Orifice Flow Calculator

Orifice flow calculations rely on Torricelli's law and Bernoulli's principle to find the velocity of fluid escaping a container under the force of gravity. The core volumetric discharge equation is expressed as: Discharge = C_d × A × (2 × g × h)^0.5, where C_d represents the dimensionless discharge coefficient, A is the cross-sectional area of the orifice, g is the acceleration due to gravity (typically 9.81 m/s²), and h is the height or pressure head of the fluid above the center of the orifice. Furthermore, if you know the diameter of a circular opening rather than its area, you can determine the area using: Area = 0.25 × π × d².

Consider a storage tank discharging water through a circular orifice at the bottom. Let us calculate the total volumetric discharge rate given the following parameters: Orifice Diameter (d) = 0.05 meters, Fluid Height (h) = 4 meters, Discharge Coefficient (C_d) = 0.62, and Gravitational Constant (g) = 9.81 m/s². First, compute the cross-sectional area of the circular orifice: Area = 0.25 × π × (0.05)² = 0.001963 m². Next, calculate the theoretical velocity component: (2 × 9.81 × 4)^0.5 = (78.48)^0.5 = 8.859 m/s. Finally, multiply these values along with the discharge coefficient to find the flow rate: Discharge = 0.62 × 0.001963 × 8.859 = 0.01078 cubic meters per second (m³/s), which equals approximately 10.78 liters per second.

To ensure your real-world measurements match theoretical estimates, always measure the fluid height from the exact centerline of the orifice to the free surface of the liquid. Be mindful that the discharge coefficient is not a universal constant; it varies depending on the Reynolds number, the sharpness of the orifice edges, and the upstream-to-downstream pipe diameter ratio. Lastly, ensure consistent metric units throughout your computations to prevent severe magnitude errors.