Solving SV(z) = ∫ ρ(z)gdz ~ ρgz

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The discussion revolves around the formula SV(z) = ∫ ρ(z)gdz and its application in a homework problem. The poster attempts to manipulate the equation but presents a vague solution, leading to confusion among respondents. Clarification is provided that the symbol "~" indicates "approximately equal to." It is noted that if the density ρ is nearly constant over the depth z, it can be factored out of the integral, simplifying the expression to ρgz. The conversation emphasizes the need for clearer communication in mathematical problem-solving.
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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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