Shell balance

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In fluid mechanics, it may be necessary to determine how the fluid velocity changes along the flow. This can be done with shell balance .

Shell is a differential element of flow. By looking at momentum and strength in a small part, it is possible to integrate above the flow to see a bigger picture of the flow as a whole. The balance determines what goes in and out of the shell. Momentum enters and leaves the shell through the incoming liquid and leaves the shell and through shear stress. In addition, there is pressure and gravitational force on the shell. The purpose of the shell balance is to determine the flow velocity profile. The velocity profile is an equation for calculating velocity based on the specific location in the stream. From here, it is possible to find the velocity for each point across the stream.

Video Shell balance

Apps

Shell balances can be used for many situations. For example, flow in pipes, the flow of some liquids around each other, or flow due to pressure difference. Although the terms in the shell balance and boundary conditions will change, the basic settings and processes are the same. This system is useful for analyzing any fluid flow applicable to the requirements listed below.

Maps Shell balance

Requirements

In order for the shell balance to function, the stream must:

1. Be a laminar stream
2. Without bends or curves in the path
3. Steady State
4. Has two boundary conditions

Boundary Conditions are used to find the integration constants.

1. Fluid - Solid Boundary: No slip condition, the speed of a liquid in solid equals the speed of solid
2. Liquid - Gas Boundary: Shear Stress = 0
Liquid - Liquid Boundary: Same velocity and shear stress in both liquids

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Perform a shell balance

Here is an outline on how to perform a basic shell balance If fluid flows between two horizontal surfaces, each with area A touching the liquid, a shell of differential heights? Y can be drawn between them as shown in the diagram below.

Dalam contoh ini, permukaan atas bergerak dengan kecepata U dan permukaan bawah stasioner
kepadatan cairan =?
viskositas cairan =?
kecepatan dalam x arah = ${\ displaystyle V_ {x}} Â Â$ , ditunjukkan oleh garis diagonal di atas. Inilah yang ingin diselesaikan oleh keseimbangan shell.

Momentum Conservation is the Key of Balanced Mussels

momentum level at - momentum level out sum of all troop = 0

To perform a shell balance, follow these basic steps:

1. Find the momentum of the shear stress

(Momentum of Shear Stress Into System) - (Momentum from Stress Shear Exit System)

The Momentum of Shear Stress goes into the shell at y and leaves the system at y Ã,? y .

Tegangan geser = ? _yx , area = A , momentum = ? _yx A

2. Find the momentum of the flow

The momentum flows into the system at x Ã, = 0 and exits at x Ã, = L

The stream is stable. Therefore, the momentum flow at x Ã, = 0 equals the flow moment at x Ã, = L . Therefore, this cancels.

3. Find the gravitational force on the shell

4. Find the strength of the pressure

5. Insert into the momentum conservation and complete the ? _yx

6. Apply Newton's law of viscosity to Newtonian fluids

? _yx = - ? ( dV _{x <} / dy )

7. Integrate to find the equations for speed and use the Limit Terms to find the integration constants

Boundary 1: Top Surface: y = 0 dan V _x = U

Boundary 2: Bottom Surface: y = D dan V _x = 0

For an example of doing a shell balance, visit the resources listed below.

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Resources

• "Solution Problem in Transport Phenomenon: Fluid Mechanics Problem" . Retrieved 2007-10-06 .

• Harriott, Peter; W. McCabe; J. Smith (2004). Operation Unit Chemical Engineering: Seventh Edition . McGraw-Hill Professional. pp.Ã, 68-132. ISBN: 9780072848236.

Source of the article : Wikipedia