How Does Water Density Change at Depths?

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SUMMARY

The discussion focuses on calculating the change in water density at a depth of 400 meters in a lake, starting with a surface density of 1030 kg/m³ and utilizing the bulk modulus of water, which is 2 x 109 Pa. The formula used is ρ = ρ0(1/(1 - dP/B)), where dP is the change in pressure calculated using hydrostatic pressure principles. The participant approximated the density change without calculus, achieving a result of 2.12618, which is close to the expected answer of 2, indicating that the approximation method is valid for this scenario.

PREREQUISITES
  • Understanding of hydrostatic pressure calculations
  • Familiarity with the bulk modulus of materials
  • Basic knowledge of density and its dependence on pressure
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the effects of pressure on fluid density in greater depth
  • Learn about the applications of the bulk modulus in different fluids
  • Explore calculus-based methods for more precise density calculations
  • Investigate hydrostatic pressure equations in various fluid dynamics scenarios
USEFUL FOR

Students studying fluid mechanics, physicists interested in hydrostatics, and engineers working with water systems will benefit from this discussion.

Abhishekdas
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Change in density of water...

Homework Statement


Calculate the approximate change in density of water in a lake at a depth of 400m below the surface. The density of water at the surface is 1030kg/m3 and bulk modulus(B) of water is 2*109...

Homework Equations


rho=rho0(1/(1-dP/B))
rho = density of water at any depth
rho0 = density of water at surface
dP= change in pressure

The Attempt at a Solution


How to calculate dP if i use h*rho*g , rho is not constant...So how do i go about it...Please help...
 
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I only know how to approximate this without calculus...it gets very,very close to the real value anyway.
First, assume that the density remains constant, and find the pressure at 400m using that density. Then recalculate the second density using that pressure.
Hope this helps!
 


Ok...thanks i will try it...
I am sorry i didnt notice your reply for a long time...
 


my answer is 2.12618 and answer in the book is 2...I guess they are expecting this answer ...But you it should be close as we are dealing with values of pressure musch lesser than Bulk modulus of water...But this is'nt a correct method is'nt it? Neway...thanks a lot for your help...
 

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