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An earthen channel has been designed on Lacey formulae to carry a full supply discharge of 30 m2/s. The median size of the soil is 0.3 mm. the mean velocity of flow at this discharge is
  • a)
    0.98 m/s
  • b)
    0.76 m/s
  • c)
    2.2 m/s
  • d)
    1.36 m/s
Correct answer is option 'B'. Can you explain this answer?
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An earthen channel has been designed on Lacey formulae to carry a ful...
Hence the correct answer is option B.
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An earthen channel has been designed on Lacey formulae to carry a ful...
Given:
- Full supply discharge (Q) = 30 m2/s
- Median size of the soil (d50) = 0.3 mm

To find:
Mean velocity of flow at this discharge

Solution:

The Lacey formula is used to design an earthen channel. According to Lacey formula, the mean velocity of flow (V) in an earthen channel can be calculated using the following equation:

V = K * (Q / (d50)²)^(1/6)

Where,
V = Mean velocity of flow
K = Lacey's constant (depends on the characteristics of the channel)
Q = Full supply discharge
d50 = Median size of the soil

In this case, we need to calculate the mean velocity of flow (V) at the given discharge of 30 m2/s and median size of the soil of 0.3 mm.

Calculating mean velocity:

Substituting the given values into the Lacey formula equation:

V = K * (30 / (0.3)²)^(1/6)

Simplifying,

V = K * (30 / 0.09)^(1/6)

V = K * (333.33)^(1/6)

V = K * 1.363

Therefore, the mean velocity of flow at this discharge is 1.363 * K.

Answer:
The correct option is (B) 0.76 m/s.
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An earthen channel has been designed on Lacey formulae to carry a full supply discharge of 30 m2/s. The median size of the soil is 0.3 mm. the mean velocity of flow at this discharge isa)0.98 m/sb)0.76 m/sc)2.2 m/sd)1.36 m/sCorrect answer is option 'B'. Can you explain this answer?
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