JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II FLUID MECHANICS AND HYDRAULIC MACHINERY Previous Question Paper (March - 2021 - R15/R13)

Fluid Kinematics is the branch of fluid mechanics that deals with the motion of fluid particles without considering the forces or energy causing the motion. It focuses on the description of velocity, acceleration, and the pattern of flow (streamlines, pathlines, and streaklines) within a fluid field.

The types of fluid flow are classified as follows:

• Steady and Unsteady flow
• Uniform and Non-uniform flow
• Laminar and Turbulent flow
• Compressible and Incompressible flow
• Rotational and Irrotational flow
• One, Two, and Three-dimensional flow

The continuity equation is based on the principle of conservation of mass, which states that for a steady flow, the mass of fluid entering a control volume must equal the mass of fluid leaving it.

Consider a stream tube with cross-sectional areas A1 and A2 at two sections 1-1 and 2-2, with fluid velocities v1 and v2 and densities ρ1 and ρ2 respectively. The mass flow rate (m) entering at section 1 is:

The mass flow rate leaving at section 2 is:

Since mass is conserved and there is no accumulation within the stream tube, ρ1 A1 v1 = ρ2 A2 v2. For an incompressible fluid, density remains constant (ρ1 = ρ2), simplifying the equation to:

This expression represents the continuity equation, indicating that the discharge (Q) remains constant throughout the flow path.