Question
Download Solution PDFIn a rectangular channel, the alternate depths are 1.5 m and 2.5 m respectively. The specific energy head (in meter) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The specific energy head in a rectangular channel with given alternate depths can be calculated using the formula:
\( E = \frac{y_1^2 + y_2^2 + y_1 \times y_2}{y_1 + y_2} \)
Calculation:
Given:
- Alternate depth \( y_1 = 1.5 \) m
- Alternate depth \( y_2 = 2.5 \) m
Substitute the given values into the formula:
\( E = \frac{(1.5)^2 + (2.5)^2 + (1.5 \times 2.5)}{1.5 + 2.5} \)
Calculate the numerator:
- \( y_1^2 = (1.5)^2 = 2.25 \, \text{m}^2 \)
- \( y_2^2 = (2.5)^2 = 6.25 \, \text{m}^2 \)
- \( y_1 \times y_2 = 1.5 \times 2.5 = 3.75 \, \text{m}^2 \)
- \( \text{Numerator} = 2.25 + 6.25 + 3.75 = 12.25 \, \text{m}^2 \)
Calculate the denominator:
\( y_1 + y_2 = 1.5 + 2.5 = 4 \, \text{m} \)
Calculate the specific energy head \( E \):
\( E = \frac{12.25 \, \text{m}^2}{4 \, \text{m}} \)
\( E = 3.06 \, \text{m} \)
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