Accelerated along inclined plane
Fluid masses subjected to acceleration along inclined plane
Key FactsGyroscopic Couple: The rate of change of angular momentum () = (In the limit).
- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.
Blaise Pascal (1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.
Leonhard Euler (1707-1783) was a pioneering Swiss mathematician and physicist.
Henry Philibert Gaspard Darcy (1803-1858) was a French engineer who made several important contributions to hydraulics.
OverviewConsider a tank open at top, containing a liquid and moving upwards along inclined plane with a uniform acceleration as shown in fig-1(a). We know that when the tank starts moving, the liquid surface falls down on the front side and rises up on the back side of the tank as shown in fig-1(b). Let,
- = Inclination of the plane with the horizontal
- = Angle, which the liquid surface makes with the horizontal, and
- = Acceleration of the tank
We know that the weight of the particle,
Similarly, the accelerating force,
Now resolving all the forces horizontally at A,
2) by (3)
- aH = horizontal component of the acceleration
- aV = vertical component of the acceleration
Example - Fluid masses subjected to acceleration along inclined plane
A rectangular box containing water is accelerated at 3m/s2 upwards on an inclined plane 30 degree to the horizontal. Find the slope of the free liquid surface.
- = 3 m/s2
Slope of the free liquid surface =