Why Does Multiplying Pressure by \(10^5\) Help in Calculating Depth?

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SUMMARY

The discussion centers on the calculation of depth using the equation P = ρgh, where pressure (P) is expressed in Pascals (Pa). A participant mistakenly used atmospheric pressure without converting it to the correct SI units, leading to confusion. The correct approach involves multiplying the pressure by \(10^5\) to convert from atmospheres to Pascals, which is essential for accurate depth calculations. The final answer for the depth is confirmed to be 4100 meters.

PREREQUISITES
  • Understanding of fluid mechanics principles, specifically hydrostatic pressure.
  • Familiarity with the equation P = ρgh and its components.
  • Knowledge of unit conversions, particularly between atmospheres and Pascals.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Study unit conversions between different pressure units, focusing on atmospheres and Pascals.
  • Learn about hydrostatic pressure and its applications in real-world scenarios.
  • Explore the implications of density variations in fluid mechanics.
  • Practice solving problems involving the calculation of depth from pressure using P = ρgh.
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Students in physics or engineering courses, educators teaching fluid mechanics, and anyone involved in underwater exploration or related fields.

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Homework Statement


a1qqh1.png

PART B

Homework Equations


P = \rho gh


The Attempt at a Solution


Well I tried doing 412 = (1025)(9.8)h.. Divide by 10045 (9.8 x 1025). And ended up getting .041..
I found out that I need to use 412 x 105 for the pressure which I have no idea why.

Any help?

Also, the answer is 4100m
 
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iRaid said:

Homework Statement


a1qqh1.png

PART B

Homework Equations


P = \rho gh


The Attempt at a Solution


Well I tried doing 412 = (1025)(9.8)h.. Divide by 10045 (9.8 x 1025). And ended up getting .041..
I found out that I need to use 412 x 105 for the pressure which I have no idea why.

Any help?

Also, the answer is 4100m

You are mixing your units. "Atmospheres" is not an mks unit. You should write units in your equations as you go, to make sure that they are consistent (LSH units = RHS units, and the units of any quantities you are adding are the same).
 
In your equation P=ρgh, P is measured in Pascals (Pa)
 
Oh right thanks
 

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