Calculator Inputs
Choose a design method, define the profile, add flow conditions, then calculate.
Formula Used
The calculator models an axisymmetric bell mouth by revolving a partial ellipse around the centerline. The throat plane is the profile origin.
x(θ) = a[sin(θ) − sin(θ₁)]r(θ) = Rₜ + b[cos(θ₁) − cos(θ)]Dₘ = 2r(θ₂), L = x(θ₂)S = ∫√(a²cos²θ + b²sin²θ) dθρ(θ) = [a²cos²θ + b²sin²θ]³ᐟ² ÷ (ab)A = π(D² − Dₕ²) ÷ 4, V = Q/ARe = ρVDₕ/μ, q = ρV²/2, ΔP = KqArc length, surface area, internal volume, and wall material volume use numerical integration. Equal-arc coordinates use a dense cumulative-length interpolation. Optional boundary-layer blockage reduces the effective flow diameter before velocity calculations.
How to Use This Calculator
- Select axes, dimensions, or ratio design mode.
- Choose one length unit for every geometry input.
- Enter the throat size and required profile dimensions.
- Set start and end angles for the elliptical segment.
- Add wall thickness, rear duct, and optional hub.
- Choose volumetric or mass flow and fluid properties.
- Select coordinate spacing and the required point count.
- Press calculate and review warnings before fabrication.
- Export CSV, SVG, DXF, or a printable PDF report.
Worked Example
Consider a 300 mm circular throat with a 240 mm axial semi-axis and a 120 mm radial semi-axis. A quarter ellipse runs from 0° to 90°. The resulting mouth diameter is 540 mm, while the bell length is 240 mm.
At 2.5 m³/s, the unobstructed throat area is about 0.0707 m². The average throat velocity is about 35.37 m/s. With air near 20°C and K = 0.04, the calculator estimates dynamic pressure and inlet loss.
| Input | Example value | Purpose |
|---|---|---|
| Throat diameter | 300 mm | Defines the downstream circular passage. |
| Semi-axis a | 240 mm | Controls axial profile length. |
| Semi-axis b | 120 mm | Controls radial flare height. |
| Angle range | 0° to 90° | Uses a complete quarter ellipse. |
| Flow rate | 2.5 m³/s | Calculates velocities and pressure terms. |
| Loss coefficient | 0.04 | Provides a simplified inlet-loss estimate. |
Ellipse Bell Mouth Design Guide
An elliptical bell mouth provides a gradual transition from a large entrance to a smaller throat. The smooth profile can reduce separation compared with a sharp-edged inlet. Actual performance still depends on the complete system and operating point.
The axial semi-axis controls how quickly the inlet contracts along its length. The radial semi-axis controls the increase between throat and mouth radii. Their ratio changes compactness, curvature, and the space required around equipment.
A full quarter ellipse normally uses angles from zero to ninety degrees. Partial angles create shorter or more specialized profiles. The calculator preserves tangent and curvature information across the selected segment.
Flow velocity is calculated from net area after subtracting an optional central hub. Reynolds number indicates the broad flow regime. Mach number warns when incompressible assumptions become less reliable.
The pressure-loss estimate uses a user-selected loss coefficient. That coefficient is not generated from geometry alone. Reliable values should come from tests, trusted references, or validated computational analysis.
Surface area helps estimate coatings, lining, or sheet requirements. Internal volume helps evaluate contained fluid or acoustic volume. Wall material volume is an approximation based on radial thickness.
Fabrication coordinates can be spaced by angle, axial distance, or arc length. Equal-angle points are simple to verify. Equal-arc points often distribute machining or inspection stations more uniformly.
The SVG drawing is intended for checking proportions and direction. CSV values should control fabrication dimensions. DXF output is a lightweight polyline suitable for importing and further checking.
External dimension conversion uses a radial offset instead of a true normal offset. This is convenient for preliminary work. Thin-wall designs generally experience smaller differences between those approaches.
A good engineering workflow compares several profiles rather than accepting one automatically. Review curvature, available length, velocity, loss, noise, and manufacturing constraints together. Confirm critical designs using qualified engineering analysis and testing.
Frequently Asked Questions
1. What is an ellipse bell mouth?
It is a smooth inlet whose meridional profile follows part of an ellipse. Revolving that profile around a centerline creates an axisymmetric entrance.
2. What do semi-axis a and semi-axis b control?
Semi-axis a controls axial development. Semi-axis b controls radial flare. Their relationship determines profile compactness and curvature.
3. Can the calculator solve ellipse axes automatically?
Yes. Select the dimensions mode, then enter throat diameter, mouth diameter, axial length, and the selected angle range.
4. Does the calculator support partial ellipses?
Yes. Start and end angles can define a partial segment, provided the end angle is larger and no more than ninety degrees.
5. How is pressure loss calculated?
The calculator multiplies throat dynamic pressure by the entered loss coefficient K. This is a simplified estimate, not a CFD prediction.
6. What does the hub diameter change?
A hub reduces net annular flow area. This raises calculated velocity for the same flow rate and changes the hydraulic diameter.
7. Which coordinate spacing should I choose?
Equal angle is easy to audit. Equal axial distance suits stations along length. Equal arc length provides uniform profile spacing.
8. Is the exported DXF production-ready?
It is a simple polyline reference. Verify units, tolerances, wall offsets, joining details, and machine requirements in your CAD workflow.
9. Can these results replace professional engineering review?
No. The calculator supports preliminary design and comparison. Safety-critical, high-speed, regulated, or expensive systems require qualified review and validation.