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Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The surface overflow rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d are designated as d30 and d15 respectively. The ratio d30/d15 (round off to two decimal places), is ___.
Correct answer is '1.41'. Can you explain this answer?
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Two identically sized primary settling tanks receive water for Type-I ...
For type-I setting, Stokes law is applicable.
Vs ∝ d2
Vs ∝ d2
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Two identically sized primary settling tanks receive water for Type-I ...
Given:
- Two identically sized primary settling tanks
- Type-I settling (discrete particles in dilute suspension)
- Laminar flow conditions
- Surface overflow rate (SOR) in Tank 1 = 30 m3/m2.d
- Surface overflow rate (SOR) in Tank 2 = 15 m3/m2.d
To Find:
- Ratio of lowest particle diameter settled completely under SOR 30 to SOR 15 (d30/d15)
Assumptions:
- The settling tanks are identical in size, shape, and design.
- The particles being settled are identical in composition and shape.
- Settling occurs under laminar flow conditions.
Explanation:
1. Surface Overflow Rate (SOR):
- Surface overflow rate (SOR) is the volume of water that overflows from a settling tank per unit area per day.
- SOR is measured in m3/m2.d.
2. Settling Velocity:
- Settling velocity is the rate at which particles settle in the settling tank.
- It is influenced by the particle size, shape, and the flow conditions.
- In laminar flow conditions, the settling velocity of particles can be calculated using Stokes' Law.
3. Stokes' Law:
- Stokes' Law describes the relationship between the settling velocity of a particle and its size.
- According to Stokes' Law, the settling velocity (V) of a particle is given by the equation V = (g * (d^2) * (ρp - ρf)) / (18 * μ), where
- V is the settling velocity,
- g is the acceleration due to gravity,
- d is the diameter of the particle,
- ρp is the density of the particle,
- ρf is the density of the fluid, and
- μ is the dynamic viscosity of the fluid.
4. Particle Settling:
- In settling tanks, particles settle based on their settling velocities.
- The particles with higher settling velocities settle out first, while particles with lower settling velocities remain in suspension for a longer time.
- The particle diameter at which it settles completely is known as the "diameter of complete sedimentation" or "diameter of complete settling."
5. Calculation:
- SOR is inversely proportional to the settling velocity of particles.
- The settling velocity is directly proportional to the square of the particle diameter.
- Let d30 be the diameter of the particle settled completely under SOR 30, and d15 be the diameter of the particle settled completely under SOR 15.
- According to Stokes' Law, the settling velocity is directly proportional to the square of the particle diameter.
- Therefore, the ratio of the settling velocities under SOR 30 and SOR 15 is (V30/V15) = (d30^2 / d15^2).
- Since the settling tanks are identical, the only difference is the SOR.
- Therefore, the ratio of SOR 30 to SOR 15 is (SOR30 / SOR15) = (V30 / V15) = (d30^2 / d15^2).
- Given that (SOR30 / SOR15) = 30 / 15 = 2
- Two identically sized primary settling tanks
- Type-I settling (discrete particles in dilute suspension)
- Laminar flow conditions
- Surface overflow rate (SOR) in Tank 1 = 30 m3/m2.d
- Surface overflow rate (SOR) in Tank 2 = 15 m3/m2.d
To Find:
- Ratio of lowest particle diameter settled completely under SOR 30 to SOR 15 (d30/d15)
Assumptions:
- The settling tanks are identical in size, shape, and design.
- The particles being settled are identical in composition and shape.
- Settling occurs under laminar flow conditions.
Explanation:
1. Surface Overflow Rate (SOR):
- Surface overflow rate (SOR) is the volume of water that overflows from a settling tank per unit area per day.
- SOR is measured in m3/m2.d.
2. Settling Velocity:
- Settling velocity is the rate at which particles settle in the settling tank.
- It is influenced by the particle size, shape, and the flow conditions.
- In laminar flow conditions, the settling velocity of particles can be calculated using Stokes' Law.
3. Stokes' Law:
- Stokes' Law describes the relationship between the settling velocity of a particle and its size.
- According to Stokes' Law, the settling velocity (V) of a particle is given by the equation V = (g * (d^2) * (ρp - ρf)) / (18 * μ), where
- V is the settling velocity,
- g is the acceleration due to gravity,
- d is the diameter of the particle,
- ρp is the density of the particle,
- ρf is the density of the fluid, and
- μ is the dynamic viscosity of the fluid.
4. Particle Settling:
- In settling tanks, particles settle based on their settling velocities.
- The particles with higher settling velocities settle out first, while particles with lower settling velocities remain in suspension for a longer time.
- The particle diameter at which it settles completely is known as the "diameter of complete sedimentation" or "diameter of complete settling."
5. Calculation:
- SOR is inversely proportional to the settling velocity of particles.
- The settling velocity is directly proportional to the square of the particle diameter.
- Let d30 be the diameter of the particle settled completely under SOR 30, and d15 be the diameter of the particle settled completely under SOR 15.
- According to Stokes' Law, the settling velocity is directly proportional to the square of the particle diameter.
- Therefore, the ratio of the settling velocities under SOR 30 and SOR 15 is (V30/V15) = (d30^2 / d15^2).
- Since the settling tanks are identical, the only difference is the SOR.
- Therefore, the ratio of SOR 30 to SOR 15 is (SOR30 / SOR15) = (V30 / V15) = (d30^2 / d15^2).
- Given that (SOR30 / SOR15) = 30 / 15 = 2
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Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The surface overflow rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d aredesignated as d30 and d15 respectively. The ratio d30/d15(round off to two decimal places), is ___.Correct answer is '1.41'. Can you explain this answer?
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Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The surface overflow rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d aredesignated as d30 and d15 respectively. The ratio d30/d15(round off to two decimal places), is ___.Correct answer is '1.41'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The surface overflow rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d aredesignated as d30 and d15 respectively. The ratio d30/d15(round off to two decimal places), is ___.Correct answer is '1.41'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The surface overflow rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d aredesignated as d30 and d15 respectively. The ratio d30/d15(round off to two decimal places), is ___.Correct answer is '1.41'. Can you explain this answer?.
Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The surface overflow rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d aredesignated as d30 and d15 respectively. The ratio d30/d15(round off to two decimal places), is ___.Correct answer is '1.41'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The surface overflow rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d aredesignated as d30 and d15 respectively. The ratio d30/d15(round off to two decimal places), is ___.Correct answer is '1.41'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The surface overflow rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d aredesignated as d30 and d15 respectively. The ratio d30/d15(round off to two decimal places), is ___.Correct answer is '1.41'. Can you explain this answer?.
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