Question

Write down the Bernoulli's Theorem and also the mathe-
metical expression. What do you mean by elastic limit?
​

Answer 1

Answer:

Bernoulli’s principle formulated by Daniel Bernoulli states that as the speed of a moving fluid increases (liquid or gas), the pressure within the fluid decreases. Although Bernoulli deduced the law, it was Leonhard Euler who derived Bernoulli’s equation in its usual form in the year 1752.

What is Bernoulli’s Principle?

Bernoulli’s principle states that

The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant.

Bernoulli’s Principle Formula

Bernoulli’s equation formula is a relation between pressure, kinetic energy, and gravitational potential energy of a fluid in a container.

The formula for Bernoulli’s principle is given as:

p + 12 ρ v2 + ρgh =constant

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

Bernoulli’s equation gives great insight into the balance between pressure, velocity, and elevation.

Explanation:

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Answer 2

Answer:

Bernoulli’s principle, also known as Bernoulli’s equation, will apply for fluids in an ideal state. Therefore, pressure and density are inversely proportional to each other. This means that a fluid with slow speed will exert more pressure than a fluid which is moving faster.

Explanation:

Finding the Work Done

First, we will calculate the work done (W1) on the fluid in the region BC. Work done is

W1 = P1A1 (v1∆t) = P1∆V

Moreover, if we consider the equation of continuity, the same volume of fluid will pass through BC and DE. Therefore, work done by the fluid on the right-hand side of the pipe or DE region is

W2 = P2A2 (v2∆t) = P2∆V

Thus, we can consider the work done on the fluid as – P2∆V. Therefore, the total work done on the fluid is

W1 – W2 = (P1 − P2) ∆V

The total work done helps to convert the gravitational potential energy and kinetic energy of the fluid. Now, consider the fluid density as ρ and the mass passing through the pipe as ∆m in the ∆t interval of time.

Hence, ∆m = ρA1 v1∆t = ρ∆V

ELASTIC LIMIT :

the maximum extent to which a solid may be stretched without permanent alteration of size or shape.