When changing the water in an aquarium or transferring fuel from a canister to a car, we have all used a hose, sucked on it to start the flow, and marveled at the result. Once the flow begins, the liquid seemingly defies gravity by climbing up to the hose's peak and then continuing to flow spontaneously out the other end. This fascinating physical phenomenon is called "siphoning." To unravel the mystery behind siphoning, atmospheric pressure, gravity, and of course, Bernoulli's principle work in concert.
The Physics of a Siphon System
The fundamental rule in a siphon system is this: The level (elevation) of the target point where the water will be discharged must be lower than the surface level of the source from which the water is drawn. To start the system, the inside of the hose must be full of liquid (no air).
When the flow begins, gravity pulls the water down the longer, lower end of the pipe. This pulling force creates a low-pressure region at the highest (peak) point of the hose. Meanwhile, atmospheric pressure acting on the water surface in the source container pushes the water toward this low-pressure peak. The pushing force of atmospheric pressure and the pulling force of gravity combine to create a continuous flow.
Siphon Velocity Calculation and Bernoulli's Equation
Let's apply Bernoulli's equation between the broad surface of the upper source container (Point 1) and the endpoint where the hose discharges the water (Point 2).
Point 1 (Source Surface): It is open to atmospheric pressure (P₁ = P_atm). Since the water surface is very large, its downward velocity is negligibly small (v₁ ≈ 0). Its elevation is z₁.
Point 2 (Hose Outlet): This is the endpoint where water flows freely into the air, so this point is also at atmospheric pressure (P₂ = P_atm). The flow velocity is v₂, and its elevation is z₂.
Writing the equation:
P₁ + ½ρv₁² + ρgz₁ = P₂ + ½ρv₂² + ρgz₂
P_atm + 0 + ρgz₁ = P_atm + ½ρv₂² + ρgz₂
The P_atm values on both sides of the equation cancel each other out. If we solve the equation for v₂ (flow velocity), we arrive at the legendary Torricelli's Law:
ρgz₁ - ρgz₂ = ½ρv₂²
ρg(z₁ - z₂) = ½ρv₂²
g × Δh = ½v₂² (Where Δh = z₁ - z₂, meaning the height difference between the source surface and the outlet end)
v₂ = √(2gΔh)
The flow velocity of the siphon depends entirely on the height difference between the two points. How high the peak point of the hose is (within certain limits) does not affect the exit velocity.
You can also model this situation using our Bernoulli Flow Pressure Calculator tool.
For Point 1, enter velocity 0, pressure 101325 (atmospheric), and elevation for example 3 m.
For Point 2, enter pressure 101325 (atmospheric), elevation 0 m, and when you select Point 2 Velocity (v2) as the variable to Solve For, the tool will give you the result √(2×9.81×3) ≈ 7.67 m/s.
Pressure Drop at the Highest Point and Cavitation Risk
There is a limit to siphoning. If we apply Bernoulli's equation this time to the very peak of the hose, we see that the fluid at this point has both high velocity and its highest potential energy (elevation). To conserve energy, the pressure must drop significantly. This pressure even drops well below atmospheric pressure (a vacuum).
If the peak point is too high above the water level (for water, the practical limit is theoretically around 10 meters, but in reality 7-8 meters due to friction), the pressure at the peak drops to the vapor pressure of the water. In this case, the water boils and forms vapor bubbles. This phenomenon is called cavitation. The vapor bubbles sever the water column in the hose, the continuity of the liquid is broken, and siphoning stops. Bernoulli's principle mathematically explains flawlessly why this limit exists.
The Role of Diameter Variations and Losses in Siphon Systems
While we focused purely on elevation differences in the ideal siphoning scenario, in real-world applications, hose diameter and local losses within the system also have dramatic effects on the flow. Theoretically, Torricelli's law (v = √(2gΔh)) dictates that flow velocity depends solely on the height difference, but this velocity can only be achieved assuming there is absolutely no resistance (friction) acting on the fluid within the pipe or hose.
In practice, when we adapt the Bernoulli equation to a real system, we must also factor in energy losses. The roughness of the hose's inner surface, the fluid's viscosity (its internal resistance to flow), and bends (elbows) in the pipe consume a portion of the fluid's kinetic energy by converting it into heat energy. Consequently, the calculated ideal flow velocity (v2) is always higher than the actual flow velocity. If you use a very thin hose, the ratio of surface friction to the flow area will increase, leading to immense energy loss, and the water may flow at perhaps half the calculated speed. In wider hoses, the impact of frictional loss is felt less.
Furthermore, when considering the vacuum effect created at the peak of the system, gases dissolved within the fluid must not be forgotten. If the pressure at the very top of the siphon line drops too low, even if the liquid doesn't undergo cavitation (vaporize), the dissolved air within it can be released to form microscopic bubbles. These air bubbles tend to accumulate at the highest point of the system. Over time, this growing air pocket disrupts the continuous column structure of the fluid, leading to a condition known as an "air lock," which can completely halt the siphoning process. This is why in large industrial siphon lines, special vacuum pumps or relief valves are used to purge these accumulating gases at the peak. In short, siphoning, which appears to be a simple physics experiment, is a formidable engineering case study encompassing the most challenging problems of fluid dynamics, such as friction, pressure drop, and multi-phase flow (liquid-gas mixture).
