Calculator Input
Example Data Table
This sample shows typical input values for an elliptical duct inlet bell mouth.
| Input | Example Value | Purpose |
|---|---|---|
| Throat Width | 250 mm | Defines the connected duct width. |
| Throat Height | 180 mm | Defines the connected duct height. |
| Mouth Width | 420 mm | Defines the wider inlet opening. |
| Mouth Height | 310 mm | Defines the wider inlet height. |
| Axial Depth | 160 mm | Controls smoothness of the flare profile. |
| Flow Rate | 0.85 m³/s | Used to estimate velocity and pressure loss. |
Formula Used
The calculator treats each station as an ellipse. Width and height are full outside profile dimensions.
Ellipse area: A = π × W / 2 × H / 2
Equivalent diameter: De = √(4A / π)
Hydraulic diameter: Dh = 4A / P
Ellipse perimeter estimate: P = π[3(a+b) - √((3a+b)(a+3b))]
Velocity: V = Q / A
Dynamic pressure: q = 0.5 × ρ × V²
Pressure loss: ΔP = K × q / Cd²
Quarter ellipse profile factor: S = 1 - √(1 - (x / L)²)
Profile width: Wx = Wt + (Wm - Wt) × S
Profile height: Hx = Ht + (Hm - Ht) × S
How to Use This Calculator
- Select the length unit used for the bell mouth dimensions.
- Enter the throat width and height of the connected duct.
- Enter the wider mouth width and height of the inlet.
- Add the axial depth from throat to mouth rim.
- Enter the flow rate in cubic meters per second.
- Use standard air density or enter another fluid density.
- Adjust discharge and loss coefficients when test data is available.
- Choose profile points for fabrication or checking stations.
- Press the calculate button to view results above the form.
- Download the result table as CSV or PDF.
Article: Calculating an Ellipse Bell Mouth
Why Bell Mouth Shape Matters
An ellipse bell mouth helps air, gas, or liquid enter a duct with less separation. The rounded inlet reduces abrupt contraction. It also lowers entry turbulence. This is useful in fans, test rigs, vents, and intake systems. A sharp edge can waste pressure. A smooth flare can protect flow quality.
Geometry Behind the Calculator
The calculator uses width and height to form an elliptical section. The throat is the smaller connected end. The mouth is the larger open end. The axial depth describes how long the flare is. Each profile station follows a quarter ellipse curve. This gives a smooth transition from throat to inlet rim. More profile points give better layout data.
Flow and Loss Evaluation
Flow rate is divided by area to find velocity. The smallest area often controls the highest velocity. Dynamic pressure is then estimated from velocity and fluid density. The loss coefficient adjusts this pressure into a pressure drop. The discharge coefficient accounts for real flow contraction. These values help compare designs before fabrication.
Design Use
A larger mouth area usually lowers entrance velocity. A deeper flare usually makes the transition smoother. Very short bell mouths may still cause separation. Very large mouths may be harder to build. The best design balances space, cost, pressure loss, and airflow quality. Use the profile table to mark stations on a pattern. Check dimensions against available space. Then verify final performance with field data or testing.
FAQs
1. What is an ellipse bell mouth?
It is a smooth elliptical inlet shape. It guides flow into a duct, pipe, fan, or test chamber with reduced entrance disturbance.
2. What dimensions are required?
You need throat width, throat height, mouth width, mouth height, axial depth, flow rate, fluid density, and coefficient values.
3. Can I use inches?
Yes. Select inches from the unit list. The calculator converts all length values internally before producing metric engineering results.
4. Why is mouth area important?
Mouth area affects entrance velocity. A larger mouth usually reduces velocity and can reduce pressure loss when the profile is smooth.
5. What is the discharge coefficient?
It represents real flow behavior compared with ideal flow. Higher values usually mean smoother entry and less effective contraction.
6. What is the loss coefficient?
It estimates energy loss caused by the inlet shape. Use measured data when available for the most reliable result.
7. What are profile points used for?
Profile points help create fabrication marks. They show width, height, area, and velocity at stations along the bell mouth.
8. Is this suitable for final engineering approval?
It is useful for planning and comparison. Final designs should be checked with standards, testing, and qualified engineering review.