Yes, as the other responders said, the corners (properly "Internal corners") are important due to ease of cleaning and 'dead zones' in product flow.
Regarding your request for specific science and calculations, the generally accepted industry convention for internal corners that are considered to be cleanable and acceptable in a food contact area is a radius of 3 mm. This means that the internal corner should be rounded off to a smooth curved shape. If you want to measure the radius of an internal corner, draw a circle of radius 3 mm in the corner of a piece of card. Using the circle as a guide, cut off the sharp square corner of the card, which will result in a rounded corner. Put the rounded part of the card into the corner of the food equipment, perpendicular to the 'walls' of the equipment. If the corner of the card doesn't fit into the corner of the equipment it is too square to be easily cleaned and shouldn't be used in food contact areas or 'splash and spill' zones of food facilities.
The comments above are generic, not specific to any type of equipment or liquid. For viscous products a cylindrical tank is probably better than a rectangular tank; the product will probably empty out better and it will be much easier to clean and sanitise than a rectangular container, even one with rounded internal corners.
There is a European non-profit organisation called EHEDG that provide excellent guidance on this topic. You can find their guidance documents at http://www.ehedg.org/guidelines/. I recommend document 8 "Hygienic Equipment Design Criteria" which is free to download.