How do Bernoulli's Equation and the Venturi Effect work?
In steady incompressible pipe flow, two fundamental conservation laws hold simultaneously: the Continuity Equation (conservation of mass, $Q = A_1 v_1 = A_2 v_2$) and Bernoulli's Principle (conservation of mechanical energy per unit volume): $P_1 + \frac{1}{2}\rho v_1^2 + \rho g z_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g z_2$.
Because a circular pipe's cross-sectional area scales with the square of its diameter ($A = \frac{\pi D^2}{4}$), halving the diameter in a constriction ($D_2 = \frac{1}{2}D_1$) reduces area to one-fourth and quadruples fluid velocity ($v_2 = 4 v_1$). This sharp rise in dynamic pressure ($\frac{1}{2}\rho v_2^2$) causes an immediate drop in static pressure $P_2$—a phenomenon discovered by Giovanni Battista Venturi in 1797 and widely used in differential flowmeters, eductors, carburetors, and aerodynamics.
Additionally, the tool computes the Reynolds Number ($\text{Re} = \frac{\rho v D}{\mu}$) for water at $20\text{ °C}$ ($\rho = 998\text{ kg/m}^3$, $\mu = 1.002\times 10^{-3}\text{ Pa·s}$), classifying flow as laminar ($\text{Re} < 2300$), transitional, or turbulent ($\text{Re} > 4000$).
Step-by-step guided experiment
1. Inverse-square diameter effect: Set $D_1 = 200\text{ mm}$ and $D_2 = 100\text{ mm}$ at $Q = 45\text{ L/s}$. Notice fluid speed jumps from $1.43\text{ m/s}$ to $5.73\text{ m/s}$ ($4\times$ faster) and the throat piezometer column drops.
2. Cavitation / vacuum onset: Narrow $D_2$ to $55\text{ mm}$ and increase flow rate $Q$ above $80\text{ L/s}$ with $P_1 = 100\text{ kPa}$. Throat velocity exceeds $30\text{ m/s}$ and $P_2$ drops into vacuum/cavitation territory.
Frequently Asked Questions (FAQ)
Why does static pressure drop inside the throat of a Venturi tube?
By conservation of mass ($Q = A_1 v_1 = A_2 v_2$), a smaller cross-sectional area $A_2$ forces fluid velocity $v_2$ to increase. By conservation of energy (Bernoulli), the rise in kinetic energy per unit volume ($\frac{1}{2}\rho v^2$) is balanced by a drop in static pressure $P_2$.
How is the Reynolds Number (Re) interpreted in pipe flow?
The Reynolds Number ($\text{Re} = \frac{\rho v D}{\mu}$) is the ratio of inertial forces to viscous forces. In circular pipes, flow is laminar when $\text{Re} < 2300$, transitional between $2300$ and $4000$, and turbulent when $\text{Re} > 4000$.
What happens if absolute pressure in the throat drops below vapor pressure?
Cavitation occurs: the liquid flashes into vapor bubbles at ambient temperature, which then implode violently as pressure recovers downstream, eroding pipe walls and pump impellers.
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