The complete manner in which that utility sink is installed is not only a serious violation of the plumbing code but it is also potentially a serious health and safety hazard.

The code requires that all fixtures attached to a drain must be equipped with a trap.

In your installation there is a hose from the sink drain opening to the floor drain. The maximum allowable vertical distance from the drain opening in the sink to the standing water level in the trap is 24" (some codes limit it to 12"). The only permissible exception is a laundry standpipe.

Generally floor drains do not have a trap on the line. Instead the the receptor has a water reservor around the drain pipe and the underside of the lid has a pipe extension that protrudes below the water line in the reservoir to provides the trap function. When the lid is removed there is no trap and consequently sewer gasses may enter into the home.

The five main gasesous components of sewer gas are Hydrogen Sulfide, Ammonia, Methane, Carbon dioxide and Nitrous Oxide all of which are asphyxiants and some of them are flamable and potentially explosive in higher concentrations. To complicate the matter even more, in high concentrations Hydrogen Sulfide has the ability to paralize the bodies olfactory nerve which means you cannot even smell the gasses.

Some of these gasses are lighter than air while others are heavier than air and they occur in differing concentrations at different times so you can never be sure if they are collecting near the floor where they would go totally unnoticed until you have a serious problem.

To make matters even worse Hydrogen Sulfide (SO2) combines with water water vapor(H2O) and forms Sulfuric Acid (H2SO4). These vapors can combine on the metal cabinet of your laundry equipment or other metal objects in the immediate area, form the acid and cause premature corrosion of the metal.

If the flamable gasses were to concentrate near the floor in a fairly large concentration they could be drawn into the burner section of a gas water heater or gas furnace and ignite a fire or explosion.

You could connect a pipe to the floor drain, sealing it in place then make a vertical riser up to a Tee where you would attach a waste arm and P-trap to your sink opening. From the top of the tee you would need to continue upward and attach the riser to a vent or run a vent line up and out through the roof.

If the plumbing code in your jurisdiction is modelled after the International Residential Code you could install an Air Admittance Valve on the riser above the tee to provide the necessary vent.

Lazypup:
WOW! You blew my mind. Thank you for the input.
I own a condo and my neighbor has been here since it was built...in the 70's. She assures me that the drain set up is original. She has the same get up, as does all of the condo's I have been in. I have called the county on my "issue" and they tell me that the records do not go back to 1972. They claim they cannot answer any of the questions I asked. Maybe I asked the wrong questions.?

In all fairness to your county officials the reason they don't have the records is because in most instances they never receive a copy of the plumbing, electrical or HVAC layout.

When you purchase a set of building plans the plans show the overall demensions of the structure as well as a complete floorplan showing the location of all end use fixtures but there is no plumbing layout, electrical layout or HVAC layout for the structure.
Why?
Because even if we were to build 100 homes from exactly the same building plans, no two of those homes would have the exact same utility layout, by example, let us consider your plumbing layout.

In order to determine the layout your plumbers needs a copy of the building floor plan showing the location of all fixtures. In addition, we need to know if the structure will be served by a municipal sewer line or a septic tank and the exact distance and location from the structure to the sewer or septic tie in as well as the depth of the tie in point.

Once we know the exact location and depth of the tie in we can then compute the exact distance from the tie in point to the fixture furthest away from that point. From the length of the run and the required pitch of the drain lines we can then determine what the minimum elevation of the structure floor must be. In southern regions where they are not confronted with frost issues often the municipal sewer lines are fairly shallow and in some instances if there is a long setback from the street or sewer line location to the structure it may be necessary to either raise the level of the floor, or install a sewage lift station. Generally it is considered much more cost effective to to add another layer or two of block on the footer wall rather than install the sewage lift station.

In all cases the shortest distance between any two points is a straight line so we generally begin by determining a straight line from the furthest watercloset to the sewer or septic tie in point and use that as the house sewer and main drain run. Here again, the municipality determines where the sewer tie in will be. It may be in the center of your lot on the street side at one location but it may come in from a corner of the lot on another and if you have a septic tank it could be anywhere around the structure so the most direct line from the furthest watercloset to the tie in point will be different at each location. Once we have figured out the house sewer and house main drain we must then compute at branch drains and since the main drain is different at each structure obviously the branch drains will also be different.

While some larger plumbing companies have Plumbers who work full time at preparing the layouts, as a rule it is the lead plumber on sites job to work it out.

When your inspector comes to inspect he or she will consult with the lead plumber to see their layout, then they do a complete walkthrough to insure that everything in the installation meets code standards but the inspector never has a copy of the actual layout print and sadly some plumbers fail to leave a copy with the homeowner. Personally I would strongly advise anyone building a home to make sure that you get a copy of the final working print of your plumbing layout and keep that for future reference.

I generally take a 3' section of 4" PVC and glue a cap on one end and a cleanout adapter and threaded plug on the opposite end, then I roll the print and put it in that tube and give that to the homeowner with the suggestion that they should also get copies of all the other tradesmens field prints and put them in the tube as well. The tube can then be hung on the ceiling near the electrical panel in a basement or in a utility room and you will have an archive set of prints for future maintenance.