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1.4 Basic Laws for Stationary Duct Parts
We first derive some basic laws for an elementary duct part, stationary in an absolute frame. The geometry is less complex than within a turbomachine. Gradually, we
will extend to basic laws that can be applied to turbomachines. Figure 1.4 shows an
elementary part of a duct. The axis of the duct part is denoted by x. The inlet section
A 1 and the outlet section A 2 are perpendicular to this axis. With a one-dimensional
representation, the flow is uniform in sections perpendicular to the axis and flow
quantities only vary in the x-direction. Density is denoted by ρ and pressure by p.
1.4.1 Conservation of Mass
With a steady flow, the mass entering the duct part during a time interval dt, also
leaves it:
(1.1)
1.4.2 Conservation of Momentum
According to Newton’s second law, the change of momentum per time unit of a
system with a constant mass equals the sum of the applied forces. We consider the
system with constant mass in the duct part at the time t. At time t + dt, the system has
moved as shown in Fig. 1.4. The momentum change during the time interval dt is
,
2 2 2
1 1 1
A v dt
A v dt
r
r
=
or
constant (mass flow rate).
m
v A
r
=
=
Fig. 1.4 Elementary duct part for mass and momentum balances
1.4 Basic Laws for Stationary Duct Parts