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?
[Physics] Pascal’s law in Fluid mechanics
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The term enclosed is a little misleading. Look at the diagram below:
Both containers are of equal size and contain the same amounts of the same liquid. The left liquid is contained by a beaker and a weightless, frictionless piston, the right is contained by a beaker that is simply open to air. Both sit side by side on the surface of the Earth (and thus subject to gravity).
In both cases Pascal's Principle applies and the pressure in the liquids can be measured by means of a manometer.
If we assume the pressure of the surrounding air to be $p_0$ then in the right hand case the pressure in the liquid will only depend on the height $h$ due to the weight of the liquid column, according to:
$p=p_0+\rho gh$, with $\rho$ the density of the liquid and $g$ Earth's acceleration.
In the left hand liquid the situation is very similar but we have to take into account the extra pressure exerted by the piston, which is $p_p=\frac{F}{A}$ with $F$ the force applied to the piston and $A$ the surface area of the piston.
We then get:
$p=p_0+\frac{F}{A}+\rho gh$.
So for left and right $p$ would be the same if $F=0$, despite the right not looking particularly enclosed.
The meaning of 'enclosed' becomes more apparent when we drill a hole in either container and liquid is now free to flow out of it. At that point Pascal's Principle no longer holds exactly.
Pascal's Principle applies only to static situations, where liquid is not free to escape its container (enclosure, if you prefer). But that does not mean pressure could no longer be measured with a manometer, only that the measurement would no longer correspond exactly to Pascal's Principle.
In the case of common hydraulic devices like car lifts, springing a leak renders the device useless because it no longer obeys Pascal's Principle.
Best Answer
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.