Conservation laws Flashcards
system approach
The word system refers to a fixed quantity of mass with a boundary. However,
with time the boundary of the system may change, but the mass remains the
same (no mass crosses system boundaries). Focus on particles
Control volume approach
An arbitrary volume in space through which fluid flows.
Like a “window” for observation in the flow
Flow may cross boundaries
Mass flow rate
The amount of mass flowing through a cross section per unit time
Volume flow rate
The volume of the fluid flowing through a cross section per unit time
Volume flow rate for incompressible fluids
For incompressible fluids, ρ=constant, the volume flow rate INTO a fixed
control volume is equal to the volume flow rate OUT of the control volume
Mass Flow rate for steady, compressible flows
ρ=ρ(x,y,z) and by definition of steady flow no
fluid property varies with time. the mass flow rate INTO a fixed control volume is equal to the
mass flow flow rate OUT of the control volume
For uniform velocities, how can the continuity equation be simplified?
If the velocity can be considered uniform across the cross section, or if
we can use an average velocity in the cross section, then we can replace
the integral with the sum
What is a streamline?
A streamline is a curve that is everywhere tangent to the
instantaneous local velocity vector
What is the bernoulli equation
The Bernoulli equation is usefull approximate relation between pressure, velocity
and elevation in regions of steady, incompressible flow, where viscous forces can be
neglected.
The Bernoulli equation states that during steady, incompressible flow with negligible
friction, the various forms of mechanical energy (kinetic, potential and flow) are
converted to each other, but their sum remains constant
Elevation head
Gravitational potential
energy, z
Pressure head
Flow work, P/γ
Velocity head
Kinetic energy, V^2/2g
Real fluids
Take into account for the effects due to fluid viscosity, μ!
During fluid motion, viscosity generates shear
stresses,τ0, which tend to resist to flow.
Their work is associated with dissipation of mechanical
energy which is converted in thermal form
Modified Bernoulli equation for real fluids
H(s) = H0- deltaH
The momentum equation is based on newtons second law. What does it say? (oklart svar, ändra!)
The sum of all external forces acting on the system is equal to the time rate of
change of linear momentum of the system
