Question
Download Solution PDFCalculate the most economic area of a rectangular channel section with width ‘B’ and depth ‘y’.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Concept:
Most economical hydraulic section:
- The discharge from a channel section increases with increases in hydraulic radius or with decrease in the wetted perimeter.
- From hydraulics viewpoint, therefore, the channel section having the least wetted perimeter for a given area has the maximum discharge; such a section is known as the best hydraulic section or most economical hydraulic section
- So for most economical hydraulic section;
- Wetted perimeter (P) = Minimum ⇒Q= maximum
Calculation:
Let us consider a rectangular channel section of width B, the depth of flow in the channel is y.
For P = minimum ⇒ \(\frac{dP}{dy}=0\)
Wetted perimeter P = B + 2y and Area A = B x y ⇒ \(B=\frac{A}{y}\)
\(P=\frac{A}{y}+2y\) and \(\frac{dP}{dy}=\frac{A}{y^2}+2\)
For maximum discharge, P=> minimum
\(\frac{dP}{dy}=0\) ⇒ \(\frac{dP}{dy}=\frac{A}{y^2}+2=0\) ⇒ \(A=2y^2\) ⇒\(B\times y=2y^2\) ⇒ \(B=2y\)
So, area A=2y2
Last updated on May 28, 2025
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