Venturi Effect Calculator

The Venturi effect combines the continuity equation and Bernoulli's equation for incompressible flow:

Continuity equation (mass conservation):

$$A_1 v_1 = A_2 v_2$$

$$v_2 = v_1 \cdot \frac{A_1}{A_2}$$

Bernoulli's equation (at the same elevation):

$$P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$$

The pressure difference between upstream and throat:

$$\Delta P = P_1 - P_2 = \frac{1}{2}\rho(v_2^2 - v_1^2)$$

Substituting the continuity equation:

$$\Delta P = \frac{1}{2}\rho v_1^2 \left[\left(\frac{A_1}{A_2}\right)^2 - 1\right]$$

Key properties of the Venturi effect:

• Velocity increases in proportion to the area ratio A₁/A₂
• Pressure decreases as the square of the velocity ratio
• If throat pressure drops below the fluid's vapor pressure, cavitation occurs
• The Venturi meter uses this pressure difference to measure flow rate

In a Venturi meter, the flow rate can be determined from the measured ΔP:

$$Q = C_d A_2 \sqrt{\frac{2 \Delta P}{\rho(1 - \beta^4)}}$$

where β = D₂/D₁ (diameter ratio) and Cd ≈ 0.98 for a well-designed Venturi tube — much higher than an orifice plate because the gradual contraction and expansion minimize losses.

The throat velocity shows how much the fluid accelerates in the constriction — higher area ratios produce greater acceleration. The pressure difference represents the energy converted from pressure to kinetic form. A larger ΔP means more suction at the throat, which is useful for aspirators and ejectors but risks cavitation if the absolute throat pressure becomes too low.