Estimate siphon flow using a supplied discharge coefficient or a fixed Darcy friction factor and fittings coefficient. A third mode finds inside diameter from a positive target flow using the quick discharge-coefficient equation.
Related Calculators
- Atmospheric Pressure Calculator
- Pressure Volume Work Calculator
- Propane Volume Calculator
- Friction Acceleration Calculator
- All Physics Calculators
Siphon Flow Rate Formula
The quick estimate uses the inside area, vertical operating head, and a supplied system discharge coefficient for losses. The preset Cd = 0.62 is illustrative; it is not a universal hose value or a conservative guarantee.
The fixed-factor loss mode solves velocity from the Bernoulli and Darcy head-loss relationships, then uses area to obtain flow. Its fixed 1 counts the free-outlet velocity head or the exit mixing loss into a large receiving reservoir. K covers additional entrance and fitting losses at the same pipe velocity; do not include that outlet term again. No separate Cd is applied in this mode.
The required-diameter mode rearranges only the quick equation. A positive target requires positive head and Cd. Zero target and zero head do not determine a unique diameter; zero target at positive head gives a zero-area mathematical limit, not a usable hose size.
- Q = siphon flow rate
- Cd = discharge coefficient
- A = inside cross-sectional area of the hose or pipe
- D = inside diameter
- H = source-surface to same-pressure free-outlet elevation drop, or the elevation difference between large source and receiving water surfaces
- g = gravitational acceleration, 9.80665 m/sยฒ
- v = water velocity
- K = additional entrance, bend, valve, and fitting loss coefficient, excluding the terminal term already counted as 1
- f = user-supplied, fixed Darcy friction factor; not a Fanning factor and not calculated from roughness or Reynolds number here
- L = total hose or pipe length
These estimates assume a full, continuously primed water line, steady incompressible flow, constant head, negligible source-surface velocity, and equal pressure at the source and receiving surface or free outlet. Use inside diameter. A zero head gives zero forward flow. Crest elevation, ambient and vapor pressure, cavitation, air leaks, inlet submergence, and startup are not checked, so a positive result does not establish that a siphon will start or remain operating.
Useful Tables
The coefficients below are illustrative sensitivity inputs, not material ratings or recommended values for a particular hose. Use system-specific engineering, manufacturer, or measured data. NIST explains that fitting-loss coefficients depend on the fitting and flow conditions. Scroll either table horizontally to read all columns on narrow screens.
| Illustrative case | Coefficient | Meaning at the same area and head |
|---|---|---|
| Example A | Cd = 0.90 | 90% of the ideal Cd = 1 flow |
| Example B | Cd = 0.75 | 75% of the ideal Cd = 1 flow |
| Example C | Cd = 0.60 | 60% of the ideal Cd = 1 flow |
| Input or property | Illustrative setting | How this calculator uses it |
|---|---|---|
| Darcy friction factor | f = 0.02 | Held fixed in fL/D; not inferred from material |
| Entrance and fitting losses | K = 1.5 | Additional losses; excludes the terminal 1 already included |
| Pipe-wall roughness | Not an input | Used with Reynolds number to determine f elsewhere; no automatic calculation here |
How to Read the Result
Use the quick mode only with an applicable system Cd. The pipe-loss mode separately uses your fixed Darcy f, total length, inside diameter, and additional K; its illustrative presets f = 0.02 and K = 1.5 do not identify the actual hose. Friction depends on roughness and Reynolds number, which this calculator does not solve. Zero f is an ideal no-wall-friction limit, not a claim about real water in a hose.
If the result is much higher than what you measure, check for trapped air, partial blockage, a pinched hose, or a smaller actual inside diameter. Small diameter changes can cause large flow changes.
Operating head is the vertical elevation-energy difference at equal endpoint pressure, not total hose length or the rise to the crest. For a submerged outlet into a large receiving reservoir, use the two water-surface elevations. Flow is shown in L/min, mยณ/h, and US gallons per minute; the required diameter is a continuous inside diameter, not a rounded commercial hose size.
