Fundamentals of Fluid Kinematics

Define a streamline as a line tangent to the velocity vector at every point, with no normal flow, yielding dx/u = dy/v = dz/w that traces fluid motion.

Explore pathline, streakline, and timeline concepts in fluid kinematics, showing how a particle's actual path, a fixed-point streak, and an instantaneous particle set relate, especially in steady flow.

Explore discharge (Q) by linking volume per time to cross-sectional area and velocity, showing that discharge equals area times velocity and that flow velocity is perpendicular to the flow area.

Explore the one-dimensional steady flow in a control volume, applying mass conservation to show that discharge at entry equals discharge at exit for incompressible fluids, using density and cross-sectional area.

learn how the generalised continuity equation describes steady and incompressible flow, showing that for incompressible fluids density is constant and the velocity divergence equals zero, with two-dimensional assumptions.

Examine the total derivative of the velocity field, its convective and local accelerations, and apply steady, incompressible flow to the continuity equation.

Analyze fluid element deformation and rotation during opposite and same direction axis rotations, revealing deformation and rotation phenomena in fluid flow, and derive angular deformation rates.

Explain vorticity as a vector that measures rotation and circulation as the macroscopic rotation around a closed loop, linking them to surface area and noting zero vorticity.

Vorticity is a vector quantity that measures rotation, while circulation is the line integral of velocity around a closed loop, with vorticity equal to circulation divided by the area.

The velocity potential function is a continuous scalar of space, and velocity components equal the negative partial derivatives with respect to x and y, indicating flow toward decreasing potential.

Explore the two-dimensional stream function and its role in steady flow, distinguishing irrotational and rotational fields, and deriving the streamline equations and discharge between streamlines.

Derive the relation between equipotential lines and streamlines, showing that their slopes multiply to minus one, proving their orthogonality except at stagnation points.