# Fluid Mechanics: Questions on 2D Flows

• Raparicio
In summary, the conversation involves studying 2D flows, specifically in a square where there is a grid of flow in horizontal and vertical directions. The flow entering and exiting the square must be the same, and the Navier-Stokes equations are used to account for pressure. The conversation then delves into discussing the equations and how to extract the flow from them.
Raparicio
Dear Friends,

I'm studying the 2D flows, and I have any questions.

In a square, there's a grid of flow in horizontal an vertical linear flow.

The flow that entry the square must be the same that exits form it.

$$\frac {\partial \Psi_e}{\partial x} -\frac {\partial \Psi_O}{\partial x}= \frac {\partial \Psi} {\partial x}= 0$$

Becouse we have presure, we must apply navier-stokes'

$$\rho [ \frac {\partial {v_x}}{\partial t} + ( \vec{v_x} \frac {\partial}{ \partial x} ) \vec{v_x} ] = \mu \frac {\partial^2} {\partial x^2} \vec {v_x} - \frac {\partial p} {\partial x}$$

How can I vinculate the presure with the flow in x and y directions?

.

I think Navier Stokes in 2D would be:

$$\rho [ \frac {\partial {v_x}}{\partial t} + ( \vec{v_x} \frac {\partial}{ \partial x} ) \vec{v_x} + ( \vec{v_y} \frac {\partial}{ \partial y} ) \vec{v_x} ] = \mu \frac {\partial^2} {\partial x^2} \vec {v_x} + \mu \frac {\partial^2} {\partial y^2} \vec {v_x} - \frac {\partial p} {\partial x}$$

and
$$\frac {\partial}{ \partial x} \vec{v_x} + \frac {\partial}{ \partial y} \vec{v_y} = 0$$

Aha!

Ah! Thanks learningphysics. Now I'm trying to extract for this formula the flow. Is it possible?

## 1. What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids and their behavior in motion. It involves the study of how fluids such as liquids and gases flow and interact with their surroundings.

## 2. What are 2D flows?

2D flows refer to fluid flows that occur in two dimensions, meaning they are confined to a plane. This is in contrast to 3D flows which occur in three dimensions and are not confined to a plane. 2D flows are often used to simplify the mathematical analysis of fluid mechanics problems.

## 3. What are some examples of 2D flows?

Some examples of 2D flows include flow around a flat plate, flow over an airfoil, and flow through a nozzle. These flows are commonly studied in fluid mechanics because they can be easily visualized and analyzed in two dimensions.

## 4. How do 2D flows differ from 3D flows?

2D flows are simplified versions of 3D flows, where the flow occurs only in two dimensions instead of three. This means that 2D flows do not take into account the effects of flow in the third dimension, such as vortices and turbulence, which can significantly impact the behavior of the fluid.

## 5. What are some real-world applications of 2D flows?

2D flows have many practical applications, such as in aerodynamics for designing airplane wings and in hydraulic engineering for designing channels and dams. They are also used in the study of ocean currents and weather patterns, and in industries such as automotive and aerospace for optimizing fluid flow in engines and other systems.

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