Leak Flow Rate Calculator

Torricelli's Law Approximation:

\[ FR = C \times A \times \sqrt{2 \times g \times h} \]

Discharge Coefficient (C):

dimensionless

Area (A):

m²

Gravity (g):

m/s²

Height (h):

Flow Rate (FR):

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1. What is Torricelli's Law Approximation?

Torricelli's law approximation calculates the flow rate of a fluid leaking from a container through an orifice. It's based on the principle that the speed of efflux is equal to the speed that a body would acquire in falling freely from the fluid surface to the orifice.

2. How Does the Calculator Work?

The calculator uses the Torricelli's law approximation:

\[ FR = C \times A \times \sqrt{2 \times g \times h} \]

Where:

\( FR \) — Flow rate (m³/s)
\( C \) — Discharge coefficient (dimensionless)
\( A \) — Area of the orifice (m²)
\( g \) — Acceleration due to gravity (m/s²)
\( h \) — Height of fluid above the orifice (m)

Explanation: The equation accounts for the theoretical flow rate of an ideal fluid, modified by the discharge coefficient to account for real-world effects like viscosity and turbulence.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is crucial for designing fluid systems, predicting leak rates, assessing drainage capacity, and ensuring proper system performance in various engineering applications.

4. Using the Calculator

Tips: Enter discharge coefficient (typically 0.6-0.8 for sharp-edged orifices), area in square meters, gravity (9.81 m/s² on Earth), and height in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical discharge coefficient value?
A: For sharp-edged circular orifices, C is typically around 0.61-0.62. The value varies based on orifice shape and Reynolds number.

Q2: Does this equation work for all fluids?
A: The equation works best for incompressible fluids like water. For compressible fluids or high-viscosity fluids, additional corrections may be needed.

Q3: What are the limitations of this approximation?
A: It assumes steady flow, negligible viscosity effects, and that the orifice is small compared to the container size. It may not be accurate for very small or very large orifices.

Q4: How does orifice shape affect the calculation?
A: Different orifice shapes have different discharge coefficients. Sharp-edged orifices typically have lower coefficients than rounded or bell-mouthed orifices.

Q5: Can this be used for pressurized containers?
A: For pressurized containers, the equation should be modified to include the pressure difference: \( FR = C \times A \times \sqrt{2 \times (g \times h + \Delta P / \rho)} \)