Torricelli’s theorem describes the velocity of fluid flowing out of an orifice under gravity.
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Torricelli’s Theorem and Its Applications
Torricelli’s theorem is a principle in fluid dynamics used to calculate the velocity of fluid flowing out of an orifice under the influence of gravity. It provides a relationship between the height of the fluid above the opening and the speed at which the fluid exits.
The Formula:
The theorem states that the velocity \(v\) of the fluid leaving the orifice is given by:
\[
v = \sqrt{2gh}
\]
where:
– \(v\) is the velocity of the fluid (m/s),
– \(g\) is the acceleration due to gravity (approximately 9.8 m/s\(^2\)),
– \(h\) is the height of the fluid above the orifice (m).
Applications:
1. **Design of Water Tanks and Reservoirs**:
– Torricelli’s theorem helps engineers predict how quickly water will drain from a tank or reservoir.
2. **Flow Rate Calculations**:
– By coupling the velocity with the cross-sectional area of the orifice, the volumetric flow rate can be determined.
3. **Hydraulic Systems**:
– It is used to model the behavior of fluids in hydraulic equipment where fluid discharge velocity is crucial.
4. **Fountain Design**:
– In fountains, the theorem assists in estimating the initial velocity required for water jets to reach a certain height.
5. **Leakage Analysis**:
– It can estimate fluid loss through holes or cracks in tanks or pipes.
Limitations:
– The theorem assumes ideal conditions, such as negligible viscosity, no air resistance, and steady flow. Real-world factors like turbulence and friction must be accounted for in practical applications.
By providing a simplified way to analyze fluid behavior, Torricelli’s theorem remains a fundamental concept in fluid mechanics and engineering design. This question related to Chapter 9 physics Class 11th NCERT. From the Chapter 9. Mechanical Properties of Fluids. Give answer according to your understanding.
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