Question

The following statements are about the laminar boundary layer over a flat plate. For each statement, answer whether the statement is true or false.
1. At a given x-location, if the Reynolds number were to increase, the boundary layer thickness would also increase.
A. True B. False
2. As outer flow velocity increases, so does the boundary layer thickness.
A. True B. False
3. As the fluid viscosity increases, so does the boundary layer thickness.
A. True B. False
4. As the fluid density increases, so does the boundary layer thickness.
A. True B. False
5. The boundary layer equations are approximations of the Navier-Stokes equation.
A. True B. False
6. The curve representing boundary layer thickness as function of x is a streamline.
A. True B. False
7. The boundary layer approximation bridges the gap between the Euler equation and the Navier-Stokes equation.
A. True B. False

Answer 1

Answer:

1. B. False

2.  B. False

3. A. True

4. B. False

5. A. True

6. A. True

7. A. True

Explanation:

1. B. False

The relation of Reynolds' number, Reₓ to boundary layer thickness δ at a point x is given by the relation

$\delta = \dfrac{x \times C}{\sqrt{Re_x} }$

That is the boundary layer thickness is inversely proportional to the square root of the Reynolds' number so that if the Reynolds' number were to increase, the boundary layer thickness would decrease

Therefore, the correct option is B. False

2.  B. False

From the relation

$Re_x = \dfrac{U_o \times x}{v}$

As the outer flow velocity increases, the boundary layer thickness diminishes

3. A. True

As the viscous force is increased the boundary layer thickness increases

4. B. False

Boundary layer thickness is inversely proportional to velocity

5. A. True

The boundary layer model developed by Ludwig Prandtl is a special case of the Navier-Stokes equation

6. A. True

Given a definite boundary layer thickness, the curve representing the boundary layer thickness is a streamline

7. A. True

The boundary layer approximation by Prandtl Euler bridges the gap between the Euler (slip boundary conditions) and Navier-Stokes (no slip boundary conditions) equations.