The Coefficient of Uniformity Calculator is a tool used to measure the evenness of distribution in various applications, such as water flow in irrigation systems, particle size distribution in soil analysis, or other processes where uniformity is critical. By quantifying how consistently a set of observed values is distributed relative to their mean, the calculator provides insights into system efficiency and reliability. The result is expressed as a percentage, with higher percentages indicating greater uniformity.
This tool simplifies the process of analyzing uniformity, making it especially valuable in engineering, agricultural, and industrial settings.
Formula of Coefficient Of Uniformity Calculator
The formula for calculating the coefficient of uniformity (CU) is:
Where:
- CU = Coefficient of uniformity (expressed as a percentage)
- Qᵢ = Observed values (e.g., flow rates or distribution amounts) for each measurement point
- Q̄ = Mean of the observed values
- ∑ Qᵢ = Total sum of all observed values
- ∑ |Qᵢ – Q̄| = Sum of the absolute deviations of each observed value from the mean
Steps to Calculate:
- Calculate the mean (Q̄):
Q̄ = ∑ Qᵢ / n
Where n is the total number of observed values. - Compute the absolute deviations:
∑ |Qᵢ – Q̄| = |Q₁ – Q̄| + |Q₂ – Q̄| + … + |Qₙ – Q̄| - Compute the total sum of observed values:
∑ Qᵢ = Q₁ + Q₂ + … + Qₙ - Substitute the calculated values into the formula for CU to find the coefficient of uniformity.
Table for Common Scenarios
| Total Observed Values (∑ Qᵢ) | Mean (Q̄) | Sum of Deviations (∑) | Coefficient of Uniformity (CU) |
|---|---|---|---|
| 1000 | 200 | 50 | 95% |
| 1500 | 300 | 100 | 93.33% |
| 2000 | 400 | 120 | 94% |
| 2500 | 500 | 200 | 92% |
| 3000 | 600 | 300 | 90% |
This table offers pre-calculated values for quick reference, making it easier to evaluate uniformity in common cases without manual computation.
Example of Coefficient Of Uniformity Calculator
Let’s calculate the coefficient of uniformity for a system with the following observations:
- Observed values: Q₁ = 190, Q₂ = 200, Q₃ = 210
- Total observed values (∑ Qᵢ) = 190 + 200 + 210 = 600
- Mean (Q̄): Q̄ = ∑ Qᵢ / n = 600 / 3 = 200
Compute the absolute deviations:
∑ |Qᵢ – Q̄| = |190 – 200| + |200 – 200| + |210 – 200| = 10 + 0 + 10 = 20
Substitute into the formula:
CU = (1 – (20 / 600)) × 100
CU = 0.9667 × 100 = 96.67%
In this example, the system has a coefficient of uniformity of 96.67%, indicating high uniformity.
Most Common FAQs
The coefficient of uniformity represents the evenness of a system’s distribution. Higher values indicate a more uniform and efficient system.
It is widely used in irrigation systems to measure water distribution, in soil analysis to evaluate particle size distribution, and in various industrial processes requiring consistency.
Yes, the calculator can process datasets with numerous observations, simplifying the computation of uniformity for large-scale systems.