Question

The free surface of oil in a tanker, at rest, is horizontal. if the tanker starts accelerating the free surface will be tilted by a angle θ. If the acceleration is a ms^-2, what will be the slope of the free surface?

Answer 1

Let us consider the following diagram.

If the tanker accelerates in the positive direction with acceleration a. consider a parcel, the fluid of mass 8m. Forces which are acting on particle w.r.t. the tanker.

Now, balancing forces (in equilibrium) along inclined direction component of weight = component of pseudo force [ma = pseudo force]

mg sin θ = ma cos θ

or g sin θ = a cos θ

or \(\frac{sin\, θ}{cos\, θ}\) = \(\frac{a}{g}\)

∴ tan θ = \(\frac{a}{g}\)

This is required slope.