerged object.
4. Is this question important for exams?
Yes, this is a frequently asked numerical problem in physics, fluid mechanics, and engineering exams.
Explore more about FLUID MECHANICS in Mathematics Notes & MCQs.
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