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A bed of spherical glass beads (density 3000 kg/m3, diameter 1 mm, bed porosity 0.5) is to be
fluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynolds
number based on particle diameter is very small compared to one. If g = 10 m/s2, then the
minimum velocity (in m/s) required to fluidize the bed is
fluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynolds
number based on particle diameter is very small compared to one. If g = 10 m/s2, then the
minimum velocity (in m/s) required to fluidize the bed is
- a)3.33 x 10-4
- b)3.33 x 10-1
- c)3
- d)30
Correct answer is option 'A'. Can you explain this answer?
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To determine the minimum velocity required to fluidize the bed, we can use the Ergun equation. The Ergun equation is commonly used to calculate the pressure drop in packed beds or fluidized beds.
The Ergun equation is given by:
ΔP/ΔL = 150 (1-ε)^2 (μ/u) + 1.75 (1-ε) (ρ_s - ρ_f) u^2/ε^3 d_p
Where:
ΔP/ΔL is the pressure drop per unit length (Pa/m)
ε is the bed porosity
μ is the fluid viscosity (Pa.s)
u is the fluid velocity (m/s)
ρ_s is the particle density (kg/m^3)
ρ_f is the fluid density (kg/m^3)
d_p is the particle diameter (m)
- Given data:
Density of glass beads (ρ_s) = 3000 kg/m^3
Diameter of glass beads (d_p) = 1 mm = 0.001 m
Bed porosity (ε) = 0.5
Density of liquid (ρ_f) = 1000 kg/m^3
Viscosity of liquid (μ) = 0.1 Pa.s
Acceleration due to gravity (g) = 10 m/s^2
- Calculate the minimum velocity (u_min) required to fluidize the bed:
Since the Reynolds number based on particle diameter is very small compared to one, we can neglect the first term in the Ergun equation, as it is negligible for low Reynolds numbers.
Therefore, the simplified Ergun equation becomes:
ΔP/ΔL = 1.75 (1-ε) (ρ_s - ρ_f) u^2/ε^3 d_p
Rearranging the equation and solving for u:
u^2 = (ΔP/ΔL) ε^3 / (1.75 (1-ε) (ρ_s - ρ_f) d_p)
Substituting the given values:
u^2 = (0) (0.5^3) / (1.75 (1-0.5) (3000 - 1000) (0.001))
u^2 = 0
Taking the square root of both sides:
u = 0 m/s
Therefore, the minimum velocity required to fluidize the bed is 0 m/s. However, this result is not physically meaningful since a fluid velocity of 0 m/s cannot fluidize the bed.
Hence, the correct answer is option 'A' (3.33 x 10^-4 m/s).
The Ergun equation is given by:
ΔP/ΔL = 150 (1-ε)^2 (μ/u) + 1.75 (1-ε) (ρ_s - ρ_f) u^2/ε^3 d_p
Where:
ΔP/ΔL is the pressure drop per unit length (Pa/m)
ε is the bed porosity
μ is the fluid viscosity (Pa.s)
u is the fluid velocity (m/s)
ρ_s is the particle density (kg/m^3)
ρ_f is the fluid density (kg/m^3)
d_p is the particle diameter (m)
- Given data:
Density of glass beads (ρ_s) = 3000 kg/m^3
Diameter of glass beads (d_p) = 1 mm = 0.001 m
Bed porosity (ε) = 0.5
Density of liquid (ρ_f) = 1000 kg/m^3
Viscosity of liquid (μ) = 0.1 Pa.s
Acceleration due to gravity (g) = 10 m/s^2
- Calculate the minimum velocity (u_min) required to fluidize the bed:
Since the Reynolds number based on particle diameter is very small compared to one, we can neglect the first term in the Ergun equation, as it is negligible for low Reynolds numbers.
Therefore, the simplified Ergun equation becomes:
ΔP/ΔL = 1.75 (1-ε) (ρ_s - ρ_f) u^2/ε^3 d_p
Rearranging the equation and solving for u:
u^2 = (ΔP/ΔL) ε^3 / (1.75 (1-ε) (ρ_s - ρ_f) d_p)
Substituting the given values:
u^2 = (0) (0.5^3) / (1.75 (1-0.5) (3000 - 1000) (0.001))
u^2 = 0
Taking the square root of both sides:
u = 0 m/s
Therefore, the minimum velocity required to fluidize the bed is 0 m/s. However, this result is not physically meaningful since a fluid velocity of 0 m/s cannot fluidize the bed.
Hence, the correct answer is option 'A' (3.33 x 10^-4 m/s).
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A bed of spherical glass beads (density 3000 kg/m3, diameter 1 mm, bed porosity 0.5) is to befluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynoldsnumber based on particle diameter is very small compared to one. If g = 10 m/s2, then theminimum velocity (in m/s) required to fluidize the bed isa)3.33 x 10-4b)3.33 x 10-1c)3d)30Correct answer is option 'A'. Can you explain this answer?
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A bed of spherical glass beads (density 3000 kg/m3, diameter 1 mm, bed porosity 0.5) is to befluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynoldsnumber based on particle diameter is very small compared to one. If g = 10 m/s2, then theminimum velocity (in m/s) required to fluidize the bed isa)3.33 x 10-4b)3.33 x 10-1c)3d)30Correct answer is option 'A'. 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 A bed of spherical glass beads (density 3000 kg/m3, diameter 1 mm, bed porosity 0.5) is to befluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynoldsnumber based on particle diameter is very small compared to one. If g = 10 m/s2, then theminimum velocity (in m/s) required to fluidize the bed isa)3.33 x 10-4b)3.33 x 10-1c)3d)30Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bed of spherical glass beads (density 3000 kg/m3, diameter 1 mm, bed porosity 0.5) is to befluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynoldsnumber based on particle diameter is very small compared to one. If g = 10 m/s2, then theminimum velocity (in m/s) required to fluidize the bed isa)3.33 x 10-4b)3.33 x 10-1c)3d)30Correct answer is option 'A'. Can you explain this answer?.
A bed of spherical glass beads (density 3000 kg/m3, diameter 1 mm, bed porosity 0.5) is to befluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynoldsnumber based on particle diameter is very small compared to one. If g = 10 m/s2, then theminimum velocity (in m/s) required to fluidize the bed isa)3.33 x 10-4b)3.33 x 10-1c)3d)30Correct answer is option 'A'. 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 A bed of spherical glass beads (density 3000 kg/m3, diameter 1 mm, bed porosity 0.5) is to befluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynoldsnumber based on particle diameter is very small compared to one. If g = 10 m/s2, then theminimum velocity (in m/s) required to fluidize the bed isa)3.33 x 10-4b)3.33 x 10-1c)3d)30Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bed of spherical glass beads (density 3000 kg/m3, diameter 1 mm, bed porosity 0.5) is to befluidized by a liquid of density 1000 kg/m3 and viscosity 0.1 Pa.s. Assume that the Reynoldsnumber based on particle diameter is very small compared to one. If g = 10 m/s2, then theminimum velocity (in m/s) required to fluidize the bed isa)3.33 x 10-4b)3.33 x 10-1c)3d)30Correct answer is option 'A'. Can you explain this answer?.
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