Hydraulics/Fluid Mechanics a.y. 2020-2021
CONSERVATION LAWS IN FLUID MECHANICS:
EULER’S EQUATION
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
,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)
, CONSERVATION LAWS: differential form of the momentum equation
Now we want to solve a differential equations to estimate the velocity field or
the pressure field in an incompressible flow of interest : the unknowns are the
three velocity components and the pressure.
We then need four equation : the continuity equation and the three scalar
equations of the momentum equation.
To derive the differential momentum equation, we consider the forces acting
on an infinitesimal cube (already seen for the static case) and we apply the
Newton’s second law. Remember the notion of stress (normal, s, and
tangential, t)
CONSERVATION LAWS IN FLUID MECHANICS:
EULER’S EQUATION
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
,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)
, CONSERVATION LAWS: differential form of the momentum equation
Now we want to solve a differential equations to estimate the velocity field or
the pressure field in an incompressible flow of interest : the unknowns are the
three velocity components and the pressure.
We then need four equation : the continuity equation and the three scalar
equations of the momentum equation.
To derive the differential momentum equation, we consider the forces acting
on an infinitesimal cube (already seen for the static case) and we apply the
Newton’s second law. Remember the notion of stress (normal, s, and
tangential, t)
