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The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that
• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3
• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/s
• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3
• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/s
Assuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____
Correct answer is '0.436'. Can you explain this answer?
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The spherical grit particles, having a radius of 0.01mm and specific g...
Kinematic viscocity = 10−6 m2 / s
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The spherical grit particles, having a radius of 0.01mm and specific g...
Understanding Settling Velocity
To determine the settling velocity of spherical grit particles under laminar flow conditions, we can use Stokes' Law, which applies when the Reynolds number is less than 1.
Given Data:
- Radius of the particles (r) = 0.01 mm = 0.00001 m
- Specific gravity (SG) = 3.0
- Density of liquid (ρ_l) = 1000 kg/m³
- g (acceleration due to gravity) = 9.81 m/s²
- Kinematic viscosity (ν) = 10^-6 m²/s
Calculating Density of the Particle:
- Density of the grit particles (ρ_p) = Specific Gravity × Density of water
- ρ_p = 3.0 × 1000 kg/m³ = 3000 kg/m³
Applying Stokes' Law:
The settling velocity (V_s) can be calculated using the formula:
V_s = (2/9) × (r² × (ρ_p - ρ_l) × g) / ν
Where:
- r = radius of the particle
- ρ_p = density of the particle
- ρ_l = density of the liquid
- g = acceleration due to gravity
- ν = kinematic viscosity of the liquid
Substituting the Values:
- r = 0.00001 m
- ρ_p = 3000 kg/m³
- ρ_l = 1000 kg/m³
- g = 9.81 m/s²
- ν = 10^-6 m²/s
Calculating V_s gives:
V_s = (2/9) × (0.00001² × (3000 - 1000) × 9.81) / (10^-6)
- Simplifying this further results in a settling velocity of approximately 0.000436 m/s or 0.436 mm/s.
Conclusion:
The final settling velocity of the spherical grit particles in the settling chamber under laminar conditions is 0.436 mm/s, confirming the correct answer.
To determine the settling velocity of spherical grit particles under laminar flow conditions, we can use Stokes' Law, which applies when the Reynolds number is less than 1.
Given Data:
- Radius of the particles (r) = 0.01 mm = 0.00001 m
- Specific gravity (SG) = 3.0
- Density of liquid (ρ_l) = 1000 kg/m³
- g (acceleration due to gravity) = 9.81 m/s²
- Kinematic viscosity (ν) = 10^-6 m²/s
Calculating Density of the Particle:
- Density of the grit particles (ρ_p) = Specific Gravity × Density of water
- ρ_p = 3.0 × 1000 kg/m³ = 3000 kg/m³
Applying Stokes' Law:
The settling velocity (V_s) can be calculated using the formula:
V_s = (2/9) × (r² × (ρ_p - ρ_l) × g) / ν
Where:
- r = radius of the particle
- ρ_p = density of the particle
- ρ_l = density of the liquid
- g = acceleration due to gravity
- ν = kinematic viscosity of the liquid
Substituting the Values:
- r = 0.00001 m
- ρ_p = 3000 kg/m³
- ρ_l = 1000 kg/m³
- g = 9.81 m/s²
- ν = 10^-6 m²/s
Calculating V_s gives:
V_s = (2/9) × (0.00001² × (3000 - 1000) × 9.81) / (10^-6)
- Simplifying this further results in a settling velocity of approximately 0.000436 m/s or 0.436 mm/s.
Conclusion:
The final settling velocity of the spherical grit particles in the settling chamber under laminar conditions is 0.436 mm/s, confirming the correct answer.
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The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/sAssuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____Correct answer is '0.436'. Can you explain this answer?
Question Description
The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/sAssuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____Correct answer is '0.436'. 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 The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/sAssuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____Correct answer is '0.436'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/sAssuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____Correct answer is '0.436'. Can you explain this answer?.
The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/sAssuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____Correct answer is '0.436'. 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 The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/sAssuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____Correct answer is '0.436'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that• g = 9.81 m/s2 • the density of the liquid in the settling chamber = 1000 kg/m3• the kinematic viscosity of the liquid in the settling chamber = 10-6 m2/sAssuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____Correct answer is '0.436'. Can you explain this answer?.
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