Questions: 90. Which of the following is true? A) A streamline can only be defined for irrotational flow. B) A streamline cannot be defined for turbulent flow. C) Streamlines cannot cross in laminar flow, but can cross in turbulent flow. D) A streamline is the path that a tiny element of fluid would take as the fluid flows. E) The velocity vector of a fluid element is always perpendicular to the streamline.

Solution Steps

Let's analyze each option to determine which one is true:

• Option A: "A streamline can only be defined for irrotational flow."
  This statement is false. Streamlines can be defined for both rotational and irrotational flows. They represent the direction of the flow at any given point and are not limited to irrotational flows.

• Option B: "A streamline cannot be defined for turbulent flow."
  This statement is false. Streamlines can be defined for turbulent flow, but they may be more complex and change rapidly over time.

• Option C: "Streamlines cannot cross in laminar flow, but can cross in turbulent flow."
  This statement is false. Streamlines cannot cross in either laminar or turbulent flow. If they were to cross, it would imply two different velocities at a single point, which is not possible.

• Option D: "A streamline is the path that a tiny element of fluid would take as the fluid flows."
  This statement is false. A streamline represents the direction of the flow at a given instant, but it is not necessarily the path a fluid element would take over time. The path a fluid element takes is called a pathline.

• Option E: "The velocity vector of a fluid element is always perpendicular to the streamline."
  This statement is false. The velocity vector of a fluid element is always tangent to the streamline, not perpendicular.

After analyzing each option, none of the statements are true as they are all based on incorrect interpretations of streamlines.

Final Answer