When an oil tanker is partially filled with oil and moves forward on a level road with uniform acceleration, the free surface of the oil will assume a parabolic curve.

This phenomenon is known as the "Piston Effect" or "U-tube effect." As the tanker accelerates forward, the oil inside experiences inertia and tends to remain stationary due to its higher density compared to air. This creates a pressure difference between the front and rear ends of the oil surface.

The pressure difference causes the oil to move towards the rear end of the tanker, forming a parabolic shape. The depth of the oil is larger at the rear end and gradually decreases towards the front, following the curve of the parabola.

It`s important to note that the free surface of the oil will not remain horizontal, nor will it be inclined with a smaller or larger depth at the rear end. The parabolic curve is the characteristic shape that the oil surface assumes under these conditions of uniform acceleration.