Relation between Conservation of Energy and Bernoulli’s Equation
Bernoulli’s theorem states that the total amount of these three energies within a constantly moving fluid, i.e., kinetic energy, potential energy, and pressure energy, will remain steady throughout the pipeline. However, several factors must be understood:
- The movement of the liquid is assumed to be constant, and there should be no alteration with respect to the pressure, speed, and consistency of the liquid at any point in time. However, if the liquid flow is unstable, there will be a change in speed, and in that case, this equation may not hold true.
- The fluid is considered to be incompressible. Since all liquids are incompressible in nature, this principle can be applied to all fluids. However, in the case of gas flow, there should be a constant density, and one can manage with little difference in pressure, velocity, and temperature.
- Another consideration is the irrotational feature of liquids, which means that the overall angular momentum throughout the liquid is zero.
- The fluid should be ideal for this principle to hold true, meaning there should be no loss of energy due to frictional activity. Hence, there is no excess energy production due to internal particle friction.
Bernoulli’s Principle
Bernoulli’s Principle is a very important concept in Fluid Mechanics which is the study of fluids (like air and water) and their interaction with other fluids. Bernoulli’s principle is also referred to as Bernoulli’s Equation or Bernoulli Theorem.
This principle was first stated by Daniel Bernoulli and then formulated in Bernoulli’s Equation by Leonhard Euler in 1752, which provides the relationship between the pressure (P) of the fluid flowing, at a height (h) of the container having kinetic and gravitational potential energy.
The conservation of energy was found to be true for flowing fluids by the statement of Bernoulli’s Principle. It may seem contradictory, but Bernoulli’s principle describes how a fluid’s velocity and pressure are related to each other.
In this article, we have provided what is Bernoulli’s principle, Bernoulli’s equation, its derivation, examples, and proof.
Table of Content
- What is Bernoulli’s Principle?
- Bernoulli’s Principle Formula
- Bernoulli’s Equation Derivation
- Principle of Continuity
- Applications of Bernoulli’s Principle and Equation
- Relation between Conservation of Energy and Bernoulli’s Equation
- Limitations of Bernoulli’s Principle