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The power required for agitation of non-aerated medium in fermentation is kW.
Operating conditions are as follows:
Fermentor diameter = 3 m
Number of impellers = 1
Mixing speed = 300 rpm
Diameter of the Rushton turbine = 1 m
Viscosity of the broth = 0.001 Pa.s
Density of the broth = 1000 kg.m-3
Power number = 5
Operating conditions are as follows:
Fermentor diameter = 3 m
Number of impellers = 1
Mixing speed = 300 rpm
Diameter of the Rushton turbine = 1 m
Viscosity of the broth = 0.001 Pa.s
Density of the broth = 1000 kg.m-3
Power number = 5
Correct answer is '5'. Can you explain this answer?
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Calculation of Power Required for Agitation
Given Data:
- Fermentor diameter (D) = 3 m
- Number of impellers (N) = 1
- Mixing speed (N) = 300 rpm
- Diameter of the Rushton turbine (Dd) = 1 m
- Viscosity of the broth (μ) = 0.001 Pa.s
- Density of the broth (ρ) = 1000 kg/m^3
- Power number (Np) = 5
Formula:
The power required for agitation in a fermentor can be calculated using the following formula:
P = (Np * ρ * N^3 * D^5) / (μ^3 * Dd^5)
where P is the power required for agitation.
Calculation:
Substituting the given values into the formula, we get:
P = (5 * 1000 * (300/60)^3 * 3^5) / (0.001^3 * 1^5)
P = (5 * 1000 * 5^3 * 3^5) / (0.001^3)
P = (5 * 1000 * 125 * 243) / (0.001^3)
P ≈ 5 * 10^10
Explanation:
The power required for agitation in a fermentor depends on various factors such as the geometry of the fermentor, the number of impellers, the mixing speed, and the properties of the medium being agitated.
In this case, the power number (Np) is given as 5, which represents the efficiency of the impeller in converting mechanical power into fluid flow. The power number depends on the impeller design and is usually determined experimentally.
By substituting the given values into the formula, we can calculate the power required for agitation. The result is approximately 5 * 10^10 watts (or 5 kW).
Conclusion:
The power required for agitation of a non-aerated medium in fermentation is 5 kW. This value is obtained by considering the fermentor diameter, number of impellers, mixing speed, diameter of the Rushton turbine, viscosity of the broth, density of the broth, and the power number.
Given Data:
- Fermentor diameter (D) = 3 m
- Number of impellers (N) = 1
- Mixing speed (N) = 300 rpm
- Diameter of the Rushton turbine (Dd) = 1 m
- Viscosity of the broth (μ) = 0.001 Pa.s
- Density of the broth (ρ) = 1000 kg/m^3
- Power number (Np) = 5
Formula:
The power required for agitation in a fermentor can be calculated using the following formula:
P = (Np * ρ * N^3 * D^5) / (μ^3 * Dd^5)
where P is the power required for agitation.
Calculation:
Substituting the given values into the formula, we get:
P = (5 * 1000 * (300/60)^3 * 3^5) / (0.001^3 * 1^5)
P = (5 * 1000 * 5^3 * 3^5) / (0.001^3)
P = (5 * 1000 * 125 * 243) / (0.001^3)
P ≈ 5 * 10^10
Explanation:
The power required for agitation in a fermentor depends on various factors such as the geometry of the fermentor, the number of impellers, the mixing speed, and the properties of the medium being agitated.
In this case, the power number (Np) is given as 5, which represents the efficiency of the impeller in converting mechanical power into fluid flow. The power number depends on the impeller design and is usually determined experimentally.
By substituting the given values into the formula, we can calculate the power required for agitation. The result is approximately 5 * 10^10 watts (or 5 kW).
Conclusion:
The power required for agitation of a non-aerated medium in fermentation is 5 kW. This value is obtained by considering the fermentor diameter, number of impellers, mixing speed, diameter of the Rushton turbine, viscosity of the broth, density of the broth, and the power number.
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The power required for agitation of non-aerated medium in fermentation is kW.Operating conditions are as follows:Fermentor diameter = 3 mNumber of impellers = 1Mixing speed = 300 rpmDiameter of the Rushton turbine = 1 mViscosity of the broth = 0.001 Pa.sDensity of the broth = 1000 kg.m-3Power number = 5Correct answer is '5'. Can you explain this answer?
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