A butterfly throttle rotates a disc on a shaft to vary the passage. This explanatory calculator isolates the projected geometry of an ideal zero-thickness circular disc; it does not predict real valve flow or sizing performance.
Throttle Valve Interactive Calculator
Set disc angle, circular bore diameter and an assumed full-open area multiplier. The calculator reports projected open fraction and area, an assumed coefficient-area product, and the change in open percentage per degree.
Equation Used
- The bore and disc are ideal circles of equal diameter.
- The disc has zero thickness and angle is measured from the closed plane.
- Projected blocked area is A cos(theta), so projected unobstructed area is A[1-cos(theta)].
- The entered multiplier is applied only to projected open area to form a labeled proxy.
- Flow, pressure drop, density, viscosity, compressibility, cavitation, choking, installed characteristic, actuator torque, leakage, strength and safe sizing are omitted.
Butterfly Throttle Geometry
A butterfly control element is a disc mounted on a rotating shaft. Turning the shaft changes how much of the circular passage the disc blocks in projection.
For the calculator, zero degrees is closed and 90 degrees is edge-on. A real valve also has shaft obstruction, disc thickness, clearances and design-specific flow behavior.
What This Explanatory Calculator Does
The tool calculates bore area and subtracts the projected area of an ideal zero-thickness disc. It also multiplies the projected opening by a user-selected factor to produce a clearly labeled coefficient-area proxy.
It does not calculate flow rate, pressure drop, Cv, Kv, leakage or actuator requirements.
Ideal Thin-disc Projection
Ablocked = A cos(theta)
Aopen = A[1 - cos(theta)]
C-A proxy = C Aopen
gain = 100 sin(theta) pi/180
The cosine projection follows directly from viewing a circular plane at an angle. The proxy is an assumed multiplier times geometric area, not a predicted valve coefficient.
Worked Geometric Example
For a 60 mm bore at 30 degrees from closed, bore area is about 2,827 mm squared and the projected open fraction is about 13.4%, giving about 379 mm squared projected open area. With an assumed multiplier of 0.85, the coefficient-area proxy is about 322 mm squared.
These are geometric and proxy outputs, not a flow or sizing result.
Model Boundary
- Physical topology: a circular butterfly disc rotating on a shaft inside a circular bore.
- Calculated: ideal projected open area, open fraction, derivative with angle and an assumed coefficient-area product.
- Not calculated: actual discharge coefficient, Cv, Kv, flow, pressure drop, fluid properties, compressibility, choking, cavitation, Reynolds effects, shaft/disc obstruction, leakage, installed characteristic, rangeability, torque, dynamics, strength or safe selection.
Frequently Asked Questions
Why is the projected open fraction 1 minus cosine?
At zero degrees the circular disc faces the bore and blocks its full projected area; at 90 degrees an ideal zero-thickness disc has zero projected area.
Is projected area the same as effective flow area?
No. Real flow depends on three-dimensional passages and losses.
Is the proxy a discharge coefficient?
No. It is the entered multiplier times projected open area.
Can this calculate Cv or Kv?
No.
Does the model include the shaft and disc thickness?
No.
Can it size a real valve or actuator?
No. Use manufacturer data and appropriate engineering standards.
References
- NASA Tech Brief, Butterfly Valve Provides Minimum Flow Distortion: a butterfly disc rotates on an actuation shaft to control flow.
- Emerson, Control Valve Handbook, Chapter 3: butterfly-valve designs and throttling characteristics vary by construction.
- Emerson, Control Valve Handbook, Chapter 2: inherent and installed flow characteristics and sizing context.
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