In a rectangular channel, the alternate depths are 1.5 m and 2.5 m respectively. The specific energy head (in meter) is

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BPSC AE Paper 6 (Civil) 14 Oct 2022 Official Paper
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  1. 4.48
  2. 3.35
  3. 3.26
  4. 3.06

Answer (Detailed Solution Below)

Option 4 : 3.06
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Detailed Solution

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Concept:

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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