What is a Bernoulli pipe flow simulator?
Bernoulli's principle links the speed of a flowing fluid to its pressure. Push water through a pipe that narrows, and the water has to move faster at the narrow part; where it moves faster, its static pressure falls. This simulator makes that trade visible.
Drag the flow slider to set how much water moves each second. Three piezometer tubes tap the pipe, and the liquid height in each one reads out the static pressure at that point.
Why look inside?
From the outside a pipe looks uniform. Showing the narrowing throat, the moving particles and the three pressure columns together makes the speed-pressure trade-off obvious: the fast middle section is always the one with the lowest column.
Two ideas matter most: the flow rate Q is the same at every section, and it is only the split between speed and pressure that changes as the pipe narrows.
1. Set the flow rate
The slider sets the flow rate Q through the pipe. Because the flow is steady, the same Q has to pass every section, so the speed at any point is decided by the area it meets there.
2. The wide section runs slow
In the wide section A₁ the water moves slowly and crowds together, so its static pressure is high. The first piezometer column stands tall to show that.
3. The narrow throat runs fast
At the narrow section A₂ the same flow is squeezed into half the area. To keep up, the water travels twice as fast, and the middle piezometer column drops because speed has been paid for out of pressure.
4. The columns show the pressure
Each piezometer tube lets liquid rise to a height proportional to the static pressure at its tap. Reading the three levels side by side shows the pressure falling into the throat and recovering afterward.
5. Back to the wide section
Downstream the pipe widens back to its original size, so the water slows down to its earlier speed. The energy that went into motion at the throat returns to pressure, and the last column rises to match the first.
What does Bernoulli's principle say?
For a fluid flowing without losses, where the flow speeds up its static pressure drops, and where it slows down the pressure rises. The total of pressure and motion energy stays the same along the pipe.
Why does the water speed up at the narrow section?
The same volume of water has to get past every section each second. Where the area is smaller the water has to move faster to keep up, so halving the area doubles the speed.
Why does the pressure drop there?
Speeding the water up takes energy, and it is paid for out of the pressure. At the throat the water is fast, so less of its energy is left as pressure and the static pressure falls.
What do the piezometer tubes show?
Each tube taps the pipe and lets liquid rise to a height proportional to the static pressure at its tap. Three tubes side by side show at a glance where the pressure is high and where it is low.
Does the flow rate change as the pipe narrows?
No. For steady flow the same flow rate Q passes every section. Only the speed and the pressure change; the amount of water per second stays the same through the throat as at the inlet.
Why does the level rise again at the outlet?
The pipe widens back to its original size, so the water slows down to its earlier speed. The energy that went into motion at the throat returns to pressure, so the level climbs back up.