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Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________
Correct answer is '3'. Can you explain this answer?
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Constant head permeability tests were performed on two soil specimens,...
For constant head permeability test,
k = QL/ah
Q → discharge
L → length of specimen
a → area of cross-section of specimen
h → constant head
Given,
Q → discharge
L → length of specimen
a → area of cross-section of specimen
h → constant head
Given,
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Constant head permeability tests were performed on two soil specimens,...
Ratio of height of the specimens:
Given that the ratio of the height of the two soil specimens (LS1: LS2) is 1.5, we can assume that LS1 is 1.5 times the height of LS2.
Ratio of the diameter of the specimens:
The ratio of the diameter of the two soil specimens (DS1: DS2) is given as 0.5, which means DS1 is half the diameter of DS2.
Ratio of the constant head applied:
The ratio of the constant head applied on the two soil specimens (hs1: hs2) is given as 2.0, which means hs1 is twice the constant head of hs2.
Discharge from both specimens:
Given that the discharge from both the specimens is equal, it implies that the volume of water flowing through both specimens is the same.
Permeability of the soil specimens:
The permeability of a soil specimen can be calculated using Darcy's law, which states that the discharge (Q) through a soil specimen is directly proportional to the cross-sectional area (A) and the hydraulic gradient (i), and inversely proportional to the coefficient of permeability (k) of the soil.
Q = A * k * i
Since the discharge is the same for both specimens, we can equate the equations for the two specimens:
A1 * k1 * i1 = A2 * k2 * i2
Ratio of the cross-sectional area of the specimens:
The cross-sectional area of a specimen is directly proportional to the square of its diameter. Therefore, we can write:
A1/A2 = (DS1/DS2)^2 = (0.5)^2 = 0.25
Ratio of the hydraulic gradients:
The hydraulic gradient is the ratio of the head loss (h) to the length (L) of the soil specimen. Since the height of the specimens is in the ratio 1.5, we can assume that the length is also in the same ratio.
L1/L2 = 1.5
Ratio of the permeability of the soil specimens:
Substituting the above ratios into the equation for discharge, we get:
(0.25) * k1 * i1 = k2 * i2
Since the discharge is the same for both specimens, the ratio of the permeability can be written as:
k1/k2 = (i2/i1) * (1/0.25)
Given that hs1/hs2 = 2, and i = h/L, we can substitute the values:
k1/k2 = (hs2/hs1) * (L2/L1) * (1/0.25)
Since L2/L1 = 1.5 and hs2/hs1 = 2, we can calculate:
k1/k2 = 2 * 1.5 * 4 = 12
Therefore, the ratio of the permeability of the soil specimens is 12:1, which simplifies to 3 when divided by 4.
Given that the ratio of the height of the two soil specimens (LS1: LS2) is 1.5, we can assume that LS1 is 1.5 times the height of LS2.
Ratio of the diameter of the specimens:
The ratio of the diameter of the two soil specimens (DS1: DS2) is given as 0.5, which means DS1 is half the diameter of DS2.
Ratio of the constant head applied:
The ratio of the constant head applied on the two soil specimens (hs1: hs2) is given as 2.0, which means hs1 is twice the constant head of hs2.
Discharge from both specimens:
Given that the discharge from both the specimens is equal, it implies that the volume of water flowing through both specimens is the same.
Permeability of the soil specimens:
The permeability of a soil specimen can be calculated using Darcy's law, which states that the discharge (Q) through a soil specimen is directly proportional to the cross-sectional area (A) and the hydraulic gradient (i), and inversely proportional to the coefficient of permeability (k) of the soil.
Q = A * k * i
Since the discharge is the same for both specimens, we can equate the equations for the two specimens:
A1 * k1 * i1 = A2 * k2 * i2
Ratio of the cross-sectional area of the specimens:
The cross-sectional area of a specimen is directly proportional to the square of its diameter. Therefore, we can write:
A1/A2 = (DS1/DS2)^2 = (0.5)^2 = 0.25
Ratio of the hydraulic gradients:
The hydraulic gradient is the ratio of the head loss (h) to the length (L) of the soil specimen. Since the height of the specimens is in the ratio 1.5, we can assume that the length is also in the same ratio.
L1/L2 = 1.5
Ratio of the permeability of the soil specimens:
Substituting the above ratios into the equation for discharge, we get:
(0.25) * k1 * i1 = k2 * i2
Since the discharge is the same for both specimens, the ratio of the permeability can be written as:
k1/k2 = (i2/i1) * (1/0.25)
Given that hs1/hs2 = 2, and i = h/L, we can substitute the values:
k1/k2 = (hs2/hs1) * (L2/L1) * (1/0.25)
Since L2/L1 = 1.5 and hs2/hs1 = 2, we can calculate:
k1/k2 = 2 * 1.5 * 4 = 12
Therefore, the ratio of the permeability of the soil specimens is 12:1, which simplifies to 3 when divided by 4.
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Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________Correct answer is '3'. Can you explain this answer?
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Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________Correct answer is '3'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________Correct answer is '3'. Can you explain this answer?.
Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________Correct answer is '3'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________Correct answer is '3'. Can you explain this answer?.
Solutions for Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________Correct answer is '3'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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