Hydraulics/Fluid Mechanics a.y. 2020-2021
CONSERVATION LAWS IN FLUID MECHANICS
Prof. Stefania Espa
DICEA-SAPIENZA UNIVERSITY OF ROME
CIVIL AND INDUSTRIAL ENGINEERING
BATCHELOR IN SUSTAINABLE BUILDING ENGINEERING
RIETI
All images uploaded are for educational purposes
,1-CONSERVATION LAWS: Introduction
Fluid mechanics is based on the conservation laws for mass, momentum, and
energy. These laws can be written in two forms:
the differential form applicable at a point
&
the integral form applicable to an extended region.
The objectives of this section will be:
• Definition of system, control volume and material volume; Reynolds
transport theorem
• Derivation of differential (local) and integral (global) derivation of the
conservation of mass, momentum and energy
• Constitutive laws for Newtonian fluids
• Navier-Stokes equations
• Euler equation (inviscid flows)
, 1-CONSERVATION LAWS: systems, control volumes and material volumes
A system is defined as a quantity of matter or a region in space chosen for
study. The mass or region outside the system is called the surroundings.
The surface that separates the system from its surroundings is called the
boundary (it can be fixed or movable):
Systems may be considered to be closed or open, depending on whether a
fixed mass or a volume in space is chosen for study. A closed system consists of
a fixed amount of mass, mass can not cross its boundary. Energy (in the form
of heat or work) can cross the boundary, also the volume of a closed system
does not have to be fixed. If, as a special case, even energy is not allowed to
cross the boundary, that system is defined as an isolate system.
CONSERVATION LAWS IN FLUID MECHANICS
Prof. Stefania Espa
DICEA-SAPIENZA UNIVERSITY OF ROME
CIVIL AND INDUSTRIAL ENGINEERING
BATCHELOR IN SUSTAINABLE BUILDING ENGINEERING
RIETI
All images uploaded are for educational purposes
,1-CONSERVATION LAWS: Introduction
Fluid mechanics is based on the conservation laws for mass, momentum, and
energy. These laws can be written in two forms:
the differential form applicable at a point
&
the integral form applicable to an extended region.
The objectives of this section will be:
• Definition of system, control volume and material volume; Reynolds
transport theorem
• Derivation of differential (local) and integral (global) derivation of the
conservation of mass, momentum and energy
• Constitutive laws for Newtonian fluids
• Navier-Stokes equations
• Euler equation (inviscid flows)
, 1-CONSERVATION LAWS: systems, control volumes and material volumes
A system is defined as a quantity of matter or a region in space chosen for
study. The mass or region outside the system is called the surroundings.
The surface that separates the system from its surroundings is called the
boundary (it can be fixed or movable):
Systems may be considered to be closed or open, depending on whether a
fixed mass or a volume in space is chosen for study. A closed system consists of
a fixed amount of mass, mass can not cross its boundary. Energy (in the form
of heat or work) can cross the boundary, also the volume of a closed system
does not have to be fixed. If, as a special case, even energy is not allowed to
cross the boundary, that system is defined as an isolate system.
