Calculate siphon flow rate, hose-loss flow, or required hose diameter using diameter, drop height, hose length, and discharge coefficient.
Related Calculators
- Atmospheric Pressure Calculator
- Pressure Volume Work Calculator
- Propane Volume Calculator
- Friction Acceleration Calculator
- All Physics Calculators
Siphon Flow Rate Formula
The quick siphon estimate uses the opening area, vertical head, and a discharge coefficient for losses.
Q = C_d \cdot A \cdot \sqrt{2gH}A = \frac{\pi D^2}{4}The hose-loss mode solves velocity from head loss, then converts velocity to flow rate.
H = \left(1 + K + f\frac{L}{D}\right)\frac{v^2}{2g}Q = A \cdot v
The required-diameter mode rearranges the quick flow equation.
D = \sqrt{\frac{4Q}{\pi C_d \sqrt{2gH}}}- Q = siphon flow rate
- Cd = discharge coefficient
- A = inside cross-sectional area of the hose or pipe
- D = inside diameter
- H = vertical drop, also called operating head
- g = gravitational acceleration, 9.80665 m/s²
- v = water velocity
- K = entrance, bend, valve, and fitting loss allowance
- f = Darcy friction factor
- L = total hose or pipe length
These equations assume water flow, a fully primed siphon, and a discharge point lower than the source water surface. The calculator uses inside diameter, not outside diameter.
Useful Tables
| Loss setting | Coefficient | Use when |
|---|---|---|
| Short smooth siphon | Cd = 0.90 | Short hose, smooth inlet, few bends |
| Typical hose siphon | Cd = 0.75 | General garden hose or tubing estimate |
| Long hose or rough inlet | Cd = 0.60 | Longer hose, rough entrance, tighter bends, or uncertain setup |
| Input | Typical value used | What it affects |
|---|---|---|
| Smooth PVC or plastic roughness | 0.0000015 m | Lower wall friction |
| Rubber garden hose roughness | 0.0000100 m | Moderate wall friction |
| Typical inlet plus two bends | K ≈ 2 | Extra local losses beyond straight hose friction |
How to Read the Result
Use the quick mode for a rough estimate. Use the hose-loss mode when the hose is long, narrow, rough, or has several bends.
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.
The vertical drop is the height difference between the source water surface and the outlet. It is not the total hose length.
