# Lagrangian motion (force on a plate)

• ponjavic
In summary, the conversation discusses solving a problem using Lagrangian motion and the use of mass conservation and force momentum equation. The problem can also be solved using continuity, specifically the equation for continuity, and the question involves calculating the drag force acting on a flat 2m wide plate. The question also mentions using a control volume with the upper boundary being a streamline.
ponjavic
I am trying to solve this problem using lagrangian motion but I have no idea how to use it.

It can be solved using mass conservation and force momentum equation but we are supposed to solve it with continuity.

Continuity:

$$\frac{ Dp }{Dt} = \delta u / \delta x + \delta v / \delta y + \delta w / \delta z$$

Now the problem is this:

Calculate the drag force acting on the flat 2m wide plate. Outside the viscous region the velocity is uniform. Use density = 1.23kg/m^3

What I can say is that, $$\frac{ \delta p }{\delta t} = 0$$

PIC

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Nobody with a clue on this one?

The exact question states:

b) Solve the problem using a control volume with the upper boundary a streamline (no mass flux crosses a streamline)

## 1. What is Lagrangian motion?

Lagrangian motion refers to the motion of a body or system of bodies under the influence of external forces, as described by the Lagrangian equations. It takes into account the kinetic and potential energy of the system, and allows for a more comprehensive analysis of the motion compared to traditional Newtonian mechanics.

## 2. How is force applied to a plate in Lagrangian motion?

In Lagrangian motion, force is applied to a plate through the use of external forces, such as gravity or an applied force. These forces are then incorporated into the Lagrangian equations, which determine the resulting motion of the plate.

## 3. What are the advantages of using Lagrangian motion over Newtonian mechanics?

One of the main advantages of using Lagrangian motion is that it allows for a more general and elegant approach to analyzing the motion of a system. It takes into account both kinetic and potential energy, and can be applied to systems with varying numbers of degrees of freedom. It also allows for the use of generalized coordinates, making it easier to solve complex problems.

## 4. How is Lagrangian motion related to Hamiltonian mechanics?

Lagrangian motion and Hamiltonian mechanics are closely related, as both are based on the principle of least action. However, Hamiltonian mechanics takes into account the energy of a system rather than its forces, and uses the Hamiltonian equations to analyze the motion.

## 5. What real-world applications use Lagrangian motion?

Lagrangian motion has many real-world applications, including in classical mechanics, fluid dynamics, and quantum mechanics. It is also used in engineering and robotics, such as in the design and control of mechanical systems. Additionally, it has been applied to the study of celestial mechanics, such as the motion of planets and other celestial bodies.

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