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Prove that the three sides of the trapezoidal section of most economical section are tangential to the semi circle on the water line
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The three sides of the trapezoidal section of most economical section are tangential to the semi-circle described on the water line. This is proved as

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Let Fig.shows the trapezoidal channel of most economical section

Let $\theta=$ angle made by the the sloping sides with horizontal

Draw $O F$ perpendicular to …

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