The Consistency Index Calculator is a tool used in fields like fluid mechanics and decision-making. It helps measure the viscosity of power-law fluids in rheology and assesses the consistency of pairwise comparison matrices in decision-making processes, such as the Analytic Hierarchy Process. This ensures accurate analysis in engineering, science, and management applications.
Formula of Consistency Index Calculator
Step 1: For Rheology (Power-Law Fluids)
The formula for the consistency index is:
K = tau / (gamma^n)
Where:
K is the consistency index in Pa·s^n
tau is the shear stress in Pa
gamma is the shear rate in 1/s
n is the flow behavior index (dimensionless)
Step 2: For Decision-Making (Saaty’s Analytic Hierarchy Process)
The formula for the consistency index is:
CI = (lambda_max - n) / (n - 1)
Where:
CI is the consistency index
lambda_max is the largest eigenvalue of the pairwise comparison matrix
n is the number of items being compared
Step 3: Gather the Required Data
For rheology, measure the shear stress, shear rate, and flow behavior index.
For decision-making, compute or obtain the largest eigenvalue of the comparison matrix and the number of items being compared.
Step 4: Substitute Values into the Formula
Use the measured or calculated values to determine the consistency index.
Step 5: Interpret the Results
In rheology, a higher consistency index indicates a more viscous fluid, while a lower value indicates less viscosity.
In decision-making, a consistency index close to zero indicates high consistency, while a higher value suggests greater inconsistency.
Table of Common Consistency Index Values
| Field | Parameter | Example Value | Interpretation |
|---|---|---|---|
| Rheology | Consistency Index (K) | 0.5 Pa·s^n | Low viscosity fluid |
| Rheology | Consistency Index (K) | 5.0 Pa·s^n | High viscosity fluid |
| Decision-Making | Consistency Index (CI) | 0.03 | High consistency in comparisons |
| Decision-Making | Consistency Index (CI) | 0.15 | Moderate inconsistency |
Example of Consistency Index Calculator
Rheology Example
A fluid has a shear stress of 10 Pa, a shear rate of 2 1/s, and a flow behavior index (n) of 0.8.
Calculate the consistency index (K):
K = 10 / (2^0.8)
K = 5.74 Pa·s^n
Decision-Making Example
A decision matrix has lambda_max = 5.2 and n = 5.
Calculate the consistency index (CI):
CI = (5.2 - 5) / (5 - 1)
CI = 0.05
Results
In rheology, the consistency index of 5.74 Pa·s^n indicates high viscosity.
In decision-making, a CI of 0.05 shows high consistency in comparisons.
Most Common FAQs
It measures fluid viscosity in rheology and evaluates judgment consistency in decision-making matrices.
A consistency index below 0.1 is generally acceptable, indicating consistent judgments.
It provides insights into the flow characteristics of non-Newtonian fluids, aiding in material and process analysis.