Solving SV(z) = ∫ ρ(z)gdz ~ ρgz

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SUMMARY

The discussion centers around the equation SV(z) = ∫ ρ(z)gdz, where ρ represents density and z denotes depth. Participants clarify that the symbol "~" indicates "approximately equal to." When density ρ is considered constant over the depth range, it can be factored out of the integral, simplifying the equation to SV(z) ≈ ρgz. This understanding is crucial for solving related problems in fluid mechanics or physics.

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  • Knowledge of fluid mechanics concepts, particularly density and gravitational force.
  • Familiarity with mathematical notation and symbols, including approximation signs.
  • Basic proficiency in applying physical formulas to real-world scenarios.
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  • Study the principles of integral calculus to enhance understanding of definite integrals.
  • Explore fluid mechanics textbooks focusing on density and buoyancy calculations.
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g0ggs123
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Homework Statement


I just need to use this formula and then apply p = density and I z= depth

Homework Equations



SV(z) = ∫ ρ(z)gdz ~ ρgz

The Attempt at a Solution


(ρ(z)(z)g))/2 and if ~ ρgz is multiple it would be (ρ(z)(z)g))/2 * ρgz which is (ρ(ρ)(z)(z)(z)g(g)))/2

Thanks for your help in advance,

Also not sure what ~ means in this instance??

G
 
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Is there a question here?

This whole post is incredibly vague.
 
g0ggs123 said:

Homework Statement


I just need to use this formula and then apply p = density and I z= depth

Homework Equations



SV(z) = ∫ ρ(z)gdz ~ ρgz

The Attempt at a Solution


(ρ(z)(z)g))/2 and if ~ ρgz is multiple it would be (ρ(z)(z)g))/2 * ρgz which is (ρ(ρ)(z)(z)(z)g(g)))/2

Thanks for your help in advance,

Also not sure what ~ means in this instance??

G
I agree with post 2, you are not making much sense.
However, the ~ sign means "approximately equal to". If ρ is substantially constant over the range of z then it can be taken out of the integral sign and you get ρgz.
 

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