# Which of the following principle is based on the conservation of energy?

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Which of the following principle is based on the conservation of energy?
1. Principle of continuity
2. Bernoulli's Principle
3. Both 1 and 2
4. Neither 1 nor 2

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Correct Answer - Option 2 : Bernoulli's Principle

CONCEPT:

• Principle of Continuity: The conservation of mass is shown in a given space occupied by fluid by the principle of continuity.
• It says that the mass discharge for steady flow in a pipe is always constant; that is,

ρVA = constant

Where A is the cross-sectional area of the pipe, ρ is the density of the fluid, and V is the mean velocity.

$ρ_1V_1A_1=ρ_2V_2A_2$

If the fluid is incompressible i.e. density is not changing when passing from one place to another place.

$A_1V_1=A_2V_2$

• Bernoulli's Principle: It states the total mechanical energy of the moving fluid comprising the energy associated with the fluid pressure (P), the gravitational potential energy of elevation ρgh, and the kinetic energy of the fluid motion ${1\over 2}$ρv2 , remains constant. i.e.

$P+ {1\over 2}ρ v^2 +ρ g h= const.$

Where p is the pressure exerted by the fluid, v is the velocity of the fluid, ρ is the density of the fluid, h is the height of the container.

EXPLANATION:

• Option 1: According to the principle of continuity,

ρVA = constant

$ρ_1V_1A_1=ρ_2V_2A_2$

So, Mass passing from one cross-section area will be the same for another cross-section area.

So here mass is conserved in the principle of continuity.

• Option 2: Bernoulli's Principle basically states that the sum of all the energies (Pressure energy, gravitational potential energy, and kinetic energy of fluid) is constant.
• One form of energy can be converted into another but the total sum will remain constant.

$P+ {1\over 2}ρ v^2 +ρ g h= const.$

here P = pressure energy

ρgh = gravitational potential energy

${1\over 2}ρ v^2$ = kinetic energy of the fluid

• So Bernoulli's Principle represents the conservation of energy.
• Hence the correct answer is option 2.