Boundary Layer Theory MCQ Quiz in मल्याळम - Objective Question with Answer for Boundary Layer Theory - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Explanation:

Boundary-Layer Thickness:

It is defined as the distance from the boundary of the solid body measured in the perpendicular direction to the point where the velocity of the fluid is approximately equal to 0.99 times the free stream velocity (U). It s denoted by the symbol (δ).

Important Points Boundary layer:

When a real fluid flows past a solid body or a solid wall, the fluid particles adhere to the boundary and the condition of no-slip occurs i.e velocity of fluid will be the same as that of the boundary.

Farther away from the boundary, the velocity will be higher and as a result of this variation, the velocity gradient will exist.

The correct answer is ' option 2'

Key Points The factors that influence the thickness of the boundary layer formation along with a flat smooth plate:

• Greater is the kinematic viscosity of the fluid greater is the boundary layer thickness.
• The boundary layer thickness decreases as the distance from the leading-edge decreases.
• The boundary layer thickness decreases with the increase in the velocity of flow of the approaching stream of fluid.
• The boundary layer thickness is considerably affected by the pressure gradient in the direction of flow.
• Flow inside the boundary layer is rotational.

Additional Information Boundary layer Theory concept was first given by L. Prandt and this concept is valid for the infinitely large medium of real fluid.

For Laminar Boundary on a smooth plate(Blasius Equation):

​  \(\delta = {5x \over \sqrt{Re}}\)                                                            

  \(Re = {ρ Vx \over μ}\)                                                                      

 Where

x= distance where the boundary layer is to be found,

Re= Reynolds number, ρ = density of the fluid,

 V= velocity of the fluid, μ = dynamic viscosity fluid

Explanation:

Power-law velocity profile:

• Both laminar and turbulent pipe flow create symmetric velocity profiles around the pipe's axis, with the highest velocity at the pipe's centre. As illustrated in the picture, laminar pipe flow produces a parabolic velocity profile. The profile is given as
  \(\frac{u}{U_{max}}=1~-~\left ( \frac{r}{R} \right )^2\), where u is the local velocity value and U_max is the maximum velocity at the centre.
• In turbulent flow, the velocity profile in the central part of the pipe (i.e. in the turbulent core) is flatter than in laminar flow. Close to the walls, the flow velocity drops rapidly. This is due to the turbulent flow's diffusivity.
• There are numerous empirical velocity profiles for turbulent pipe flow. The power-law velocity profile is the simplest and most well-known:
  \(\frac{u}{U_{max}}~=~\left(\frac{y}{R}\right)^{\frac{1}{n}}\) or \(\frac{u}{U_{max}}~=~\left(1~-~\frac{r}{R}\right)^{\frac{1}{n}}\), where n is a constant whose value depends on the Reynolds number.
• The one-seventh power-law velocity profile approximates many industrial pipes flows:
  \(\frac{u}{U_{max}}~=~\left(\frac{y}{R}\right)^{\frac{1}{7}}\)

Explanation:

Boundary layer separation:

(i) The boundary layer thickness is considerably affected by the pressure gradient in the direction of flow.

(ii) if dp/dx is zero, then the boundary layer continues to grow in thickness along a flat plate.

(iii) With the decreasing pressure in the direction of flow i.e. with negative pressure gradient, the boundary layer tends to be reduced in thickness.

(iv) With positive pressure gradient, the boundary layer thickness rapidly decreases the momentum in the boundary layer. 

(v) The adverse (positive) pressure gradient plus the boundary shear decreases the momentum in the boundary layer. 

(vi) If kinetic energy of the fluid is not able to overcome the adverse pressure gradient and shear, this results in separation of boundary layers. Thus, the positive pressure gradient helps in boundary layer separation.

(vii) The point on the solid at which the boundary layer is on the verge of separation from the surface is called point of separation.

Location of separation point:

(i) if \({\left( {\frac{{du}}{{dx}}} \right)_{x = 0}} > 0\), the flow will not separate

(ii) \({\left( {\frac{{du}}{{dx}}} \right)_{x = 0}} = 0\), the flow is on the verge of separation

(iii) \({\left( {\frac{{du}}{{dx}}} \right)_{x = 0}} < 0\), the flow has separated

Explanation:

A very thin layer of fluid in the immediate neighbourhood of the solid boundary, where the variation of velocity from zero at the solid boundary to the free stream velocity in the direction normal to the boundary takes place is known as the boundary layer. In this layer, the flow is viscous and rotational.

Outside the boundary layer, flows can be regarded as ideal, i.e. irrotational and frictionless.

Concept:

Drag force is the resistance force caused by the motion of a body through a fluid, such as water or air. It acts opposite to the direction of motion. This is the relative velocity between the body and the fluid. It is given by:

\({\rm{F}} = \frac{1}{2}{{\rm{C}}_{\rm{d}}}{\rm{\rho A}}{{\rm{v}}^2}\)

Where,

C_d = Drag coefficient which depends on Reynolds Number, ρ = Density of medium/fluid, A = Projected area, and v is the velocity.

Clearly, from the options it can be seen that drag force is dependent on projected area, mass density and velocity.

Important points:

C_d values are:

\({{\rm{C}}_{\rm{d}}} = \frac{{24}}{{{{\rm{R}}_{\rm{e}}}}}\)

Explanation:

• A boundary layer is a thin layer of viscous fluid close to the solid surface of a wall in contact with a moving stream in which (within its thickness δ) the flow velocity varies from zero at the wall (where the flow “sticks” to the wall because of its viscosity) up to U∞ (free stream velocity) at the boundary.
• In a flow field, viscous stresses are very prominent within this layer.
• It is defined by Reynold numbers.

Explanation:

streamlined body:

It is defined as the body whose surface coincides with the streamline when the body is placed in the flow. Flow separation takes place only at the trailing edge in such cases.

• The boundary layer in such bodies must be attached to the surface of the body for a long time as possible and hence behind a streamlined body wake formation zone will be very small and consequently, pressure drag will be very small.
• Thus, the total drag on the streamlined body will be due to friction (shear) only.
• A streamlined body is a shape that lowers the friction drag between a fluid, like air and water, and an object moving through that fluid. Drag is a force that slows down motion. Friction drag is a special kind of drag.

Explanation:

Total drag = Pressure drag + Viscous drag

Since given fluid is ideal i.e. it has zero viscosity, so viscous or friction drag is zero.

Since sphere is symmetrical in shape and it is subjected to hydrostatic pressure all around the sphere in such a way that net force or pressure drag is zero.

Hence, total drag is always zero when an ideal fluid past through a sphere.

Important Points

Definition of Ideal Fluid:

An ideal fluid must satisfy the following conditions:

1. Frictionless or inviscid fluid.

2. In compressible

Explanation:

• Flow separation occurs when the boundary layer travels far enough against an adverse pressure gradient that the speed of the boundary layer relative to the object falls almost to zero
• It has been observed that the flow is reversed in the vicinity of the wall under certain conditions

• A favorable pressure gradient is one in which the pressure decreases in the flow direction (i.e., dp/dx < 0)
• It tends to overcome the slowing of fluid particles caused by friction in the boundary layer
• This pressure gradient arises when the freestream velocity U is increasing with x, for example, in the converging flow field in a nozzle
• On the other hand, an adverse pressure gradient is one in which pressure increases in the flow direction (i.e., dp/dx > 0)
• It will cause fluid particles in the boundary-layer to slow down at a greater rate than that due to boundary-layer friction alone
• If the adverse pressure gradient is severe enough, the fluid particles in the boundary layer will actually be brought to rest
• When this occurs, the particles will be forced away from the body surface (a phenomenon called flow separation) as they make room for following particles, ultimately leading to a wake in which flow is turbulent