Power requirement of roll crushers: horsepower demand varies most directly with which operating parameters in continuous service?

Introduction / Context:
Roll crushers are used for medium reduction of friable materials. Understanding how horsepower (HP) demand scales with operating conditions guides motor selection and energy budgeting. Two intuitive variables are reduction ratio and capacity, both of which influence breakage work per unit time.

Given Data / Assumptions:

• Throughput is measured as mass per unit time.
• Reduction ratio relates feed top size to product top size.
• Material properties (hardness, abrasiveness) are assumed constant for the comparison.

Concept / Approach:
Power is the rate of doing work. At higher throughput, more material is broken per unit time, increasing power. At higher reduction ratio, more energy is required per unit mass to reach a finer product, also increasing power. Hence HP rises with both capacity and reduction ratio when other factors are fixed.

Step-by-Step Solution:
Relate energy per mass to target size via comminution considerations.Relate power to energy rate: Power = (energy per mass) * (mass flow rate).Conclude HP ∝ capacity and ∝ reduction ratio for a given material.

Verification / Alternative check:
Empirical sizing charts for roll crushers and drives reflect higher motor ratings for higher capacities and tighter product top sizes (greater reduction ratios).

Why Other Options Are Wrong:
Reduction ratio only: ignores the per-time effect of capacity.Capacity only: ignores the additional work required for greater size reduction.Neither: contradicts basic energy-rate logic.

Common Pitfalls:
Underestimating the power rise when both throughput and reduction ratio are increased simultaneously; this can lead to motor overload or roll slippage.

Final Answer:
Both (a) & (b)