How is the Bernoulli Equation Used to Evaluate Continuity of Flow

The Bernoulli theorem was given by Daniel Bernoulli. According to Bernoulli theorem when the speed of moving fluid increases then the pressure inside the fluid decreases. Although Bernoulli derived the law, it was Leonhard Euler who, in 1752, derived the Bernoulli equation in its usual form.

The relationship between the pressure of a fluid which flows to its elevation and its velocity is given by an equation called the Bernoulli equation. This equation is based on conservation of energy and their conversion into each other. As dictated by Daniel Bernoulli, it is broadly known as the Bernoulli Principle. This principle can be used in several applications, like spray guns, venturi meters, nozzles, etc. By applying Bernoulli's principle, we can figure out many real-world engineering problems that are related to fluid flow.

Bernoulli theorem formula

The formula of Bernoulli's principle is a relationship between pressure, kinetic energy, and gravitational potential energy of a fluid which is kept inside a container.

Bernoulli theorem formula is given as

p+1/2 ⍴×v²+⍴×g×h=constant

Here,

p = pressure exerted by fluid

p= density of fluid

v = Fluid velocity

g = Acceleration due to gravity

h = height of container

Bernoulli's equation provides a relationship between pressure, velocity and elevation.

Bernoulli's Equation Derivation

Let us consider a pipe with variable diameter and height through which a fluid flows which is incompressible. The relation between the cross-sectional area of A, the speed of flow v, the height from ground y, and pressure p at two points 1 and 2.

Assumption:

Density of incompressible fluid is constant at both points.

The energy of the fluid is conserved because the value of viscous forces in the fluid is zero.

Hence, work done on the fluid is

Principle of Continuity

When the fluid is streamlined and incompressible, then the mass of fluid flowing through different cross-sections is the same.

Let us consider a container. Liquid is entered from one end of the container and left from the other end. Now let,

Use of Bernoulli's Principle

Bernoulli's Principle has many applications. Some of the uses of Bernoulli's Principle are given here.

1. Bernoulli's principle is used to examine the unsteady flow which is applicable in the theory of ocean surface waves and acoustics.
2. Bernoulli theorem is also used for approximation of parameters such as pressure and velocity of the fluid.
3. Venturi meter is a device which is based on Bernoulli's principle and used for determining the rate of flow of liquid through the pipes.

Bernoulli's principle example

Conclusion

Daniel Bernoulli explained how the liquid speed influences the fluid pressure known as Bernoulli effect and also explained kinetic theory of gases. These two were the greatest contributions of Daniel Bernoulli in Science and these made him famous.

From Bernoulli's effect Daniel Bernoulli tried to study that if a fluid flows through a region where the speed rises, then the pressure will reduce. Bernoulli's effects determine several real-life applications like airplane wings are used for giving a lift to the plane.

Bernoulli's principle is used to examine the unsteady flow which is applicable in the theory of ocean surface waves and acoustics.

Bernoulli theorem is also used for approximation of parameters such as pressure and velocity of the fluid.

Bernoulli's equation is applicable to fluids having zero viscosity or non-viscous fluids. The fluids have to be incompressible and the elastic energy of fluid is also not taken.

Frequently asked questions

Get answers to the most common queries related to the NEET UG Examination Preparation.

Q1. What do you mean by Bernoulli's Equation?

Ans. The Bernoulli equation is the statement of the conservation of energy for flowing fluids. Bernoulli equation is...Read full

Q2. Define head loss in Bernoulli's Equation.

Ans. Head loss in Bernoulli's equation is the description of reduction in the total pressure. Total pressure is th...Read full

Q3. What is the Principle of Continuity? Determine the equation.

Ans. When the fluid is streamlined and incompressible, then the mass of fluid flowing through different cross-sectio...Read full

Q4. Write some uses of Bernoulli's Principle.

Ans. There are many uses of Bernoulli's Principle, some of which are given below. ...Read full

Ans. The Bernoulli equation is the statement of the conservation of energy for flowing fluids. Bernoulli equation is considered as the qualitative behaviour which reduces the pressure in the high velocity regions.

Ans. Head loss in Bernoulli's equation is the description of reduction in the total pressure. Total pressure is the sum of the velocity head, pressure head, and the elevation head of the fluid which flows through the hydraulic system.

Ans. When the fluid is streamlined and incompressible, then the mass of fluid flowing through different cross-sections is the same.

Let us consider a container. Liquid is entered from one end of the container and left from the other end. Now let,

= density of fluid

v 1 = Liquid velocity at one end

v 2 = Liquid velocity at another end

A = area

t = time

Rate of mass Enter the container = Rate of leave Enter the container

Rate of mass Enter the container = A 1 V 1 t

Rate of mass leave the container = A 2 V 2 t

By combining above two equations, we get

A 1 V 1 = A 2 V 2

This is called the Principle of Continuity.

Ans. There are many uses of Bernoulli's Principle, some of which are given below.

Bernoulli's principle is used to examine the unsteady flow which is applicable in the theory of ocean surface waves and acoustics.

Bernoulli theorem is also used for approximation of parameters such as pressure and velocity of the fluid.

Venturi meter is a device which is based on Bernoulli's principle and used for determining the rate of flow of liquid through the pipes.

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Source: https://unacademy.com/content/neet-ug/study-material/physics/bernoullis-principle-and-its-applications/

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