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A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what is the new value of kc in mm/s, up to 2 digits after the decimal point? ______
Important : you should answer only the numeric value
Correct answer is '1.148'. Can you explain this answer?
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Given information:
- Mass transfer coefficient, kc = 1 mm/s
- Correlation: Sh = 0.025 Re^0.6 Sc^0.33
To find the new value of kc when the velocity and diameter are both doubled, we need to calculate the new values of Re (Reynolds number) and Sc (Schmidt number) using the given correlation.
1. New Reynolds number (Re):
- Reynolds number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces.
- It is given by the formula: Re = (ρVD)/μ, where ρ is the fluid density, V is the fluid velocity, D is the pipe diameter, and μ is the fluid viscosity.
- If the velocity and diameter are both doubled, the new Reynolds number can be calculated as: Re' = (ρ(2V)(2D))/μ = 4(ρVD)/μ = 4Re
2. New Schmidt number (Sc):
- Schmidt number is a dimensionless quantity that represents the ratio of momentum diffusivity to mass diffusivity.
- It is given by the formula: Sc = μ/ρD, where μ is the fluid viscosity, ρ is the fluid density, and D is the pipe diameter.
- If the diameter is doubled, the new Schmidt number can be calculated as: Sc' = μ/(ρ(2D)) = (1/2)(μ/ρD) = (1/2)Sc
3. Using the new values of Re' and Sc', we can calculate the new value of Sh (Sherwood number) using the given correlation:
- Sh' = 0.025 (Re')^0.6 (Sc')^0.33
- Substituting the values of Re' = 4Re and Sc' = (1/2)Sc, we get:
Sh' = 0.025 (4Re)^0.6 ((1/2)Sc)^0.33
Sh' = 0.025 (4^0.6) Re^0.6 (Sc^0.33) (1/2)^0.33
Sh' = 0.025 (1.5874) Re^0.6 (Sc^0.33) (0.7937)
Sh' = 0.0317 Re^0.6 Sc^0.33
4. The mass transfer coefficient (kc) is related to the Sherwood number (Sh) by the equation:
kc = Sh/D
where D is the pipe diameter.
- Substituting the value of Sh' = 0.0317 Re^0.6 Sc^0.33 and D' = 2D, we get:
kc' = Sh'/D'
kc' = (0.0317 Re^0.6 Sc^0.33)/(2D)
kc' = (0.0317/2) (Re^0.6 Sc^0.33)/D
kc' = 0.01585 (Re^0.6 Sc^0.33)/D
5. Comparing the new value of kc' with the given value of kc = 1 mm/s, we can write the equation:
kc' = kc (Re^0.6 Sc^0.33)/D
6. Substituting the values of kc
- Mass transfer coefficient, kc = 1 mm/s
- Correlation: Sh = 0.025 Re^0.6 Sc^0.33
To find the new value of kc when the velocity and diameter are both doubled, we need to calculate the new values of Re (Reynolds number) and Sc (Schmidt number) using the given correlation.
1. New Reynolds number (Re):
- Reynolds number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces.
- It is given by the formula: Re = (ρVD)/μ, where ρ is the fluid density, V is the fluid velocity, D is the pipe diameter, and μ is the fluid viscosity.
- If the velocity and diameter are both doubled, the new Reynolds number can be calculated as: Re' = (ρ(2V)(2D))/μ = 4(ρVD)/μ = 4Re
2. New Schmidt number (Sc):
- Schmidt number is a dimensionless quantity that represents the ratio of momentum diffusivity to mass diffusivity.
- It is given by the formula: Sc = μ/ρD, where μ is the fluid viscosity, ρ is the fluid density, and D is the pipe diameter.
- If the diameter is doubled, the new Schmidt number can be calculated as: Sc' = μ/(ρ(2D)) = (1/2)(μ/ρD) = (1/2)Sc
3. Using the new values of Re' and Sc', we can calculate the new value of Sh (Sherwood number) using the given correlation:
- Sh' = 0.025 (Re')^0.6 (Sc')^0.33
- Substituting the values of Re' = 4Re and Sc' = (1/2)Sc, we get:
Sh' = 0.025 (4Re)^0.6 ((1/2)Sc)^0.33
Sh' = 0.025 (4^0.6) Re^0.6 (Sc^0.33) (1/2)^0.33
Sh' = 0.025 (1.5874) Re^0.6 (Sc^0.33) (0.7937)
Sh' = 0.0317 Re^0.6 Sc^0.33
4. The mass transfer coefficient (kc) is related to the Sherwood number (Sh) by the equation:
kc = Sh/D
where D is the pipe diameter.
- Substituting the value of Sh' = 0.0317 Re^0.6 Sc^0.33 and D' = 2D, we get:
kc' = Sh'/D'
kc' = (0.0317 Re^0.6 Sc^0.33)/(2D)
kc' = (0.0317/2) (Re^0.6 Sc^0.33)/D
kc' = 0.01585 (Re^0.6 Sc^0.33)/D
5. Comparing the new value of kc' with the given value of kc = 1 mm/s, we can write the equation:
kc' = kc (Re^0.6 Sc^0.33)/D
6. Substituting the values of kc
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A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. Can you explain this answer?
Question Description
A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. 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 study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. 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 study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. Can you explain this answer?.
A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. 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 study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. 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 study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. Can you explain this answer?.
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A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. Can you explain this answer?, a detailed solution for A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. Can you explain this answer? has been provided alongside types of A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient kc has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re0.6 Sc0.33 .If the velocity of the fluid and the diameter of the pipe are both doubled, what isthe new value of kc in mm/s, up to 2 digits after the decimal point?______Important : you should answer only the numeric valueCorrect answer is '1.148'. Can you explain this answer? theory, EduRev gives you an
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