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Scroll Case (Spiral Casing) Cross-Section & Free Vortex Flow Calculator

Easily calculate and compute scroll case (spiral casing) cross-section & free vortex flow calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
3.76 m²

Inlet Scroll Cross-Section Area (A_inlet)

Inlet Scroll Cross-Section Area (A_inlet)

3.76 m²

Inlet Inscribed Diameter Meters

2.19

Halfway Area180 Deg M2

1.88

Quarter Area90 Deg M2

0.94

Free Vortex Constant K

28

3.76 — m²

Calculation Breakdown

  1. Applied FormulaModels logarithmic spiral casing geometry, tangential velocity distribution v_θ · r = const (free vortex), and progressive cross-sectional area reduction around Francis turbine runners.v_\theta \cdot r = K = \text{const}, \quad Q(\theta) = Q_{\text{tot}} \left(\frac{\theta}{360^\circ}\right), \quad A(\theta) = \frac{Q(\theta)}{v_{\text{mean}}}

Spiral Casing Free Vortex Sizing Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.91.92.83.8Inlet Scroll Cross-Section Area (A_inlet)

What Is the Scroll Case (Spiral Casing) Cross-Section & Free Vortex Flow Calculator?

This tool computes scroll case (spiral casing) cross-section & free vortex flow calculator with high precision arithmetic.

How Does the Scroll Case (Spiral Casing) Cross-Section & Free Vortex Flow Calculator Work?

Models logarithmic spiral casing geometry, tangential velocity distribution v_θ · r = const (free vortex), and progressive cross-sectional area reduction around Francis turbine runners.

Scroll Case (Spiral Casing) Cross-Section & Free Vortex Flow Calculator Formula & Variables

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

vθ⋅r=K=const,Q(θ)=Qtot(θ360∘),A(θ)=Q(θ)vmeanv_\theta \cdot r = K = \text{const}, \quad Q(\theta) = Q_{\text{tot}} \left(\frac{\theta}{360^\circ}\right), \quad A(\theta) = \frac{Q(\theta)}{v_{\text{mean}}}

Models logarithmic spiral casing geometry, tangential velocity distribution v_θ · r = const (free vortex), and progressive cross-sectional area reduction around Francis turbine runners.

How to Use the Scroll Case (Spiral Casing) Cross-Section & Free Vortex Flow Calculator

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

Step-by-Step Example Calculation

Scroll Case (Spiral Casing) Cross-Section & Free Vortex Flow Calculator Example

Input Values:

totalTurbineFlowM3PerS:32
inletFlowVelocityMPerS:8.5
runnerInletRadiusMeters:2.2
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required m².

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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