Ideal Venturi-meter relation
\( p_1 + \tfrac{1}{2}\rho V_1^2 = p_2 + \tfrac{1}{2}\rho V_2^2 \)
\( Q = A_1V_1 = A_2V_2 \)
\( \displaystyle Q = A_2\sqrt{\frac{2(p_1-p_2)}{\rho\left[1-(A_2/A_1)^2\right]}} \)
\( \displaystyle V_1 = \frac{Q}{A_1},\qquad V_2 = \frac{Q}{A_2} \)
Symbols
- Q — theoretical volume flow rate (m3/s)
- V1, V2 — average velocities at sections (1) and (2) (m/s)
- p1 − p2 — pressure difference across the meter (Pa)
- A1, A2 — upstream and throat cross-sectional areas (m2)
- ρ — fluid density (kg/m3)
- Assumptions — horizontal, steady, inviscid, incompressible flow
Schematic placeholder
Venturi meter with section (1) upstream and section (2) at the throat.
Add the actual sketch here later.
Add the actual sketch here later.
Default shown for water. Change it to explore other incompressible fluids.
A₂ = —
A₂ (m²)
—
Q (m³/s)
—
V₁ (m/s)
—
V₂ (m/s)
—
\[ Q \propto \sqrt{\Delta p} \]
\[ \Delta p = p_1 - p_2 \]
\[ z_1 = z_2 \quad \text{for horizontal flow} \]
This page uses the ideal Venturi-meter equation for steady, inviscid, incompressible, horizontal flow between sections (1) and (2). The flowrate varies with the square root of the pressure difference across the meter. In practice, the actual measured flowrate is often slightly smaller than the theoretical value, so a discharge coefficient may be used.