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A settling tank in a water treatment plant is designed for a surface overflow rate of 30m3/day.m2. Assume specific gravity of the sediment particles = 2.65 , density of water 1000kg/m3 , dynamic viscosity of water = .001 N.s /m2 , and stokes law is valid. The approximate minimum size of particles that would be completly removed is:?
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A settling tank in a water treatment plant is designed for a surface o...
Answer:
Explanation:
The settling tank is designed for a surface overflow rate of 30 m3/day.m2. To determine the minimum size of particles that would be completely removed, we need to use Stoke's law. Stoke's law relates the settling velocity of particles in a fluid to the size, shape, and density of the particles, as well as the viscosity and density of the fluid.
Stoke's Law: V = (2/9) * (ρp - ρf) * g * r2 / η
Where,
V = settling velocity (m/s)
ρp = density of particle (kg/m3)
ρf = density of fluid (kg/m3)
g = acceleration due to gravity (m/s2)
r = radius of particle (m)
η = dynamic viscosity of fluid (N.s/m2)
Calculation:
Given, surface overflow rate = 30 m3/day.m2
Density of water, ρf = 1000 kg/m3
Dynamic viscosity of water, η = 0.001 N.s/m2
Density of sediment particles, ρp = 2.65
We can calculate the settling velocity of particles using Stoke's law. However, we don't have the radius of the particle. So, we need to assume a particle size that would be the minimum size that would be completely removed.
Let's assume a particle size of 0.01 mm (10 µm).
Using Stoke's Law:
V = (2/9) * (ρp - ρf) * g * r2 / η
V = (2/9) * (2.65 - 1) * 9.81 * (0.00001)2 / 0.001
V = 0.000000021 m/s
Now, we can calculate the settling time for a particle of size 10 µm using the settling velocity we just calculated.
Settling Time:
t = h / V
t = 1 / (30 / (24 * 3600)) / (0.000000021)
t = 11.4 days
This means that a particle with a size of 10 µm would take approximately 11.4 days to settle in the settling tank. Therefore, particles smaller than 10 µm would not be completely removed from the water in the settling tank.
Explanation:
The settling tank is designed for a surface overflow rate of 30 m3/day.m2. To determine the minimum size of particles that would be completely removed, we need to use Stoke's law. Stoke's law relates the settling velocity of particles in a fluid to the size, shape, and density of the particles, as well as the viscosity and density of the fluid.
Stoke's Law: V = (2/9) * (ρp - ρf) * g * r2 / η
Where,
V = settling velocity (m/s)
ρp = density of particle (kg/m3)
ρf = density of fluid (kg/m3)
g = acceleration due to gravity (m/s2)
r = radius of particle (m)
η = dynamic viscosity of fluid (N.s/m2)
Calculation:
Given, surface overflow rate = 30 m3/day.m2
Density of water, ρf = 1000 kg/m3
Dynamic viscosity of water, η = 0.001 N.s/m2
Density of sediment particles, ρp = 2.65
We can calculate the settling velocity of particles using Stoke's law. However, we don't have the radius of the particle. So, we need to assume a particle size that would be the minimum size that would be completely removed.
Let's assume a particle size of 0.01 mm (10 µm).
Using Stoke's Law:
V = (2/9) * (ρp - ρf) * g * r2 / η
V = (2/9) * (2.65 - 1) * 9.81 * (0.00001)2 / 0.001
V = 0.000000021 m/s
Now, we can calculate the settling time for a particle of size 10 µm using the settling velocity we just calculated.
Settling Time:
t = h / V
t = 1 / (30 / (24 * 3600)) / (0.000000021)
t = 11.4 days
This means that a particle with a size of 10 µm would take approximately 11.4 days to settle in the settling tank. Therefore, particles smaller than 10 µm would not be completely removed from the water in the settling tank.
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A settling tank in a water treatment plant is designed for a surface overflow rate of 30m3/day.m2. Assume specific gravity of the sediment particles = 2.65 , density of water 1000kg/m3 , dynamic viscosity of water = .001 N.s /m2 , and stokes law is valid. The approximate minimum size of particles that would be completly removed is:?
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A settling tank in a water treatment plant is designed for a surface overflow rate of 30m3/day.m2. Assume specific gravity of the sediment particles = 2.65 , density of water 1000kg/m3 , dynamic viscosity of water = .001 N.s /m2 , and stokes law is valid. The approximate minimum size of particles that would be completly removed is:? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A settling tank in a water treatment plant is designed for a surface overflow rate of 30m3/day.m2. Assume specific gravity of the sediment particles = 2.65 , density of water 1000kg/m3 , dynamic viscosity of water = .001 N.s /m2 , and stokes law is valid. The approximate minimum size of particles that would be completly removed is:? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A settling tank in a water treatment plant is designed for a surface overflow rate of 30m3/day.m2. Assume specific gravity of the sediment particles = 2.65 , density of water 1000kg/m3 , dynamic viscosity of water = .001 N.s /m2 , and stokes law is valid. The approximate minimum size of particles that would be completly removed is:?.
A settling tank in a water treatment plant is designed for a surface overflow rate of 30m3/day.m2. Assume specific gravity of the sediment particles = 2.65 , density of water 1000kg/m3 , dynamic viscosity of water = .001 N.s /m2 , and stokes law is valid. The approximate minimum size of particles that would be completly removed is:? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A settling tank in a water treatment plant is designed for a surface overflow rate of 30m3/day.m2. Assume specific gravity of the sediment particles = 2.65 , density of water 1000kg/m3 , dynamic viscosity of water = .001 N.s /m2 , and stokes law is valid. The approximate minimum size of particles that would be completly removed is:? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A settling tank in a water treatment plant is designed for a surface overflow rate of 30m3/day.m2. Assume specific gravity of the sediment particles = 2.65 , density of water 1000kg/m3 , dynamic viscosity of water = .001 N.s /m2 , and stokes law is valid. The approximate minimum size of particles that would be completly removed is:?.
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