Pascal's law in Fluid mechanics Can we apply pascals law for accelerating fluids? If, yes then why.
In a hydraulic lift, when pressure is applied at one end, the liquid in the tube accelerates so how can Pascal's law still valid?
 A: No, Pascal's Law is strictly speaking not valid for accelerating fluids as acceleration introduces inertial forces the law doesn't account for. The pressure at the bottom of a barrel that accelerates upwards (e.g.) would be higher than for an identical barrel that does not accelerate.
Pascal's Law is also not valid in hydraulic lifts during lifting. During lifting acceleration takes place in the connecting tube, as you wrote.
But we use Pascal's Law in hydraulics because we only consider the initial state of the lift and the end state of  the lift. The initial state and end state are both static, so there Pascal's Law applies, but not during the transition from initial to end state. In reality we are mostly interested in the difference between initial and end states, in the case of lifts and we can still use Pascal's Law for that purpose.
This is not to say that in accelerating fluids transmission of pressure no longer applies (it does) but Pascal's formulation doesn't take accelerations into account and wasn't intended for that purpose.
