# Computational Fluid Dynamics Questions and Answers – Turbulent Boundary Layer

This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Turbulent Boundary Layer”.

1. For flows over a flat plate, at length scales near to the length of the flat plate, which of these is correct?
a) Inertial force is zero
b) Inertial force is large
c) Inertial force is equal to viscous force
d) Viscous force is large

Explanation: Reynolds number depends on the length scale taken for the calculation. At the length scales near to that of the length of the flat plate, the Reynolds number will be high. Therefore, the inertial forces will be large.

2. Which of these statements is correct?
a) Inertia forces dominate in the flow far from the wall
b) Viscous forces dominate in the flow far from the wall
c) Inertia forces are small in the flow far from the wall
d) Viscous forces are large in the flow near the wall

Explanation: As the flow of a fluid near the wall moves away from the wall, the Reynolds number of the flow increases accounting to the increase in the distance. This leads to high inertial forces and low viscous forces.

3. Which of these laws define the dimensionless quantities u+ and y+?
a) Velocity-defect law
b) Log-law
c) Newton’s law of viscosity
d) Law of the wall

Explanation: The law of the wall is the relationship between the mean flow velocity and the distance from the wall derived using dimensional analysis. This gives the relationship between two important dimensionless quantities u+ and y+.

4. What is u+?
a) The ratio of velocity parallel to the wall to the friction velocity
b) The ratio of the friction velocity to velocity parallel to the wall
c) The ratio of free-stream velocity and friction velocity
d) The ratio of friction velocity and free-stream velocity

Explanation: u+ is the dimensionless velocity. It is defined as the ratio of the velocity of fluid particle parallel to the wall at a particular distance from the wall to the friction velocity. Friction velocity is the square root of the ratio of shear stress to the density of fluid.

5. The velocity at a point far away from the wall is defined by ____________
a) Power law
b) Log-law
c) Velocity-defect law
d) Newton’s law of viscosity

Explanation: Far away from the wall the fluid flow is retarded by the wall shear stress. The velocity (U) at such a point is defined as
$$\frac{U_{max}-U}{u_\tau} =function(\frac{y}{\delta})$$
This is called velocity-defect law.
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6. The fluid layer which is in contact with a smooth wall is called ____________
a) Inviscid layer
b) Linear sub-layer
c) Log-law layer
d) Wake-law layer

Explanation: In the fluid layer which is in contact with a smooth wall, the value of dimensionless velocity and dimensionless cross-stream distance tend to be the same. Because of this linear relationship, the layer is named linear sub-layer.

7. What is the range of y+ in the viscous sub-layer?
a) 0<y+<20
b) 0<y+<5
c) 0<y+<10
d) 0<y+<15

Explanation: This is the layer which is in immediate contact with the smooth wall. It obeys Newton’s law of viscosity. The shear stress in this layer is constant and approximately equal to that of the wall. It extends from the wall till y+ reaches 5.

8. The layer with viscous and turbulent stresses in equal magnitude is called _____________
a) Viscous sub-layer
b) Log-law layer
c) Buffer layer
d) Velocity-defect layer

Explanation: The layer above the linear sub-layer has equally important turbulent and viscous stresses. Neither of these is dominating nor inconsiderable. A layer in this area where both the viscous and turbulent stresses are of equal magnitude is called the buffer layer.

9. What is the other name of the velocity-defect law?
a) Linear law
b) Log law
c) Law of the wall
d) Law of the wake

Explanation: Velocity defect law is applicable to the layer far away from the wall. This layer has less viscous effects and inertia forces are dominating here. The velocity-defect law is otherwise called the law of the wake.

10. What is the range of y+ in the log-law layer?
a) 30<y+<500
b) 20<y+<500
c) 30<y+<400
d) 20<y+<400

Explanation: The log-law layer extends outside the viscous or linear sub-layer. Here, both viscous and turbulent effects are important. It ranges between 30<y+<500. It is called log-law layer because of the logarithmic relationship between u+ and y+.

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