Formula of object immersed in water

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The discussion centers on the formula for the pressure exerted by an object immersed in water, specifically questioning why the equation uses P(yc)A instead of P(yc^2)A. The definition of yc, as given in equation 3-18, is clarified to be the average depth of the area, calculated as yc = (1/A)∫Ay dA. This leads to the conclusion that the correct expression for pressure is P(yc)A, not P(yc^2)A. The participants confirm that the derivation aligns with the definitions provided in the referenced equations. The focus remains on understanding the application of the average depth in pressure calculations.
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Homework Statement


why the y ſ P dA will equal to P yc A ? why not P (yc^2) A ? since yc = ſ y dA / A

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It comes from the definition of yc at 3-18.
 
haruspex said:
It comes from the definition of yc at 3-18.
according to 3-18 , i would get P (yc^2) A instead of P (yc) A ... am i correct ?
 
werson tan said:
according to 3-18 , i would get P (yc^2) A instead of P (yc) A ... am i correct ?
No.
3-18 defines ##y_c=\frac 1A\int_AydA##. So at 3-20, ##P_0\int_AydA=P_0Ay_c##.
How do you get yc2 terms?
 
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