Question

A 100 mm plate type disc is atomizing 5 kg/min of skim milk at 15,000 rpm. What is the disc peripheral velocity?

• A. 5 m/s
• B. 54.4 m/s
• C. 45.4 m/s
• D. 78.5 m/s

Hint:

To quickly calculate disc tip speed, use the relation \(v = \frac{\pi D n}{60}\). Ensure the disc diameter is converted to meters to obtain the velocity in meters per second (m/s).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In rotary disc atomizers used in spray dryers, liquid feed is accelerated to high speeds by a rotating disc.
The liquid is disintegrated into fine droplets at the edge of the disc by centrifugal force.
The peripheral velocity (or tip speed) of the disc determines the energy available for atomization and directly influences the final particle size of the dried powder.
Key Formula or Approach:
The peripheral velocity (\(v\)) of a rotating circular disc is calculated using the formula:
\[ v = \pi \times D \times N \] where:
\(D\) is the diameter of the disc in meters (m).
\(N\) is the rotational speed of the disc in revolutions per second (rps).

Step 2: Detailed Explanation:
We are given the following parameters:
Diameter of the disc, \(D = 100\,\text{mm} = 0.1\,\text{m}\).
Rotational speed, \(n = 15,000\,\text{rpm}\).
First, convert the rotational speed from rpm to rps:
\[ N = \frac{15,000}{60} = 250\,\text{rps} \] Now, calculate the peripheral velocity:
\[ v = \pi \times 0.1\,\text{m} \times 250\,\text{rps} \] \[ v = 25\pi\,\text{m/s} \] Using the value of \(\pi \approx 3.14159\):
\[ v \approx 25 \times 3.14159 = 78.54\,\text{m/s} \] This peripheral velocity of 78.5 m/s provides the shear forces required to atomize skim milk into fine droplets, enabling rapid drying in the hot air stream.
The feed rate of 5 kg/min does not affect the peripheral velocity, as tip speed depends solely on disc diameter and rotational speed.

Step 3: Final Answer:
Therefore, the disc peripheral velocity is 78.5 m/s.