Measuring mixing power — Which instrument(s) can be used to assess power consumption in a stirred vessel?

Introduction:
Power input is a key scaling parameter affecting mixing, heat transfer, and mass transfer. Several practical methods exist to quantify the mechanical power delivered to the fluid by an agitator. This question reviews standard instrumentation choices.

Given Data / Assumptions:

• AC motor drive with accessible electrical measurements.
• Mechanical linkage where torque can be measured.
• Steady-state operation for reliable readings.

Concept / Approach:
Power can be determined mechanically via torque and speed (P = 2 * pi * N * T) using a dynamometer or shaft strain gauges. Alternatively, electrical input measured by a wattmeter provides motor power, which can be corrected for motor and drivetrain efficiency to estimate impeller power. All listed instruments are valid pathways to assess power consumption in practice.

Step-by-Step Solution:
Option (a): Dynamometer directly measures torque on the drive line.Option (b): Strain gauges convert shaft strain to torque, enabling P calculation using rotational speed.Option (c): Wattmeter reads electrical power; subtract losses for mechanical power at the shaft.Therefore, all are acceptable approaches to assess power.

Verification / Alternative check:
Comparing methods after accounting for efficiency typically yields consistent power numbers; discrepancies signal calibration issues or unsteady operation.

Why Other Options Are Wrong:

• (e) Calorimetry is rarely used for routine mixing power in industry; the listed instruments are standard.

Common Pitfalls:
Ignoring motor efficiency when using electrical readings; misplacing strain gauges leading to erroneous torque estimates; neglecting transient loads during aeration that require averaging.

Final Answer:
All of these