Fluid Kinematics

Fluid kinematics deals with the geometry of motion: velocity, acceleration, and flow patterns, without considering the forces causing the motion.

Types of Flow

• Steady Flow: Properties (velocity, pressure) at a point do not change with time ($\partial V/\partial t = 0$).
• Unsteady Flow: Properties change with time.
• Uniform Flow: Velocity vector is constant along a streamline ($\partial V/\partial s = 0$).
• Non-Uniform Flow: Velocity changes along a streamline.
• Laminar Flow: Fluid particles move in smooth layers; viscous forces dominate.
• Turbulent Flow: Fluid particles move erratically; inertial forces dominate.

Continuity Equation

The continuity equation is based on the principle of Conservation of Mass. For a control volume:

$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{V}) = 0$

For Steady, Incompressible Flow (constant $\rho$): Flow rate in = Flow rate out

$Q = A_1 V_1 = A_2 V_2$

• $Q$ = Discharge (Volume flow rate) [$m^3/s$]
• $A$ = Cross-sectional area [$m^2$]
• $V$ = Average velocity [$m/s$]

Flow Nets

A flow net is a grid of streamlines and equipotential lines (lines of constant head) used to visualize flow in 2D.

• Streamlines are tangent to the velocity vector.
• There is no flow across a streamline.

Solved Problems