What is the formula for the weight of a fluid block?

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SUMMARY

The weight of a fluid block is calculated using the formula W = ρg[(R^2) - π(R^2)] for a specific geometric configuration involving a square and a quarter circle. The term "1m" refers to the length of the fluid block being considered, which is 1 meter into the paper, indicating the weight per unit length. The formula accounts for the difference in area between the square and the quarter circle, essential for determining the fluid's weight accurately.

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  • Understanding of fluid density (ρ) and gravitational acceleration (g).
  • Familiarity with geometric shapes, specifically squares and circles.
  • Knowledge of basic physics principles related to weight and volume.
  • Ability to manipulate algebraic expressions involving π and area calculations.
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  • Study the derivation of fluid weight formulas in physics textbooks.
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werson tan
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Homework Statement


why the formula of weight of fluid block is given by the formula of ρg[ (R^2) - pi(R^2) ] 1?

what does the 1m mean here ?
shouldn't it = ρg (pi) (R^2) h ?
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The Attempt at a Solution

 

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It's a square minus a quarter circle. ##W## is the weight of 1 m length (i.e. into the paper) of the area shaded grey in the right picture in Fig 3-36.
 
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