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If during a permeability test on a soil sample with a falling head permeameter, equal time intervals are noted for drop of head of from h1 to h2 and again from h2 to h3 then which one of the following relations would hold good?
- a)h32 = h1h2
- b)h22 = h1h3
- c)h1 2 = h2 h3
- d)(h1-h2) =(h2-h3)
Correct answer is option 'B'. Can you explain this answer?
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If during a permeability test on a soil sample with a falling head pe...
Explanation:
In a falling head permeameter test, the head (h) of water in the standpipe is measured at regular time intervals as it falls through the soil sample. The head drop is recorded as h1, h2, and h3 at the respective time intervals.
The falling head permeameter test is used to determine the coefficient of permeability (k) of the soil sample. The coefficient of permeability is given by the relation:
k = (2.303 × L × A) / (t × log(h1/h2))
Where:
k = Coefficient of permeability
L = Length of the soil sample
A = Cross-sectional area of the soil sample
t = Time interval between h1 and h2
Analysis:
In the given question, the time intervals for the head drop from h1 to h2 and from h2 to h3 are stated to be equal. Let us assume the time interval to be 't'.
From the given information, we can write the following relations:
h1 - h2 = k × t × log(h1/h2)
h2 - h3 = k × t × log(h2/h3)
Simplification:
To determine the relation between h1, h2, and h3, we need to eliminate the term 't' from the above equations.
Dividing equation 1 by equation 2, we get:
(h1 - h2) / (h2 - h3) = (log(h1/h2)) / (log(h2/h3))
Taking the antilogarithm of both sides, we get:
(h1 - h2) / (h2 - h3) = (h1/h2) / (h2/h3)
Simplifying further, we get:
(h1 - h2) / (h2 - h3) = (h1/h2) × (h3/h2)
Final Relation:
(h1 - h2) / (h2 - h3) = h1 × h3 / h2^2
Comparing the above relation with the given options:
(h1 - h2) / (h2 - h3) = h1 × h3 / h2^2
Therefore, option B is the correct relation that holds good in this case.
Conclusion:
In a falling head permeameter test, if the time intervals for the head drop from h1 to h2 and from h2 to h3 are equal, then the relation (h1 - h2) / (h2 - h3) = h1 × h3 / h2^2 holds true.
In a falling head permeameter test, the head (h) of water in the standpipe is measured at regular time intervals as it falls through the soil sample. The head drop is recorded as h1, h2, and h3 at the respective time intervals.
The falling head permeameter test is used to determine the coefficient of permeability (k) of the soil sample. The coefficient of permeability is given by the relation:
k = (2.303 × L × A) / (t × log(h1/h2))
Where:
k = Coefficient of permeability
L = Length of the soil sample
A = Cross-sectional area of the soil sample
t = Time interval between h1 and h2
Analysis:
In the given question, the time intervals for the head drop from h1 to h2 and from h2 to h3 are stated to be equal. Let us assume the time interval to be 't'.
From the given information, we can write the following relations:
h1 - h2 = k × t × log(h1/h2)
h2 - h3 = k × t × log(h2/h3)
Simplification:
To determine the relation between h1, h2, and h3, we need to eliminate the term 't' from the above equations.
Dividing equation 1 by equation 2, we get:
(h1 - h2) / (h2 - h3) = (log(h1/h2)) / (log(h2/h3))
Taking the antilogarithm of both sides, we get:
(h1 - h2) / (h2 - h3) = (h1/h2) / (h2/h3)
Simplifying further, we get:
(h1 - h2) / (h2 - h3) = (h1/h2) × (h3/h2)
Final Relation:
(h1 - h2) / (h2 - h3) = h1 × h3 / h2^2
Comparing the above relation with the given options:
Option B:
(h1 - h2) / (h2 - h3) = h1 × h3 / h2^2
Therefore, option B is the correct relation that holds good in this case.
Conclusion:
In a falling head permeameter test, if the time intervals for the head drop from h1 to h2 and from h2 to h3 are equal, then the relation (h1 - h2) / (h2 - h3) = h1 × h3 / h2^2 holds true.
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Community Answer
If during a permeability test on a soil sample with a falling head pe...
⇒ h 2 2 =h1 h3
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If during a permeability test on a soil sample with a falling head permeameter, equal time intervals are noted for drop of head of from h1 to h2 and again from h2 to h3 then which one of the following relations would hold good?a)h32 = h1h2b)h22 = h1h3c)h1 2 = h2 h3d)(h1-h2) =(h2-h3)Correct answer is option 'B'. Can you explain this answer?
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