fluid kinematics streamlines laminar turbulent flow continuity equation - One Line Questions

1. The continuity equation in its differential form for a steady, incompressible flow is: — ∂u/∂x + ∂v/∂y + ∂w/∂z = 0
2. If the flow is unsteady, the continuity equation in differential form becomes: — ∂u/∂x + ∂v/∂y + ∂w/∂z = -∂ρ/∂t
3. For a 2D, steady, incompressible flow, the continuity equation simplifies to: — ∂u/∂x + ∂v/∂y = 0
4. The condition for the existence of a velocity potential function for an incompressible flow is: — ∇ × V = 0 (irrotational)
5. The critical Reynolds number for flow in a pipe is approximately: — 2300
6. What is a streamtube (or stream filament)? — A bundle of adjacent streamlines
7. For one-dimensional, steady flow of an incompressible fluid, the continuity equation can be expressed as: — A1*V1 = A2*V2
8. In the continuity equation A1*V1 = A2*V2 for incompressible flow, A represents: — Area of the flow cross-section
9. For a fluid flow to be classified as 'steady', the velocity at any given point must: — Be constant over time
10. Which equation relates velocity components and their derivatives for a steady, incompressible flow? — Continuity Equation
11. The stream function, ψ, is defined for which type of flow in two dimensions? — Incompressible flow (rotational or irrotational)
12. The condition ∂u/∂x + ∂v/∂y + ∂w/∂z = 0 is the mathematical representation of the continuity equation for: — Incompressible flow
13. Consider flow through a converging nozzle. If the fluid is incompressible and the flow is steady, what happens to the flow velocity as the area decreases? — Increases
14. The continuity equation in its general form for a control volume is based on the principle that: — Mass is conserved
15. What is a potential flow? — Flow that is irrotational and inviscid
16. In a streamtube, the flow is such that: — No fluid can cross the boundary of the streamtube
17. An irrotational flow is one where: — The vorticity is zero
18. In fluid kinematics, a rotational flow is one where: — Fluid elements rotate about their own axes
19. The term 'kinematics' in fluid kinematics refers to the study of: — Motion and its description
20. The ratio of inertial forces to viscous forces in a fluid flow is represented by which dimensionless number? — Reynolds Number
21. If the cross-sectional area of a pipe carrying an incompressible fluid decreases, what happens to the velocity of the fluid, assuming steady flow? — It increases
22. A streamline is defined as a line drawn in a fluid such that: — It is always parallel to the velocity vector of the fluid particle passing through it
23. What is the physical significance of the difference in stream function values between two streamlines? — It represents the volume flow rate per unit width between the streamlines
24. Which type of flow is typically observed at high velocities or in low viscosity fluids? — Turbulent flow
25. A high Reynolds number generally indicates: — Turbulent flow
26. Which flow regime is characterized by the absence of significant viscous effects and fluid compressibility? — Potential flow
27. The continuity equation is a statement of the principle of: — Mass conservation
28. In the differential form of the continuity equation (∂u/∂x + ∂v/∂y + ∂w/∂z = 0), u, v, and w represent: — Velocity components in x, y, and z directions
29. Laminar flow is characterized by: — Smooth, orderly fluid motion in layers
30. The velocity potential function, Φ, exists for which type of flow? — Irrotational flow only
31. Turbulent flow is characterized by: — Irregular, chaotic motion with eddies and mixing
32. Which of the following is a characteristic of turbulent flow that is generally absent in laminar flow? — Eddy formation and significant mixing
33. In turbulent flow, the velocity at any point fluctuates: — Randomly and chaotically
34. The Reynolds number is a dimensionless quantity used to predict the transition between which two types of flow? — Laminar and turbulent flow
35. Which of the following is a path traced by a single fluid particle over time? — Pathline
36. Which type of line shows the instantaneous positions of all fluid particles that have passed through a given point over a period of time? — Streakline
37. In steady flow, which of the following is true? — Streamlines, pathlines, and streaklines are identical
38. For a 2D incompressible flow, if u = 2x and v = -2y, what is the continuity equation's implication? — The flow satisfies continuity (∂u/∂x + ∂v/∂y = 0)
39. What does fluid kinematics primarily study? — The motion of fluids without considering the forces causing motion
40. In the context of fluid kinematics, a 'streakline' is: — The locus of points of all particles that have passed through a fixed point
41. In a steady flow, the difference in the stream function between two adjacent streamlines represents: — The volume flow rate per unit depth between the streamlines
42. The concept of streamlines is most useful for visualizing: — The direction of fluid velocity at any point
43. Flow in a very wide and shallow channel with a low velocity is likely to be: — Laminar
44. Which type of flow is typically observed at very low velocities or in highly viscous fluids? —
45. A low Reynolds number generally indicates: — Laminar flow
46. For a 2D incompressible flow, the relationship between the stream function (ψ) and velocity components (u, v) is given by: — u = ∂ψ/∂y, v = -∂ψ/∂x
47. Which of the following is NOT a primary characteristic used to describe fluid motion in kinematics? — Pressure
48. Which of the following is a consequence of the continuity equation for incompressible flow? — If area decreases, velocity must increase
49. The continuity equation in integral form for steady flow states that the net rate of mass flow across a control surface is: — Zero
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