The three terms of Bernoulli’s equation represent pressure, velocity, and elevation. In a Venturi tube, changes in the liquid column (pressure) help reveal how velocity and elevation change. With no friction loss, total head stays constant, so pressure measurements can be used to calculate velocity and elevation at each location. This makes a Venturi tube a useful way to build an intuitive understanding of Bernoulli’s equation. Change the tube geometry and flow conditions to see how pressure head, velocity head, and elevation head respond.
Water at 20°C · ρ = 1000 kg/m³ · g = 9.81 m/s² · atmospheric pressure 101.325 kPa
Steady, incompressible 1D teaching model. Set the inlet conditions; the remaining values are calculated.
Tube geometry and flow conditions
Q = A₁v₁ = A₂v₂ · A = πD²/4
Throat D ↓ → A ↓ → v ↑ → velocity head ↑ → pressure head ↓ (fixed inlet conditions, elevation, and loss)
Advanced settings · inlet elevation and loss head
Loss applies only in With loss mode. The entered hL is distributed linearly from inlet to outlet; it does not predict real pipe friction or CFD results. The throat elevation is midway between inlet and outlet elevations.
Vertical segments: datum → tube centerline → liquid surface (HGL) → EGL. Equivalent pressure tubes read centerline static pressure and contain water only up to the HGL. The velocity-head and elevation-head lines are not water. The tube tops are fixed 4.5 m above the datum; // marks the omitted portion. The scale adjusts automatically. Only tube diameter is exaggerated twofold, and particles indicate average velocity.
Calculated results · the three terms
A negative static-pressure term appears as a hatched bar extending downward. Negative gauge pressure remains in the calculation rather than being clamped to zero. The tube diagram always uses meters for height, regardless of display mode.
| Group | Value | ① Inlet | ② Throat | ③ Outlet |
|---|
Changing inlet velocity, static pressure, or elevation also changes the supplied total head. “Constant” in Ideal mode means equal total head across locations for one set of inputs. Outlet pressure is not separately fixed at atmospheric pressure.
Things to try
- Reduce the throat diameter from 40 mm to 30 mm. With the same inlet conditions, flow rate stays constant while throat velocity and dynamic pressure increase. Static pressure and the liquid-column height decrease.
- Raise the outlet elevation. Since diameter and flow rate stay the same, outlet velocity is unchanged. Pressure head decreases by the amount that elevation head increases.
- Switch the display to Pressure. Compare dynamic pressure divided by density and gravitational acceleration with velocity head in Head mode.
- Select With loss and increase the loss head under Advanced settings. The EGL and total head fall along the flow direction. Zero loss gives the same result as Ideal.
How velocity and static pressure are calculated at each location
The inlet velocity, static pressure, elevation, and tube diameters are the starting conditions. The flow rate is , and continuity keeps it constant at every location. Rearranging the local flow rate as shows how velocity depends on tube diameter. Once the total head at the inlet is known, the velocity and elevation at each location can be used to calculate its static pressure.
Static pressure, velocity, and elevation cannot all be prescribed independently at every location. Outlet pressure is also a calculated result of the inlet conditions and tube geometry; simultaneously imposing an outlet open to the atmosphere would be inconsistent. In Ideal mode, total head is constant across locations for a given set of inputs. Changing inlet velocity or pressure changes the supplied total head itself. Keep this in mind as you adjust the Venturi tube.
How to read the diagrams
In the tube diagram, elevation head extends from the datum to the centerline, pressure head from the centerline to the liquid surface, and velocity head from the liquid surface to the EGL. Values and totals appear beneath each location in matching colors. The colored lines for velocity and elevation head are not actual water columns. Turning off HGL/EGL hides the guide lines and velocity-head markers, but the liquid columns remain.
The tube diameter is exaggerated twofold vertically, while centerline, liquid-surface, HGL, and EGL elevations use the actual meter scale. The pressure tubes represent equivalent connections that read static pressure at the centerline. Their tops are fixed 4.5 m above the datum; // marks the omitted portion outside the view. Automatic scale adjustment may change the tube’s apparent length, but its actual top elevation remains fixed.
The head diagram starts with elevation head at the datum, then adds pressure head and velocity head in sequence. The three terms are offset horizontally so negative pressure head remains visible. Each bar starts where the preceding term ends; the black line shows the total. All vertical lengths use the same scale.
The piezometer liquid columns extend from the centerline measurement points to the HGL. When centerline static pressure is below atmospheric pressure, an open liquid column cannot be maintained, so the diagram hides it and shows a notice. A negative gauge pressure is still a valid calculated value.
In Pressure mode, Total is . This differs from stagnation pressure , which excludes the elevation term. For more on dynamic pressure, see What is dynamic pressure? (Korean).
Model assumptions
This experiment is a steady, incompressible, one-dimensional model of water at 20°C. It uses cross-sectional average velocity and sets the kinetic-energy correction factor to 1. Diameters determine the areas of circular tube sections, and the tube elevation varies gradually from inlet to outlet. The particles indicate differences in velocity; they do not trace actual turbulent particle paths.
In With loss mode, the entered total loss is distributed linearly along the tube. The model does not calculate Darcy–Weisbach friction or geometry-specific loss coefficients, so it cannot predict the performance of a real Venturi flow meter. It also does not calculate transient flow caused by changing geometry, liquid-column oscillations, separation, or cavitation.
Input combinations that could approach water’s vapor pressure of approximately 2.34 kPa absolute are rejected by a conservative pressure bound; the previous settings remain in place. This threshold differs from zero gauge pressure. The model does not predict where cavitation occurs or the size of any bubbles.
The relationships are based on the USBR references for Venturi flow meters and energy balance and head.