M095 · Fluid mechanics

Siphon, Pressure Limit & Cavitation

Raise a siphon crest, change outlet drop and prime or break the liquid column. Trace absolute pressure along the actual tube, reject the vapor boundary and estimate transport resistance from timed collection.

Inference status $\text{Ready}$

Accepted transport flow $\text{Ready}$

Candidate probe speed $\text{Ready}$

Candidate probe gauge pressure $\text{Ready}$

Candidate probe absolute pressure $\text{Ready}$

Minimum candidate absolute pressure $\text{Ready}$

Minimum margin above vapor pressure $\text{Ready}$

Probe centreline elevation $\text{Ready}$

Tube centreline length $\text{Ready}$

Candidate probe energy head $\text{Ready}$

Candidate probe hydraulic head $\text{Ready}$

Candidate total loss head $\text{Ready}$

Candidate energy budget residual $\text{Ready}$

Acquired stations $\text{Ready}$

Flow inferred from raw readings $\text{Ready}$

Fit coordinate residual $\text{Ready}$

Single-phase status $\text{Ready}$

Single-phase candidate flow $\text{Ready}$

Accepted collected volume $\text{Ready}$

Collection duration $\text{Ready}$

Total resistance inferred from data $\text{Ready}$

GEOMETRY / PRESSURE / ACQUIRE

Will this siphon sustain a liquid column?

Crest above source surface

z_c-z_S

2.00\,m

Outlet drop below source

z_S-z_o

1.00\,m

Column filled: no / yes

b

1.00\,

Collection duration

t

10.00\,s

Tube inner diameter

D

40.00\,mm

Reference Darcy friction factor

f_D

0.02\,

Reference total minor loss

K_\Sigma

1.20\,

Volume noise bound

\epsilon_V

0.00\,mL

Probe path fraction

\xi_p

0.50\,

Liquid density

\rho

1000.00\,kg/m^3

Gravity

g

9.81\,m/s^2

Ambient absolute pressure

p_a

101.33\,kPa

Specified vapor pressure

p_v

2.34\,kPa

The source surface is held at a fixed level and its speed is neglected. The pipe outlet is open to the same atmosphere; the receiver is a constant-level drained sink. Collection duration integrates accepted steady transport, with no reservoir depletion. Tube radii are displayed four times larger; centreline heights remain metric.

A prescribed Darcy factor covers wall losses. The total minor coefficient is split equally between the entrance and two circular bends. Priming is imposed; no startup is computed. The lowest pressure is checked along the entire tube. Vapor risk empties the displayed column and blocks acquisition; bubble growth, dissolved gas and two-phase dynamics are omitted.

Fit acquired time and volume with a free intercept to estimate flow and total resistance. Those readings cannot separate wall friction from minor losses. Time and probe changes preserve records; configuration or noise changes clear them. CSV excludes the reference losses. Repeated times replace old readings; noise is reproducible and bounded.

Fixed source level and atmospheric free outlet; prescribed losses. Priming is imposed and vapor pressure is a screening boundary. Bubble growth, startup and two-phase flow are not simulated.

Start with the essentials

Focus question: Why does a taller crest threaten flow without providing its driving head?
One-sentence intuition: The outlet drop supplies energy; the crest and accumulated losses lower the absolute pressure.

Core mathematical model

The outlet sets the energy budget

\begin{aligned}v&=\sqrt{\frac{2g(z_S-z_o)}{1+f_D L/D+K_\Sigma}}\\Q&=Av\end{aligned}

The kinetic outlet term remains even in the no-loss comparison.

Trace absolute pressure

\begin{aligned}p_{\mathrm{abs}}(s)&=p_a+\rho g\left[z_S-z(s)\right]\\&\quad-\frac{\rho v^2}{2}-\rho g h_L(s)\end{aligned}

The lowest pressure can lie just after the crest when friction and bend losses are present.

Check before accepting transport

\begin{gathered}\text{primed},\quad z_S>z_o,\\\min_s p_{\mathrm{abs}}(s)>p_v\end{gathered}

All three conditions are required. Rejected candidates remain diagnostic curves, with no collected volume.

Measure flow with timed collection

V_i=b+\widehat Q t_i

A free intercept accommodates a sensor tare offset; only acquired readings enter the fit.

Infer total resistance only

\widehat R=\frac{2g(z_S-z_o)}{(\widehat Q/A)^2}-1

Volumes cannot separate Darcy friction from minor losses.

Common difficulties

Gauge and absolute pressure

Typical misconceptionA negative gauge pressure always means the liquid cannot flow.

Better mental modelAdd ambient pressure before comparing with the specified vapor pressure. The entire path is checked.

A fit is an inference

Typical misconceptionThe fitted coefficient is a reference slider in disguise.

Better mental modelClear the record and the estimate disappears. Noise can yield an unphysical negative coefficient; unconstrained fits are not clipped or safety certificates.

Run the experiment

01
Prime the column
Select Unprimed tube, then Prime the tube.
What to observe: An unprimed tube carries no accepted transport even if the candidate energy budget is favorable.
02
Move the outlet
Lower the outlet and compare the no-loss case.
What to observe: Outlet drop sets speed; crest height alone does not drive the ideal flow.
03
Find the pressure boundary
Raise the crest or lower ambient pressure; inspect the marked lowest-pressure station.
What to observe: The column is rejected when its candidate pressure reaches the specified vapor pressure.
04
Collect and infer
Return to Primed siphon, acquire timed volumes and export the raw record.
What to observe: A volume slope estimates flow and total resistance; it cannot identify separate loss mechanisms.