Analyse a siphon that carries liquid up and over a point higher than the upper surface, with no pump. Adjust the crest (highest-point) height, the drop and the pipe size to see the flow velocity, flow rate and crest pressure update in real time, and find a design that will not break the column by cavitation.
Parameters
Crest height h₁
m
Height of the pipe crest above the upper surface
Outlet drop h₂
m
Drop from the upper surface to the outlet (the driving head)
Pipe inner diameter D
mm
Total pipe length L
m
Pipe friction factor f
Darcy friction factor, set by the pipe roughness
Atmospheric pressure P_atm
kPa
Varies with altitude and weather; lower at high elevation
Results
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Velocity V (m/s)
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Flow rate Q (L/min)
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Crest pressure (kPa abs)
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Driving drop h₂ (m)
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Crest pressure margin (kPa)
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Operating verdict
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Siphon cross-section — flow animation
The tube rises from the upper pool over the crest (h₁) and descends to the outlet (h₂ below). Colour shows the in-pipe pressure — darkest near the crest. The column splits if the pressure falls below the vapour pressure.
Velocity V vs driving drop h₂
Crest pressure vs crest height h₁
Theory & Key Formulas
$$V=\sqrt{\dfrac{2g\,h_2}{1+f\,L/D+K}}$$
Flow velocity V, derived from the energy equation between the upper surface and the outlet. h₂: driving drop, f: pipe friction factor, L: total pipe length, D: pipe inner diameter, K: minor loss coefficient (entrance, exit and bends; here K=1.5), g=9.81 m/s².
$$p_{crest}=p_{atm}-\rho g h_1-\tfrac12\rho V^2\!\left(1+f\dfrac{0.4L}{D}\right)$$
Absolute pressure at the crest (highest point). Bernoulli's equation is applied from the upper surface to the crest, including the friction of the up-leg (about 40% of the total pipe length). ρ=998 kg/m³ (water).
When the crest pressure p_crest falls to the vapour pressure of water p_vap (about 2.34 kPa at 20°C), the water boils on the spot and the siphon breaks by cavitation.
What is the Siphon Flow Simulator?
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A "siphon" is that tube you bend up over an edge and then down to drain a fish tank or transfer fuel, right? With no pump and no power, why does the liquid flow on its own?
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Exactly that. It looks mysterious because the liquid seems to "climb upward". Roughly speaking, two effects are at work. One is atmospheric pressure: in the short inlet leg, the outside air pressure pushes the liquid up. The other is the weight of the liquid column in the long outlet leg, which pulls downward and drags the whole column down. So what really drives it is just the difference between the upper surface and the outlet height — the "drop h₂".
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So as long as there is a drop h₂, the liquid flows no matter how high I lift the tube? When I raise the "crest height h₁" on the left, the velocity chart doesn't change at all.
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Good observation. In theory the velocity V is set only by the drop h₂ and the pipe losses — crest height h₁ never appears in the velocity formula, because the energy spent climbing the crest is returned when descending the same height on the outlet side. But — raising h₁ too far causes a problem somewhere else. That is the "crest pressure". Watch the blue number on the lower right and push h₁ up to 9 m.
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Oh, you're right! The crest pressure (kPa abs) keeps dropping and finally the verdict turns red. It says "Siphon broken". What is happening there?
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That is the most interesting and the scariest part of a siphon. The liquid at the highest point can only hold a pressure equal to atmospheric minus "the weight of the column below it". The higher h₁ is, the lower the crest pressure. And when the pressure drops far enough to reach the vapour pressure of water (about 2.34 kPa at 20°C), the water boils right there at room temperature. Bubbles form and the continuous column of water snaps. That is "breaking by cavitation", and the siphon stops.
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I see... so how high can the crest go? Is there a limiting height?
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For water, the theoretical limit is the atmospheric pressure expressed as a water column — about 10.3 m. Divide standard atmospheric pressure (101.3 kPa) by ρg and you get that value. But that is the ideal figure for "zero flow, zero loss". In reality the dynamic-pressure drop from the velocity and the pipe friction are added, so the safe operating limit is around 7-8 m. Try lowering the atmospheric-pressure slider on the left: at high altitude where the air pressure is low, this limit drops further still. That is why a siphon-type drain in the mountains is designed with a low crest.
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One last thing. If I want more flow rate, what should I change?
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The most effective move is to widen the pipe. The friction loss f·L/D is inversely proportional to the diameter D, so a wider pipe sharply cuts the loss and raises the velocity. And since the cross-sectional area A scales with D squared, the flow rate Q = V·A jumps. You can also shorten the pipe, take a larger drop h₂, or use a smooth-bore pipe to reduce the friction f. But raising the velocity too far lowers the crest pressure and brings it closer to breaking, so in practice you decide while watching the balance between flow rate and the breaking margin.
Frequently Asked Questions
A siphon works through two effects: atmospheric pressure pushes the liquid up the short inlet leg, while the weight of the liquid column in the longer outlet leg pulls the whole column down. The flow is driven only by the net drop h2 between the upper surface and the outlet, with no pump needed. The energy used to climb over the crest is returned on the way down the same height on the outlet side, so what finally drives the flow is the drop h2. The key point is that the pressure at the crest falls below atmospheric by the weight of the liquid below it, and if it drops too far the flow breaks.
Write the energy equation from the upper surface to the outlet, balancing the outlet kinetic energy and losses (pipe friction f·L/D plus minor losses K≈1.5 for entrance, exit and bends) against the drop h2. The velocity is V = sqrt(2g·h2 / (1 + f·L/D + K)). The flow rate is Q = V·A, with the pipe area A = πD²/4, and is also reported in L/min. A larger drop, a wider and shorter pipe, and lower friction all increase the velocity and flow rate.
When the absolute pressure at the crest falls to the vapour pressure of water (about 2.34 kPa at 20°C), the water boils on the spot, vapour bubbles form, and the continuous liquid column is split. This is the breaking of the siphon by cavitation. Raising the crest height h1, or raising the velocity, lowers the crest pressure. The theoretical crest-height limit for water is about 10.3 m of atmospheric head, and in practice it is kept to 7-8 m. This tool shows the difference between the crest pressure and the vapour pressure as a pressure margin.
The theoretical upper limit is the atmospheric pressure expressed as a column of water, p_atm/(ρg), which is about 10.3 m at standard atmospheric pressure. However, this is the ideal value for zero flow and no losses. In reality the dynamic-pressure drop from the velocity and the pipe friction loss are added, so the crest height that can be operated safely falls to about 7-8 m. Cavitation can also start early because dissolved air is released at local low pressures, so the design needs margin. This tool lets you watch the crest pressure approach the vapour pressure.
Real-World Applications
Draining tanks and transferring liquids: Changing aquarium water, the hand pump used for kerosene, and a siphon for decanting wine — many everyday liquid transfers are siphons. The advantage is that liquid can be moved over an edge higher than the upper level without tilting or lifting the container, and the only driving force is the drop created by placing the outlet below the upper surface. The lower the outlet, the faster the flow.
Siphon spillways on dams and intake weirs: Dams and balancing reservoirs use siphon-type overflow structures that automatically discharge water once it exceeds the design level. When the level rises above the crest, the pipe fills completely and siphon action starts a vigorous discharge. No pump and no power are needed, and it stops automatically when the level falls, so it has value as a safety device that works even during a power outage.
Water supply, irrigation and toilet flush mechanisms: Siphon pipes that cross irrigation channels (inverted siphons) and the flushing bowl of a household toilet both use siphon action. In a toilet, the siphon starts the instant the water level passes the crest of the bowl trap, sucking out the waste in one rush to flush. The design of the crest height and pipe diameter governs the flushing performance.
Fluid-mechanics education and CAE verification: A siphon is an excellent teaching example that brings together Bernoulli's equation, the energy equation, vapour pressure and cavitation all at once. When handling a siphon in a CFD analysis, getting a first estimate of the velocity and crest pressure with a one-dimensional energy calculation like this tool lets you sanity-check the result before investing in mesh and turbulence models. The condition where the crest pressure falls below the vapour pressure can also serve as a verification case for a cavitation model.
Common Misconceptions and Pitfalls
The most common pitfall is the either/or misconception that "a siphon runs on atmospheric pressure alone" or "it runs on the cohesion of the liquid (molecular pull) alone". In reality both play a part, but an ordinary water siphon is governed by the pressure difference. Atmospheric pressure pushes the water up on the inlet side, and the weight of the long liquid column on the outlet side pulls the whole column down — this pressure balance is the essence. That is exactly why the phenomenon occurs where the column splits when the crest pressure drops to the vapour pressure and the liquid boils. In a vacuum where the air pressure is essentially zero, an ordinary water siphon does not work (a special siphon driven by cohesion alone is a separate matter).
Next is the misconception that "since the flow rate does not change as long as there is a drop, the crest can be made as high as you like". It is true that the crest height h₁ does not appear in the velocity formula V. However, the crest pressure p_crest falls linearly the higher h₁ is. If h₁ is too large, the pressure reaches the vapour pressure, cavitation occurs, the liquid column splits and the flow stops completely. When the "crest pressure margin" in this tool gets small, that is a danger signal. Designing close to the theoretical limit of about 10.3 m is forbidden; accounting for the velocity-driven pressure drop too, it should be kept to 7-8 m in practice.
Finally, there is the assumption that "once it starts flowing, a siphon will not stop even if the upper surface falls". A siphon runs as long as the pipe is continuously full of liquid, but it stops with the column broken if the upper surface drops below the pipe inlet and sucks in air, or if the outlet rises above the upper surface and the drop disappears. Also, when the temperature rises the vapour pressure increases, so cavitation occurs more easily at the same crest height. The vapour pressure of about 2.34 kPa at 20°C rises to about 7.4 kPa at 40°C and about 20 kPa at 60°C. A siphon handling hot water needs a larger crest-pressure margin than it would at room temperature.
How to Use
Set h₁ (inlet depth below source surface) and h₂ (outlet depth below crest) in metres—typical ranges 0.5–3 m for industrial siphons.
Enter pipe diameter (mm) and total length (m); common configurations use 25–100 mm diameter PVC or steel.
The simulator calculates flow velocity, discharge in L/min, absolute crest pressure, and checks if vapour pressure is exceeded; green verdict means stable siphon action.
Worked Example
Water siphon with h₁ = 1.2 m, h₂ = 0.8 m, 50 mm diameter pipe, 15 m total length: Velocity ≈ 1.58 m/s, Flow rate Q ≈ 185 L/min, Crest pressure ≈ 9.2 kPa abs, Pressure margin ≈ 2.3 kPa above water vapour pressure (0.6 kPa at 20°C). This margin confirms priming is stable without cavitation risk.
Practical Notes
Crest pressure must stay above vapour pressure (0.6 kPa for water at 20°C, rising to 2.3 kPa at 30°C); maintain h₂ ≥ 0.6 m to avoid siphon break.
Longer pipes increase friction losses; a 30 m siphon loses roughly 15–20% flow versus 10 m at same diameter.
Outlet must remain submerged or below the crest for continuous siphon; if h₂ becomes negative (outlet above crest), flow stops immediately.
Cold water has lower vapour pressure margin, making siphons more stable; warm liquids (oils, hot water) reduce safe operating windows.