As other have pointed out, the main utility is to allow easier cleaning of the tank cars from sediment (solid precipitates). Usually, there is a drain in the lowest point.
The reason that it is in the middle is that in this way, you can allow double the incline compared to if you had the drain at one of the ends for the same height. For example, if the allowed height difference is about 15 cm, and about 15 m length, then if you had the drain in:
- the edge, the angle would be $\arctan\left(\frac{0.15}{15}\right)=0.57^\circ$ or 1%.
- the middle , the angle would be $\arctan\left(\frac{0.15}{7.5}\right)=1.14^\circ$ or 2%.
The steeper angle helps gravity assisted cleaning.
