Velocity of a point in a flow: Explanation

The velocity of a point in a flow refers to the speed and direction of movement of the point. It is an important parameter in fluid mechanics and is used to study the behavior of fluids in different applications. The velocity of a point in a flow can be determined by considering the path of the flow and the direction of movement of the point.

Streamline

A streamline is a line that is tangent to the velocity vector at every point. It is a path that a fluid particle would follow as it moves through the flow field. Streamlines are useful in visualizing the flow pattern and understanding the behavior of the fluid.

Tangent to streamline

The velocity of a point in a flow is tangent to the streamline. This means that the direction of the velocity vector is the same as the direction of the tangent to the streamline at that point. The velocity vector is perpendicular to the pressure gradient and is parallel to the streamline.

Pathline

A pathline is the actual path that a fluid particle follows as it moves through the flow field. It is the trajectory of a fluid particle over time. Pathlines can be used to study the behavior of fluid particles and to understand the flow pattern.

Tangent to pathline

The velocity of a point in a flow is not tangent to the pathline. This is because the pathline is the actual path that the fluid particle follows, and the velocity vector is the direction of movement at a given point in time. The direction of the velocity vector can change as the fluid particle moves along its pathline.

Conclusion

In conclusion, the correct answer to the question is option B, which states that the velocity of a point in a flow is tangent to the streamline. This means that the direction of the velocity vector is parallel to the tangent to the streamline at that point. It is important to understand the behavior of the velocity vector in order to study the behavior of fluids in different applications.