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Architecture Engineering QUESTION #2351
Question 1
For the most hydraulically efficient (economical) trapezoidal open channel cross-section, the hydraulic radius \(R\) at the optimal condition is related to the flow depth \(y\) by:
  • \(R = \dfrac{y}{4}\)
  • \(R = \dfrac{y}{2}\)✔️
  • \(R = y\)
  • \(R = 2y\)
Correct Answer Explanation
For the most economical trapezoidal section, the condition is \(R = y/2\) (hydraulic radius equals half the flow depth). This is equivalent to the condition that the channel can be inscribed in a semicircle of radius \(y\). For a rectangular channel, the economical condition \(b = 2y\) also yields \(R = y/2\).