Programme

Physical Properties of Fluids
• Density and Compressibility
• Vapor Pressure
• Viscosity
• Surface Tension

Fluid Statics
• Stress at a point and its dependence on orientation
• 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 subject to gravitational force
• Hydrostatic thrust on a plane surface
• Hydrostatic thrust on a curved surface
• Rigid-body motion of a liquid Relative equilibrium

Fluid kinematics
• Material derivative
• Reynolds transport theorem
• Velocity field in the neighborhood of a point

Fluid dynamics
• Conservation of mass equation
 Integral form
 Differential form
• Constitutive relations
• Conservation of momentum equation
 Integral form
 Differential form
• Euler’s equation and its projection onto the intrinsic coordinate system
• Conservation of total energy in a non-ideal fluid
• Conservation of angular momentum equation

Applications of Bernoulli’s theorem and the integral form of the momentum conservation equation
• Behavior of the piezometric head during the steady flow of a liquid in a curved-axis pipe
• Applications of Bernoulli’s theorem
 Efflux from a circular orifice at the bottom of a reservoir
 Efflux from a raised rectangular sluice gate at the bottom of a channel
 Efflux from a rectangular opening in a vertical wall
 Pitot tube
 Venturi tube
• Applications of the integral form of the momentum conservation equation
 Force exerted by a free jet on a curved vane
 Drag force acting on a body immersed in a uniform flow
 Propeller
 Torque acting on the shaft of a hydraulic machine

Uniform and steady flow in pipes
• Equations of motion
• Time averages in turbulent flow
• Laminar flow
• Turbulent flow
• Experimental determination of the resistance coefficient
• Minor (concentrated) head losses

Dimensionless form of the equations of motion

Flows at low Reynolds numbers
• Flow between parallel flat plates
• Hydrodynamic lubrication
• Steady, uniform flow in a cylindrical pipe
• Sphere in a uniform flow of a viscous fluid
• Flow between concentric cylinders

Boundary Layer
• Introduction
• Boundary layer equations
• Boundary layer on a flat plate
• Effects of pressure gradient – ​​Boundary layer separation
• Forces acting on bodies immersed in a uniform flow
• Flow around a cylinder as the Reynolds number increases
• Integral equation of the boundary layer

Ideal Fluids
• Equations of motion
• Irrotational flow
• 2D irrotational flow
• Potentials for uniform flow and source/sink
• Free vortex potential
• Doublet potential
• Flow around a semi-infinite body
• Flow around a cylinder
• Force exerted on a body immersed in a uniform flow

Compressible Fluids
• Flow regimes
• Steady isentropic flow of an ideal gas
• Stagnation pressure
• Mass flow rate through a convergent-divergent duct (Venturi tube)
• Flow through a convergent-divergent duct (Venturi tube)
• Steady flow of an ideal gas in a long pipe of constant cross-section
• Normal shock wave

Prerequisiti

Algebra, Trigonometry, Geometry, Mathematical Analysis, Physics

Core Documentation

Lecture notes given by the instructor

Attendance

Strongly recommended

Type of evaluation

There are two options: a) Three partial exams held during the course, each consisting of two exercises and one open-ended question. If these are passed, the final assessment is positive and is calculated as the arithmetic mean of the grades obtained in the three tests. b) A written exam consisting of three exercises, followed by an oral exam—for which passing the written exam is a prerequisite—involving a topic chosen by the instructor, which the student must then explain.