Question

In the design of extrusion system, the magnitude of the screw power number is dependent on the screw rotational -

• A. Reynold's Number
• B. Prandtl Number
• C. Sherwood Number
• D. Nusselt Number

Hint:

In highly viscous food extrusion (laminar flow regime, \(\text{Re}_{\text{rot}} < 10\)), the Power Number is inversely proportional to the Reynolds Number (\(N_p \propto 1/\text{Re}_{\text{rot}}\)), meaning power consumption is dominated by viscous drag.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Dimensional analysis of food extruders and fluid mixing systems utilizes dimensionless numbers to relate motor power consumption to operating conditions and fluid rheological properties.

Step 2: Detailed Explanation:
In an extrusion system, the power number (\(N_p\) or \(P / (\rho N^3 D^5)\)) represents the ratio of drag forces to inertial forces.
For a rotating screw, the flow regime and power consumption are functionally dependent on the rotational Reynolds Number (\(\text{Re}_{\text{rot}}\)), which is defined as:
\[ \text{Re}_{\text{rot}} = \frac{\rho \cdot N \cdot D^2}{\mu} \]
where:
- \(N\) is the screw rotational speed.
- \(D\) is the screw diameter.
- \(\rho\) is the fluid density.
- \(\mu\) is the viscosity of the food melt.
The Prandtl, Nusselt, and Sherwood numbers are associated with heat and mass transfer, not fluid power dynamics.

Step 3: Final Answer:
The screw power number depends on the rotational Reynold's Number, which corresponds to option (A).