Explanation Given: The figure is And, edges of plate are the curves y = x 1 3 and y = − x 1 3 . Formula used: Force on a plate with horizontal strip at depth h and width w is given by F = ρ g ∫ 0 a ( h ) ⋅ ( w ) d y Where height and width both function of y and ρ is density. a is the height of the plate from water surface. Calculation: Consider the figure The objective is to calculate the fluid force on a side of the plate in given figure which is submerged in a fluid density ρ = 1200 kg/m 3 . And given that, edges of plate are the curves at y = x 1 3 and y = − x 1 3 . We can write y = x 1 3 as x = y 3 and y = − x 1 3 as x = − y 3 . So, at height y , the plate extends from point ( − y 3 , y ) to ( y 3 , y ) . Then, the width of the plate is y 3 − ( − y 3 ) = y 3 + y 3 = 2 y 3 The water surface is at height 2 on y − axis

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Chapter 8.3, Problem 16E

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The fluid force on a side of the plate in given figure which is submerged in a fluid density ρ=1200 kg/m3.

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Chapter 8.3, Problem 15E

Chapter 8.3, Problem 17E

Chapter 8 Solutions

Calculus: Early Transcendentals

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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The fluid force on a side of the plate in given figure which is submerged in a fluid density ρ = 1200 kg/m 3 .

Solution Summary: The author explains the formula used to calculate the fluid force on a plate with horizontal strip at depth h and width w.

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To calculate:

The fluid force on a side of the plate in given figure which is submerged in a fluid density ρ=1200 kg/m3.

Want to see the full answer?

Chapter 8 Solutions

The fluid force on a side of the plate in given figure which is submerged in a fluid density ρ = 1200 kg/m 3 .

Solution Summary: The author explains the formula used to calculate the fluid force on a plate with horizontal strip at depth h and width w.

Concept explainers

Videos

To calculate: The fluid force on a side of the plate in given figure which is submerged in a fluid density ρ=1200 kg/m3.

Want to see the full answer?

Chapter 8 Solutions

To calculate:

The fluid force on a side of the plate in given figure which is submerged in a fluid density ρ=1200 kg/m3.