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Torricelli’s Theorem

Torricelli’s Theorem: Real-Life Interactive Example of Bernoulli’s Principle for Velocity of Efflux

Real-Life Context: Torricelli’s theorem applies Bernoulli’s principle to calculate the speed of fluid flowing out of a small hole in a container, like water draining from a punctured bottle, a leaking tank, or even in fire hoses. It’s used in engineering for tank drainage times, irrigation systems, and understanding fluid jets.

How to Interact: Adjust the sliders for fluid depth \( h \) (above the hole) and gravity \( g \). Watch the water jet animate with a parabolic trajectory, see the efflux velocity update, and observe the energy terms in the bar chart.

Bar heights show potential energy converting to kinetic energy. Total remains constant.


2.0

9.81
Torricelli: \( v = \sqrt{2gh} \) = 0 m/s
Bernoulli: ρgh = ½ρv²
Surface (Point 1)
Potential: 0 Pa
Kinetic: ~0 Pa
Pressure: Atm
Efflux (Point 2)
Potential: 0 Pa
Kinetic: 0 Pa
Pressure: Atm

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