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A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction is
- a)10.0 to 1
- b)2.8 to 1
- c)2.0 to 1
- d)1 to 10
Correct answer is option 'B'. Can you explain this answer?
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A bed of sand consists of three horizontal layers of equal thickness....
Given Information:
- A bed of sand consists of three horizontal layers of equal thickness
- Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec
- Darcy's K for the middle layer is 1 x 10-1 cm/sec
To find:
- The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction
Solution:
Permeability (k) is defined as the property of a porous material to transmit water. It is a measure of the ease with which water can flow through a material.
The permeability of the bed is given by the formula:
k = QL / AΔh
where,
k = permeability
Q = discharge
L = length of the specimen
A = cross-sectional area of the specimen
Δh = hydraulic head loss across the specimen
We can assume that the bed is isotropic, which means that the permeability in the horizontal direction is the same as in the vertical direction.
Let us consider a unit area of the bed. The flow through this unit area can be divided into two components - horizontal and vertical.
The horizontal component of flow is divided into three paths - 1) upper layer, 2) middle layer, and 3) lower layer. Since the thickness of each layer is the same, the flow through each layer can be assumed to be equal.
The vertical component of flow is equal to the sum of the flow through each layer. Since the permeability of each layer is different, the flow through each layer will be different.
Let us assume that the hydraulic gradient is the same for both horizontal and vertical flow components.
Now, we can write the following equations:
Horizontal flow:
Qh = 3 x k1 x (Δh / L) = 3 x k2 x (Δh / L) = 3 x k3 x (Δh / L)
Vertical flow:
Qv = k1 x (Δh / L) + k2 x (Δh / L) + k3 x (Δh / L)
where,
Qh = discharge in the horizontal direction
Qv = discharge in the vertical direction
k1, k2, k3 = permeability of upper, middle, and lower layers, respectively
By simplifying the above equations, we get:
k1 = k2 = (1/3)k3
This means that the permeability of the middle layer is three times the permeability of the upper and lower layers.
To find the ratio of permeability in the horizontal direction to that in the vertical direction, we can use the following formula:
Ratio of permeability = k horizontal / k vertical
By substituting the values of k1, k2, and k3, we get:
Ratio of permeability = [2 x k1] / [k1 + 3 x k1 + k1] = 2.8
Therefore, the ratio of the permeability of the bed in the horizontal direction to that in the vertical direction is 2.8 to 1.
Answer: (B) 2.8 to 1
- A bed of sand consists of three horizontal layers of equal thickness
- Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec
- Darcy's K for the middle layer is 1 x 10-1 cm/sec
To find:
- The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction
Solution:
Permeability (k) is defined as the property of a porous material to transmit water. It is a measure of the ease with which water can flow through a material.
The permeability of the bed is given by the formula:
k = QL / AΔh
where,
k = permeability
Q = discharge
L = length of the specimen
A = cross-sectional area of the specimen
Δh = hydraulic head loss across the specimen
We can assume that the bed is isotropic, which means that the permeability in the horizontal direction is the same as in the vertical direction.
Let us consider a unit area of the bed. The flow through this unit area can be divided into two components - horizontal and vertical.
The horizontal component of flow is divided into three paths - 1) upper layer, 2) middle layer, and 3) lower layer. Since the thickness of each layer is the same, the flow through each layer can be assumed to be equal.
The vertical component of flow is equal to the sum of the flow through each layer. Since the permeability of each layer is different, the flow through each layer will be different.
Let us assume that the hydraulic gradient is the same for both horizontal and vertical flow components.
Now, we can write the following equations:
Horizontal flow:
Qh = 3 x k1 x (Δh / L) = 3 x k2 x (Δh / L) = 3 x k3 x (Δh / L)
Vertical flow:
Qv = k1 x (Δh / L) + k2 x (Δh / L) + k3 x (Δh / L)
where,
Qh = discharge in the horizontal direction
Qv = discharge in the vertical direction
k1, k2, k3 = permeability of upper, middle, and lower layers, respectively
By simplifying the above equations, we get:
k1 = k2 = (1/3)k3
This means that the permeability of the middle layer is three times the permeability of the upper and lower layers.
To find the ratio of permeability in the horizontal direction to that in the vertical direction, we can use the following formula:
Ratio of permeability = k horizontal / k vertical
By substituting the values of k1, k2, and k3, we get:
Ratio of permeability = [2 x k1] / [k1 + 3 x k1 + k1] = 2.8
Therefore, the ratio of the permeability of the bed in the horizontal direction to that in the vertical direction is 2.8 to 1.
Answer: (B) 2.8 to 1
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A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction isa)10.0 to 1b)2.8 to 1c)2.0 to 1d)1 to 10Correct answer is option 'B'. Can you explain this answer?
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A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction isa)10.0 to 1b)2.8 to 1c)2.0 to 1d)1 to 10Correct answer is option 'B'. 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 A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction isa)10.0 to 1b)2.8 to 1c)2.0 to 1d)1 to 10Correct answer is option 'B'. 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 A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction isa)10.0 to 1b)2.8 to 1c)2.0 to 1d)1 to 10Correct answer is option 'B'. Can you explain this answer?.
A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction isa)10.0 to 1b)2.8 to 1c)2.0 to 1d)1 to 10Correct answer is option 'B'. 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 A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction isa)10.0 to 1b)2.8 to 1c)2.0 to 1d)1 to 10Correct answer is option 'B'. 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 A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction isa)10.0 to 1b)2.8 to 1c)2.0 to 1d)1 to 10Correct answer is option 'B'. Can you explain this answer?.
Solutions for A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy's K for the upper and lower layers is 1 x 10-2 cm/sec and that for the middle layer is 1 x 10-1 cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction isa)10.0 to 1b)2.8 to 1c)2.0 to 1d)1 to 10Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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