Wall Shear Stress - 2

# Wall Shear Stress - 2 | Fluid Mechanics for Mechanical Engineering PDF Download

Seperation of Boundary Layer

• It has been observed that the flow is reversed at the vicinity of the wall under certain conditions.
• The phenomenon is termed as separation of boundary layer
• Separation takes place due to excessive momentum loss near the wall in a boundary layer trying to move downstream against increasing pressure, i.e.,  , which is called adverse pressure gradient.
• Figure 29.2 shows the flow past a circular cylinder, in an infinite medium

1. Up to  θ = 900, the flow area is like a constricted passage and the flow behaviour is like that of a nozzle.
2. Beyond θ = 90 the flow area is diverged, therefore, the flow behaviour is much similar to a diffuser

• This dictates the inviscid pressure distribution on the cylinder which is shown by a firm line in Fig. 29.2.

Here

Pw   :  pressure in the free stream

U    :  velocity in the free stream and

P       : is the local pressure on the cylinder.

Fig. 29.2   Flow separation and formation of wake behind a circular cylinder

1. Until θ = 900 the pressure force and the force due to streamwise acceleration i.e. inertia forces are acting in the same direction (pressure gradient beingnegative/favourable)
2. Beyond θ = 900 , the pressure gradient is positive or adverse. Due to the adverse pressure gradient the pressure force and the force due to acceleration will be opposing each other in the in viscid zone of this part.

So long as no viscous effect is considered, the situation does not cause any sensation.
In the viscid region (near the solid boundary),

1. Up to θ = 900 , the viscous force opposes the combined pressure force and the force due to acceleration. Fluid particles overcome this viscous resistance
due to continuous conversion of pressure force into kinetic energy.
2. Beyond θ = 900 , within the viscous zone, the flow structure becomes different. It is seen that the force due to acceleration is opposed by both the viscous force and pressure force.

• Depending upon the magnitude of adverse pressure gradient, somewhere around θ = 900the fluid particles, in the boundary layer are separated from the wall and driven in the upstream direction. However, the far field external stream pushes back these separated layers together with it and develops a broad pulsating wake behind the cylinder.
• The mathematical explanation of flow-separation : The point of separation may be defined as the limit between forward and reverse flow in the layer very close to the wall, i.e., at the point of separation

( 29.16)

This means that the shear stress at the wall, tw = 0 . But at this point, the adverse pressure continues to exist and at the downstream of this point the flow acts in a reverse direction resulting in a back flow.

• We can also explain flow separation using the argument about the second derivative of velocity u at the wall. From the dimensional form of the momentum  at the wall, where u = v = 0, we can write

( 29.17)

• Consider the situation due to a favourable pressure gradient where  we have,

1.      . (From Eq. (29.17))
2. As we proceed towards the free stream, the velocity u approaches  U asymptotically, so   decreases at a continuously lesser rate in y direction.
3.  This means that  remains less than zero near the edge of the boundary layer.
4.  The curvature of a velocity profile  is always negative as shown in (Fig. 29.3a)
1. At the boundary, the curvature of the profile must be positive (since  ).
2. Near the interface of boundary layer and free stream the previous argument regarding    and still holds good and the curvature is negative.
3.  Thus we observe that for an adverse pressure gradient, there must exist a point for which = 0 . This point is known as point of inflection of the velocity profile in the boundary layer as shown in Fig. 29.3b
4. However, point of separation means  = 0 at the wall.
5.    at the wall since separation can only occur due to adverse pressure gradient. But we have already seen that at the edge of the boundary layer,  . It is therefore, clear that if there is a point of separation, there must exist a point of inflection in the velocity profile.

1. Let us reconsider the flow past a circular cylinder and continue our discussion on the wake behind a cylinder. The pressure distribution which was shown by the firm line in Fig. 21.5 is obtained from the potential flow theory. However. somewhere near θ = 900 (in experiments it has been observed to be at θ = 810) . the boundary layer detaches itself from the wall.
2. Meanwhile, pressure in the wake remains close to separation-point-pressure since the eddies (formed as a consequence of the retarded layers being carried together with the upper layer through the action of shear) cannot convert rotational kinetic energy into pressure head. The actual pressure distribution is shown by the dotted line in Fig. 29.3.
3. Since the wake zone pressure is less than that of the forward stagnation point (pressure at point A in Fig. 29.3), the cylinder experiences a drag force which is basically attributed to the pressure difference.

The drag force, brought about by the pressure difference is known as form drag whereas the shear stress at the wall gives rise to skin friction dragGenerally, these two drag forces together are responsible for resultant drag on a body

The document Wall Shear Stress - 2 | Fluid Mechanics for Mechanical Engineering is a part of the Mechanical Engineering Course Fluid Mechanics for Mechanical Engineering.
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## Fluid Mechanics for Mechanical Engineering

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## FAQs on Wall Shear Stress - 2 - Fluid Mechanics for Mechanical Engineering

 1. What is wall shear stress in mechanical engineering?
Ans. Wall shear stress is the force per unit area exerted on a solid boundary by a fluid flowing along it. In mechanical engineering, it is a measure of the frictional resistance between the fluid and the solid surface, and plays a crucial role in the design and analysis of various systems such as pipes, ducts, and channels.
 2. How is wall shear stress calculated?
Ans. The calculation of wall shear stress involves the use of fluid mechanics principles and mathematical equations. In general, it can be calculated by dividing the shear force acting on the wall by the area of the wall. This can be expressed mathematically as τ = F/A, where τ represents the wall shear stress, F is the shear force, and A is the area of the wall.
 3. What factors affect wall shear stress?
Ans. Several factors influence wall shear stress in mechanical engineering. These include the velocity of the fluid, the viscosity of the fluid, the roughness of the wall surface, and the geometry of the flow. Higher fluid velocities and lower viscosities generally result in higher wall shear stress, while smoother wall surfaces and streamlined flow geometries tend to reduce it.
 4. Why is wall shear stress important in mechanical engineering?
Ans. Wall shear stress is of great importance in mechanical engineering because it affects the performance and integrity of various systems. For example, in pipes and channels, high wall shear stress can lead to increased energy losses and pipe erosion. In heat exchangers, it influences the heat transfer rate. Understanding and controlling wall shear stress is essential for optimizing the design and operation of mechanical systems.
 5. How can wall shear stress be controlled or reduced?
Ans. There are several methods for controlling or reducing wall shear stress in mechanical engineering. Some common approaches include using flow control devices such as baffles or flow straighteners, modifying the surface roughness of the wall, altering the flow geometry to reduce turbulence, and applying appropriate lubricants or coatings to the wall surface. These measures can help minimize the detrimental effects of high wall shear stress and improve the overall performance of the system.

## Fluid Mechanics for Mechanical Engineering

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