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1. Which method is used exclusively in fluid mechanics? Explanation: In Fluid Mechanics, the matter of concern is the general state of motion at various points in the fluid system (as in **Eulerian approach**) rather than the motion of each particle (as in Lagrangian approach).The Eulerian method **treats the particle phase as a continuum and develops its conservation equations on a control volume basis and in a similar form as that for the fluid phase**. The Lagrangian method considers particles as a discrete phase and tracks the pathway of each individual particle.Lagrangian approach deals with individual particles and calculates the trajectory of each particle separately, whereas the Eulerian approach deals with concentration of particles and calculates the overall diffusion and convection of a number of particles.

## What is the Eulerian method?

The Eulerian method **treats the particle phase as a continuum and develops its conservation equations on a control volume basis and in a similar form as that for the fluid phase**. The Lagrangian method considers particles as a discrete phase and tracks the pathway of each individual particle.

## What is Lagrangian and Eulerian method?

Lagrangian approach deals with individual particles and calculates the trajectory of each particle separately, whereas the Eulerian approach deals with concentration of particles and calculates the overall diffusion and convection of a number of particles.

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## Which method is most commonly used in fluid mechanics for analysis?

Which method is most commonly used in fluid mechanics for analysis? Explanation: In **Eulerian method**,we describe velocity, acceleration pressure etc at a point in flow field. hence, it is also most commonly used in fluid mechanics.

## Which of the following method is used for the study of flow of fluids?

**Particle image velocimetry**, an experimental method for visualizing and analyzing fluid flow, also takes advantage of the highly visual nature of fluid flow.

## What is the Lagrangian of a system?

Lagrangian function, also called Lagrangian, **quantity that characterizes the state of a physical system**. In mechanics, the Lagrangian function is just the kinetic energy (energy of motion) minus the potential energy (energy of position).

## What is Reynolds transport theorem in fluid mechanics?

Reynolds transport theorem states that the rate of change of an extensive property N, for the system is equal to the time rate of change of N within the control volume and the net rate of flux of the property N through the control surface.

## What is the difference between Lagrangian and Hamiltonian?

The key difference between Lagrangian and Hamiltonian mechanics is that **Lagrangian mechanics describe the difference between kinetic and potential energies, whereas Hamiltonian mechanics describe the sum of kinetic and potential energies**.

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## What is Navier Stokes equation in fluid mechanics?

Navier-Stokes equation, in fluid mechanics, **a partial differential equation that describes the flow of incompressible fluids**. The equation is a generalization of the equation devised by Swiss mathematician Leonhard Euler in the 18th century to describe the flow of incompressible and frictionless fluids.

## Is streamline a Eulerian?

Streamline: A line everywhere tangent to the fluid velocity v at a given instant (flow snapshot). **It is a strictly Eulerian concept**.

## Which method is used exclusively in fluid mechanics?

Solution: Explanation: In Fluid Mechanics, the matter of concern is the general state of motion at various points in the fluid system (as in Eulerian approach) rather than the motion of each particle (as in Lagrangian approach). Hence, the **Eulerian method** is extensively used in Fluid Mechanics.

## Which one of the following experiments is used for the study of dynamics flow of fluids *?

**Reynold’s Experiment** is used for the study of the flow of fluids.

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## What is Bernoulli equation used for?

Bernoulli’s principle is used for **studying the unsteady potential flow** which is used in the theory of ocean surface waves and acoustics. It is also used for approximation of parameters like pressure and speed of the fluid.

## Which method is used to measure the flow rate of liquid?

Answer. To measure the flow rate of liquid THE **FLOAT METHOD** is used and it also known as cross sectional method.

## Which of the following devices is used for the measurement of liquid flow through a channel?

**Venturimeter and orifice meter** are directly used to measure the discharge of the flow through the pipes.

## Which of the following devices is used for the measurement of liquid flow through an open channel?

Explanation: **Venturimeter**: It is a device to measure the rate of flow of fluid flowing through a pipe. Weirs can be used to measure flow rates in open channels and rivers. A Notch is used for measuring the rate of flow of a liquid through a small channel of the tank.

## What is Lagrangian multiplier method?

In mathematical optimization, the method of Lagrange multipliers is **a strategy for finding the local maxima and minima of a function subject to equality constraints** (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).

## How do you use the Lagrange method?

**Method of Lagrange Multipliers**

- Solve the following system of equations. ∇f(x,y,z)=λ∇g(x,y,z)g(x,y,z)=k.
- Plug in all solutions, (x,y,z) ( x , y , z ) , from the first step into f(x,y,z) f ( x , y , z ) and identify the minimum and maximum values, provided they exist and ∇g≠→0 ∇ g ≠ 0 → at the point.

## What is the Euler Lagrange equation used for?

Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for **solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it**.

## What is conservation of mass in fluid mechanics?

The principle of conservation of mass states that **the mass of a body is constant during its motion**. This can be stated in the rate form as the rate of change with time of the mass of a body being zero.

## Is the Reynolds transport theorem a vector equation?

The transport theorem (or transport equation, rate of change transport theorem or basic kinematic equation) is **a vector equation** that relates the time derivative of a Euclidean vector as evaluated in a non-rotating coordinate system to its time derivative in a rotating reference frame.

## What are the differences between Newtonian Lagrangian and Hamiltonian dynamics?

**Newtonian mechanics explains motion in terms of forces whilst Lagrangian mechanics explains motion in terms of energy** whereas Quantum mechanics explains motion in terms of probabilities. Hamiltonian is the bridge between Lagrangian and Quantum .

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## What is the Hamiltonian used for?

Hamiltonian function, also called Hamiltonian, mathematical definition introduced in 1835 by Sir William Rowan Hamilton **to express the rate of change in time of the condition of a dynamic physical system**—one regarded as a set of moving particles.

## Why Hamilton is preferred over Lagrangian?

The most striking advantage of Hamiltonian over Lagrangian is that **we reduce 2nd order set of differential equations to a first order set of differential equation which is easier to solve**. If a system with n degrees of freedom has an ignorable coordinate q.

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