Streamlines and Equipotential Lines in a Flow Field

Streamlines and equipotential lines are commonly used in fluid mechanics to analyze and visualize the flow patterns in a flow field. Streamlines represent the paths followed by fluid particles in the flow, while equipotential lines represent regions of equal potential in the flow. In a flow field, these lines can have different relationships with each other.

Parallel Streamlines and Equipotential Lines

If the streamlines and equipotential lines are parallel, it means that they never intersect each other and maintain a constant distance. This scenario implies that the flow field is uniform and there is no change in velocity or potential in any direction. However, in most flow fields, this condition is not met.

Streamlines and Equipotential Lines Cutting at any Angle

In some flow fields, the streamlines and equipotential lines can intersect each other at various angles. This occurs when there is a change in velocity or potential in different directions. Examples of such flow fields include flow around a cylinder or flow over an airfoil. The angle at which the lines intersect indicates the direction and magnitude of the change in velocity or potential.

Orthogonal Streamlines and Equipotential Lines

When the streamlines and equipotential lines are orthogonal everywhere in the flow field, it means that they intersect each other at right angles. This condition occurs in potential flow fields, where the flow is irrotational and incompressible. In such flow fields, the streamlines represent the flow direction, and the equipotential lines represent the pressure distribution.

Cutting Orthogonally at Stagnation Points

However, at stagnation points, the streamlines and equipotential lines do not cut each other orthogonally. Stagnation points are locations in the flow field where the velocity of the fluid becomes zero, typically due to the presence of an obstacle or a sudden change in the flow geometry. At these points, the equipotential lines become tangent to the obstacle, and the streamlines bend around it. As a result, the streamlines and equipotential lines do not intersect each other at right angles at stagnation points.

Therefore, the correct answer is option 'D', which states that the streamlines and equipotential lines cut orthogonally everywhere in the flow field except at the stagnation points.