Explanation Given information: The depth of the water reservoir dropped 20 feet in a drought. Formula used: The Nth Trapezoidal Rule approximately to ∫ a b f ( x ) d x is T N = 1 2 Δ x ( y 0 + 2 y 1 + 2 y 2 + ... + 2 y N − 1 + y N ) Where Δ x = b − a N a n d y j = f ( x j ) The formula for fluid force is F = ρ g ∫ a b y f ( y ) d y where ρ is the fluid density and g = 9.8 m / s 2 is the acceleration due to gravity, y is the depth from a to b and f ( y ) is the horizontal width of the side at depth y. Calculation: ρ = 6.367 is the water density and g = 9.8 m / s 2 is the acceleration due to gravity. Then the value of force F is given by F = 6.367 × 9.8 ∫ 0 100 y f ( y ) d y = 62.4 ∫ 0 100 y f ( y ) d y = 62.4 × 1 2 Δ x ( y 0 + 2 y 1 + 2 y 2 +

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 8.3, Problem 12E

To determine

To estimate:

The fluid force on the wall using Trapezoidal Rule.

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Chapter 8.3, Problem 11E

Chapter 8.3, Problem 13E

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Chapter 8 Solutions

Calculus: Early Transcendentals

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To estimate: The fluid force on the wall using Trapezoidal Rule.

Solution Summary: The author calculates the fluid force on the wall using the Trapezoidal Rule. The depth of the water reservoir dropped 20 feet in a drought.