Unit Operations

Step 1: Understand the mechanism of a hammer mill. A hammer mill consists of a rotating shaft to which a series of hammers are mounted. As the shaft rotates at very high speed, the hammers swing out and strike the material fed into the mill.

Step 2: Identify the primary action. The material is shattered and broken down by these high-speed collisions with the hammers. This action is defined as impact. While other forces like shear and compression (attrition) may also play a minor role as particles are pushed against the screen, the dominant and primary force responsible for size reduction is impact.

Step 1: Recall the three main empirical laws of comminution (size reduction). These laws relate the energy input (E) to the change in particle size from an initial diameter (d ) to a final diameter (d ). Rittinger's Law (1867): States that the energy required is proportional to the new surface area created. It is most applicable to fine grinding. Kick's Law (1885): States that the energy required is proportional to the logarithm of the reduction ratio. It is most applicable to coarse crushing of large particles. Bond's Law (1952): States that the energy required is proportional to the crack length produced, and it is the most widely used law for general crushing and grinding. The question specifically asks for the law involving the logarithm, which is Kick's Law.

Step 1: Define the "Centrifuge effect". This term typically refers to the G-force, which is the ratio of the centrifugal acceleration ( ) to the acceleration due to gravity (g).

Step 2: Write the formula for centrifugal acceleration. where is the angular velocity in radians per second and r is the radius in meters.

Step 3: Convert units and plug in the values. = 523.6 rad/s (The unit /sec implies rad/sec as it's an angular velocity)
r = 10 cm = 0.1 m
Step 4: Calculate the G-force. Use g 9.81 m/s . This value matches option (A).

Step 1: Recall the principles of sedimentation, governed by Stokes' Law for particles in the laminar flow regime. The terminal settling velocity ( ) is given by:
Step 2: Analyze how each factor in the options relates to the formula.
A. Gravitational pull (g): This is the primary driving force for settling and is present in the formula.
B. Density of the particle ( ): The settling rate is proportional to the density difference between the particle and the fluid. Particle density is a key part of this.
C. Buoyancy force: This upward force is represented by the density of the fluid ( ). The net downward force depends on the difference between particle density and fluid density ( ). So buoyancy is crucial.
D. Size of the particle ( ): The velocity is proportional to the square of the particle diameter. Larger particles settle much faster.
All four factors are fundamentally important in determining the settling rate.