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Francis Turbine Specific Speed & Runner Diameter Calculator

Easily calculate and compute francis turbine specific speed & runner diameter calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
1.52 m

Runner Discharge Diameter (D_runner)

Runner Discharge Diameter (D_runner)

1.52 m

Specific Speed Ns Metric

267.1

Peripheral Blade Velocity M Per S

39.8

Turbine Suitability

IDEAL FRANCIS REGIME (Peak Efficiency > 94%)

1.52 — m

Calculation Breakdown

  1. Applied FormulaModels medium-head Francis reaction turbine runner diameter D1, specific speed Ns, optimal rotational speed, and runner blade height for maximum peak hydraulic efficiency.N_s = \frac{N \sqrt{P}}{H^{5/4}}, \quad D_1 = \frac{60 \cdot 0.82 \sqrt{2 g H}}{\pi N}, \quad \text{Range: } 60 \le N_s \le 350

Francis Turbine Specific Speed & Runner Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.40.81.11.5Runner Discharge Diameter (D_runner)

What Is the Francis Turbine Specific Speed & Runner Diameter Calculator?

This tool computes francis turbine specific speed & runner diameter calculator with high precision arithmetic.

How Does the Francis Turbine Specific Speed & Runner Diameter Calculator Work?

Models medium-head Francis reaction turbine runner diameter D1, specific speed Ns, optimal rotational speed, and runner blade height for maximum peak hydraulic efficiency.

Francis Turbine Specific Speed & Runner Diameter Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Ns=NPH5/4,D1=60⋅0.822gHπN,Range: 60≤Ns≤350N_s = \frac{N \sqrt{P}}{H^{5/4}}, \quad D_1 = \frac{60 \cdot 0.82 \sqrt{2 g H}}{\pi N}, \quad \text{Range: } 60 \le N_s \le 350

Models medium-head Francis reaction turbine runner diameter D1, specific speed Ns, optimal rotational speed, and runner blade height for maximum peak hydraulic efficiency.

How to Use the Francis Turbine Specific Speed & Runner Diameter Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Francis Turbine Specific Speed & Runner Diameter Calculator Example

Input Values:

netHeadMeters:120
turbinePowerOutputMw:45
rotationalSpeedRpm:500
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required m.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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