Lecture 9: Lagrangian and Eulerian approaches; Euler's acceleration formula
Eulerian approach (a field approach)
Identify (or label) a certain fixed location in the flow field and follow change in its property, as different materials pass through that location. In such case, the following property, say temperature is recorded by the sensor :
Note that the recorded temperatures are associated with the fixed location in the flow-fluid, having different fluid elements at different times.
The time- change of the temperature in such a measurement is denoted as which is called the partial derivativeof the temperature with respect to time. Note that the suffix (x,y,z) implies that the observer records the change in the property at the fixed location (x,y,z).
is also called the local rate of change of that property (temperature in this case).