Università Roma Tre

Physical properties of fluids
• Density and Compressibility
• Vapor pressure
• Viscosity
• Surface tension

Statics of Fluids
• Stress in one point and dependence on position
• Fundamental equation of fluid statics
• Equilibrium of a finite mass of fluid at rest
• Effects of compressibility on the pressure distribution in a fluid at rest subjected to the force of gravity
• Hydrostatic thrust on a flat surface
• Hydrostatic thrust on a curved surface
• Rigid motion of a liquid. Relative balance

Fluid kinematics
• The material derivative
• Reynolds' theorem
• The velocity field around a point

Fluid dynamics
• Mass conservation equation
 Integral form
 Differential form
• Constitutive relationships
• Equation of conservation of momentum
 Integral form
 Differential form
• Euler's equation and its projection on the intrinsic triad
• Conservation of total energy in a non-ideal fluid
• Momentum conservation equation

Applications of Bernoulli's theorem and of the momentum conservation equation in integral form
• Behavior of the piezometric height in the stationary motion of a liquid in a curved axis pipe
• Applications of Bernoulli's theorem
 Outflow from a circular hole on the bottom of a tank
 Outflow from raised rectangular bulkhead on the bottom of a channel
 Outflow from rectangular opening on vertical wall
 Pitot tube
 Venturi tube
• Applications of the momentum conservation equation in integral form
 Thrust exerted by a free jet on a curved blade
 Drag force acting on a body immersed in a uniform current
 Propeller
 Torque acting on the shaft of a hydraulic machine

Uniform and stationary motion in pipes
• Equations of motion
• Time averaging in the turbulent regime
• The laminar regime
• Turbulent regime
• Experimental determination of the drag coefficient
• Concentrated pressure drops

Dimensionless form of the equations of motion

Motions at low Reynolds numbers
• Motion between flat parallel plates
• Hydrodynamic lubrication
• Stationary and uniform motion in a cylindrical tube
• Sphere hit by a uniform current of a viscous fluid
• Motion between concentric cylinders

Boundary layer
• Introduction
• The boundary layer equations
• Boundary layer on flat slab
• Pressure Gradient Effects – Boundary Layer Detachment
• Forces acting on bodies immersed in a uniform current
• Flow around a cylinder as the Reynolds number increases
• Integral equation of the boundary layer

Ideal fluids
• Equations of motion
• Irrotational motion
• 2D irrotational motion
• Uniform motion and source/sink potentials
• Free vortex potential
• Doublet potential
• Flow around a semibody
• Flow around a cylinder
• Force exerted on a body immersed in a uniform current

Compressible fluids
• Regimes of movement
• Stationary isentropic flow of an ideal gas
• Stagnation pressure
• Mass flow flowing in a convergent-divergent (Venturi tube)
• Flow in a convergent-divergent (Venturi tube)
• Stationary flow of an ideal gas in a long tube with constant section
• Normal shock wave

Lecture notes and exercises distributed by the teacher.