Objective Questions

Objective Questions

1. Velocity components in x and y directions are given by \(u=ay\) and \(v=bx\) for a potential flow. In this flow, the streamlines represent:

a family of straight lines.

a family of circles.

a family of parabolas.

a family of hyperbolas.

2. Superposition of the stream functions of a uniform flow and a line source in a potential flow generates a dividing streamline called as ____

A

B

C

D

3. For a flow, if the potential function is given by \(\phi = k\theta\), where \(k\) is an arbitrary constant. The stream function of the flow will be given by

\(\frac{k}{r}\)

\(\frac{k}{\ln{r}}\)

\(k \ln{r}\)

\(k \ln{\theta}\)

4. Since the curl of the gradient of a scalar is always vanished and thus for a fluid flow the velocity field can be represented as the gradient of a scalar function \(\phi\) known as the velocity potential \(u = \nabla \phi\). Which of the following is TRUE?

\(\nabla u = 0\)

\(∇ \times u = 0\)

\(∇^2 \phi = 0\)

all the above

5. The length and radius of the line source are 50 and 5 mm, respectively. For the line source, if the radial velocity is \(5\,m/s\) the volume flow rate will be

\(3.25 \times 10^{−3}\,m^3 s^{−1}\)

\(5.35 \times 10^{−3}\,m^3 s^{−1}\)

\(7.85 \times 10^{−3}\,m^3 s^{−1}\)

\(9.75 \times 10^{−3}\,m^3 s^{−1}\)

6. For a two-dimensional irrotational flow, which of the following relation is correct?

\(\frac{\partial v}{\partial x} + \frac{\partial u}{\partial y} = 0\)

\(\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} = 0\)

\(\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0\)

\(\frac{\partial u}{\partial x} - \frac{\partial v}{\partial y} = 0\)

7. The inherent feature of the free vortex flow streamlines is

concentric

sinusoidal

non-concentric

linear

8. The characteristic of ideal fluid flow will not be satisfied by

sink

uniform flow

superimposition of elementary flows

forced vortex

9. The stream function (\(\psi\)) for a doublet flow is given by

\(\frac{k}{2\pi}\frac{\sin{\theta}}{r}\)

\(-\frac{k}{2\pi}\frac{\sin{\theta}}{r}\)

\(\frac{2\pi}{k}\frac{\sin{\theta}}{r}\)

\(\frac{k}{4\pi}\frac{\sin{\theta}}{r}\)

10. The solutions of the Laplace’s equation are termed as

Harmonic functions

Laplacian functions

higher order functions

Exponential functions

11. Given an arbitrary function (which is smooth enough) \(\phi(x,y)\) and the associated velocity vector field \(\bar{U} = \nabla \phi\). The velocity field:

satisfies conservation of mass for an incompressible flow

is irrotational

both of the above

none of the above

12. Given two potentials \(\phi_1\) and \(\phi_2\), and the associated velocity vector fields, \(\bar{U}_1 = \nabla \phi_1\) and \(\bar{U}_2 = \nabla \phi_2\), we add the potentials to find a new potential \(\phi_3 = \phi_1 + \phi_2\). Assuming an inviscid, incompressible flow:

\(p3 = p1 + p_2\)

\(\bar{U}3 = \bar{U}1 + \bar{U}_2\)

both of the above

none of the above

13. In a 2D incompressible, inviscid flow with a uniform freestream, which of the following is true regarding drag over the bodies? (c - cylinder, a - airfoil)

\(D_{c} > D_{a}\)

\(D_{c} < D_{a}\)

\(D_{c} = D_{a}\)

not enough information

14. Assuming 2D, incompressible, steady potential flow around an airfoil, which is true:

if \(L' = \rho U_\infty \Gamma\), then the Kutta condition must be satisfied.

if the lift is non-zero, then the Kutta condition must be satisfied.

both of the above

none of the above

15. Which of the lines are not from the thin airfoil theory in the following diagram? ANSWER TO BE SET.

A1 and A3

A1 and A2

A2 and A3

A1

A2

A3

all the above

none of the above

16. According to thin airfoil theory for a cambered airfoil, which is true:

\(M_{c/4}\) is zero when the lift is zero

\(M_{c/4}\) is constant with respect to angle of attack

both of the above

none of the above

17. It is known that the \(C_L-\alpha\) plot for airfoil A1 is calculated using thin airfoil theory. Identify all the correct statements. ANSWER TO BE GIVEN.

\(C_L-\alpha\) plot for airfoil A2 may also have been calculated using thin airfoil theory

\(C_L-\alpha\) plot for airfoil A3 may also have been calculated using thin airfoil theory

\(C_L-\alpha\) plot for airfoil A4 may also have been calculated using thin airfoil theory

\(C_L-\alpha\) plot for airfoil A3 is definitely not calculated using thin airfoil theory

Airfoil A1 is a symmetric airfoil

Airfoil A3 has a positive camber

For airfoil A4, the moment at c/4 is constant with respect to angle of attack

Not enough information (please explain your reasons if you choose this.

18. Which is most likely true:

\(p_{edge} < p_{wall}\)

\(p_{edge} > p_{wall}\)

\(p_{edge} \approx p_{wall}\)

Not enough information (please explain your reasons if you choose this.)

19. Consider the motion of two fluid elements:

20. Which of these fluid element motions could be from an incompressible flow:

a

b

both

neither

not enough information

21. An irrotational flow is always incompressible.

True

False

Cannot say

22. Coefficient of friction (\(C_f\)) for laminar boundary layer is smaller than the turbulent boundary layer.

True

False

Insufficient information

23. Aircraft are flying in the following formation at low subsonic speeds. Only consider the vorticity generated by aircraft A.

Aircraft B will experience upwash

Aircraft B will experience downwash

Aircraft C will experience upwash

Aircraft C will experience downwash

Aircraft D will experience upwash

Aircraft D will experience downwash

24. For an asymmetric airfoil, thin airfoil theory states that

center of pressure is at \(c/4\)

aerodynamic center is at \(c/4\)

both are at \(c/4\)

neither are at \(c/4\)

Aerodynamic center is at \(c/4\). But cp can be anywhere.

25. If two rectilinear vortices (pointing in different directions) cross each other at a point

They must be of same strength

They can be of different strength

This cannot happen

Insufficient information

26. For a 3D incompressible flow, which is true:

If \(L = 0\) then \(D = 0\).

If \(D = 0\) then \(L = 0\).

If \(L \neq 0\) then \(D \neq 0\).

All the above

27. Vorticity on a rectilinear line vortex is

some finite value

infinite

Cannot say

28. Vorticity is well defined at every point in a vortex sheet

True

False

29. Parasite Drag =

Skin friction drag + induced drag

Skin friction drag + pressure drag

induced drag + pressure drag

induced drag + pressure drag + skin friction drag

30. Sectional lift (2D \(L'\)) is constant along the span of an elliptical wing

True

False

31. For the coefficient of induced drag (\(C_{D_i}\)) of a wing, which of the following statement is true? \(\alpha\) denotes the wing angle of attack.

\(C{Di} \propto \alpha\)

\(C{Di} \propto \alpha^2\)

\(C{Di} \propto \frac{1}{\alpha}\)

\(C{Di} \propto \frac{1}{\alpha^2}\)

32. For a symmetric airfoil modelled using thin airfoil theory, location of aerodynamic center changes with angle of attack.

True

False

Insufficient information

33. Assuming Prandtl’s lifting line in being applied: The span efficiency factor (\(e\)) does not change with angle of attack.

True

False

Insufficient information

34. Kelvin’s circulation theorem is true for:

an incompressible flow

an irrotational flow

a barotropic flow

none of the above

All of the above

35. Which one among these represents an potential flow?

An unsteady, Inviscid, isentropic compressible flow in a nozzle

A steady viscous flow

Incompressible flow over a 2D circular cylinder

All of these