Flow and Bernoulli's principle.

Step 1 of 6

Faster where it is narrow

Put your thumb over the end of a garden hose and the water comes out faster. The tap still sends the same number of litres a second, so where the opening is smaller the water must move faster to get them all through. Water hardly compresses, so whatever goes in one end of a pipe must pass every section at the same rate. That is the continuity equation:

$Q = Av$⁠

The flow rate $Q$⁠ equals the section’s area $A$⁠ times the water’s speed $v$⁠. The Scene has a Venturi tube: it is 80 mm wide, narrows smoothly to a short throat, and widens slowly back. The Flow rate and the Throat width are fixed now.

Step 2 of 6

The columns

Six glass columns stand on small holes along the top of the pipe, each open to the air at the top. Water rises in a column until its weight balances the pressure in the pipe below, so each column’s height gauges the pressure there: 10 cm of water is about 1 kPa above the air’s pressure. Here it is a Straight pipe, and the Flow rate is fixed.

Step 3 of 6

Bernoulli’s equation

Daniel Bernoulli put it in one rule in 1738: along the flow, the pressure and the motion share a fixed budget of energy. In each cubic metre of water the pressure $p$⁠ counts as energy, and so does the motion, $\tfrac{1}{2}\rho v^2$⁠. For steady flow without friction, at one height:

$p + \tfrac{1}{2}\rho v^2 = \text{const}$$p + \tfrac{1}{2}\rho v^2 =$$\text{const}$⁠

Show pressure and speed is on Pressure and speed: the water turns from blue to amber where its pressure falls, and beside each column a blue bar for pressure carries an amber bar for speed. Every pair reaches the same dashed line.

Step 4 of 6

Twice the flow

Here the Flow rate is 1 L/s, and the Throat width is fixed at 40 mm.

Step 5 of 6

Below the air’s pressure

If the water is fast enough, the pressure in the throat can fall below the pressure of the air outside. Then no water at all can stand in the column over the throat: it empties, and air is drawn in through the hole and swept away as bubbles. The inlet’s pressure is always held at 36 cm of water, as if a pump were turned up and down to keep it there.

Step 6 of 6

An atomiser

Engineers use this on purpose. A laboratory water pump sucks air out of a flask this way, and an old car’s carburettor drew petrol into the air rushing through a narrow throat. A perfume atomiser works the same way.