In a centrifugual pump casing, the flow of water leaving the impeller, is

ANS:C - free vortex motion

Free vortex motion refers to a specific type of fluid flow pattern in which the fluid particles rotate about a central axis without any radial or tangential acceleration or deceleration. In a free vortex, the velocity of the fluid particles at any given radius remains constant. Here's an explanation of the key characteristics of free vortex motion:

1. Rotation About a Central Axis: In a free vortex, the fluid particles rotate around a central axis, similar to water swirling down a drain or a tornado rotating about its center. This rotation occurs due to the conservation of angular momentum, where the angular velocity of the fluid particles is inversely proportional to their radial distance from the center.
2. Constant Angular Velocity: In a free vortex, the angular velocity of the fluid particles remains constant at any given radius from the center. This means that fluid particles farther from the center rotate more slowly than those closer to the center.
3. No Radial or Tangential Acceleration: In a free vortex, there is no radial or tangential acceleration or deceleration of the fluid particles. The velocity of the fluid particles remains constant in both the radial and tangential directions.
4. Conservation of Angular Momentum: The conservation of angular momentum governs the behavior of fluid particles in a free vortex. As the fluid rotates, the angular momentum of the fluid particles remains constant unless acted upon by external forces.

Free vortex motion is an idealized concept and is rarely encountered in real-world fluid flow situations. It provides a simplified model for understanding certain aspects of fluid dynamics, such as the behavior of rotating flows and the principles of conservation of angular momentum. In practical applications, deviations from free vortex motion occur due to factors such as friction, viscosity, and external forces, which can cause changes in the fluid flow pattern. However, the concept of free vortex motion remains a valuable tool for understanding fundamental principles in fluid mechanics and for analyzing certain flow phenomena.