A primed siphon carries water through a filled tube from a source to an outlet below its water surface. The animation shows that flow path. The calculator estimates Q=Cd A sqrt(2g delta-h) for a selected head and coefficient; it does not establish priming, crest-pressure limits or a complete conduit-loss model.
Primed Siphon and Discharge Estimate
Explore a primed siphon flow path and estimate discharge from selected diameter, net head and coefficient.
Equation Used
- The entered head difference is positive and externally established.
- Water-property variation is neglected and g=9.81 m/s squared.
- Cd is a user-selected lumped coefficient, not an independently derived loss percentage.
- Priming, column continuity, crest pressure, vapor margin, conduit length, roughness, fittings and transient behavior are excluded.
The diagram assumes a filled tube and a maintained source level; priming and crest-pressure limits need a separate check.
Supported selected-head estimate
For tube inside diameter D, area A=pi D squared/4. With a positive selected head difference delta-h, ideal speed is sqrt(2g delta-h). Multiplying by a selected discharge coefficient Cd gives an estimated speed and Q=Cd A sqrt(2g delta-h).
The estimate is conditional. It does not determine whether a physical siphon can prime or sustain a continuous column.
Use and boundary
Use the calculator only for transparent selected-head sensitivity estimates. A real siphon analysis additionally needs the conduit path, length, roughness and fittings, crest elevation, priming state, ambient pressure, vapor pressure and downstream boundary.
Selected-head discharge model
A=pi D squared/4; v_ideal=sqrt(2g delta-h); v_est=Cd v_ideal; Q=A v_est.
Default selected-value example
For D=25 mm, delta-h=1.5 m and selected Cd=0.22, area is about 490.9 mm squared, ideal speed is about 5.425 m/s, selected estimated speed is about 1.194 m/s and estimated flow is about 35.2 L/min.
Priming and sustained flow
The tube must first contain a continuous liquid column. Air entering the intake or accumulating at the crest can interrupt the siphon. The outlet must remain below the source surface for the illustrated flow direction. Actual flow also depends on pipe friction, fittings and the pressure available at the crest; a selected coefficient alone does not check those conditions.
Questions
Does a positive head guarantee siphon flow?
No. A primed continuous liquid column and admissible crest pressure are also required.
Is Cd a measured efficiency?
Not necessarily. It is an entered lumped coefficient for this selected model.
Does this check cavitation?
No. Ambient pressure, vapor pressure and crest elevation are not inputs.
References
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), page 147, figure 545: siphon operation and air removal. The animation shows a basic primed tube, without that example’s auxiliary priming chamber.
References & Further Reading
- Wikipedia contributors. Siphon. Wikipedia
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