What Is the Torricelli's Law Fluid Discharge Velocity Calculator?
Torricelli’s Law, discovered in 1643 by Italian physicist Evangelista Torricelli, determines the velocity at which liquid drains from an opening in a container.
It is widely used in civil hydraulics, chemical processing, drainage tank design, and reservoir floodgates.
How Does the Torricelli's Law Fluid Discharge Velocity Calculator Work?
The hydrostatic pressure head P = ρ·g·h at the orifice converts into dynamic kinetic energy (1/2 ρ v²).
Canceling fluid density yields the ideal exit speed v = √(2gh).
The actual volumetric discharge Q is found by multiplying by orifice area and discharge coefficient C_d.
Torricelli's Law Fluid Discharge Velocity Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Conservation of mechanical energy dictates that potential energy of fluid head converts into kinetic exit energy, reduced by discharge coefficient C_d.
How to Use the Torricelli's Law Fluid Discharge Velocity Calculator
- Enter the liquid depth above the orifice in meters.
- Enter the orifice hole diameter in millimeters.
- Adjust C_d based on opening geometry (0.62 default for standard sharp hole).
Step-by-Step Example Calculation
5-Meter Water Tank with 50 mm Drain
Input Values:
Understanding Your Result
Discharge Flow Rate: Volume emptied per second (L/s) and gallons per minute (GPM).
Exit Velocity: Streamline jet speed in meters per second.
Jet Thrust: Inward reactive force exerted by the escaping stream.
Factors That Affect the Result
- Liquid Height: Flow velocity scales with the square root of fluid depth (√h).
- Orifice Diameter: Volumetric throughput scales with the square of diameter (d²).
When Should You Use This Calculator?
- Rainwater detention basin drain sizing and retention pond outflow calculations.
- Industrial chemical tank gravity feed and emergency dump valve sizing.
Assumptions & Limitations
- Assumes open unpressurized tank with free atmospheric surface.
- Assumes orifice area is much smaller than tank surface area (<1/10).
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard fluid mechanics equation conforming to ISO 5167 orifice calibration.