In this lecture we discuss steady state/unsteady state condition for velocity fields.
Steady state
The steady state condition for a flow-field implies that the velocity field and any property associated with the flow field remain unchanged with time. In other words, local derivative of the velocity is zero.
Mathematically, 0. The concentration and temperature fields, if associated will also be under steady–state:
As explained below, may or may not be zero.
Consider the flow of a fluid through a convergent nozzle. If the velocity field is steady, or the flow–field is under steady-state conditions, . However, an observer moving with the flow field will experience ‘acceleration' as he moves from the larger diameter-section to the smaller diameter-section of the nozzle. This is because the velocity increases as the diameter of the nozzle decreases. Therefore, velocity remains unchanged with time anywhere in the flow- field. However, it has a spatial variation, or
(Fig. 10a)
, , (between 1-2)
The last expression is tantamount to saying that the velocity of a labeled or marked material-particle is not constant, as it moves from the larger section to the smaller section of the nozzle.
0. The concentration and temperature fields, if associated will also be under steady–state: 
may or may not be zero. 
. However, an observer moving with the flow field will experience ‘acceleration' as he moves from the larger diameter-section to the smaller diameter-section of the nozzle. This is because the velocity increases as the diameter of the nozzle decreases. Therefore, velocity remains unchanged with time anywhere in the flow- field. However, it has a spatial variation, or 
, 
, 
(between 1-2) 
