is there any formula in computing the required compressor for an ice plant with a capacity of 7 tons/day?

Answer 1

Yes a rule of thumb is 1hp=1 ton btu's 1 pound of water drops 1 degree f. in one unit of btu's. 1 ton is 12000 btu's. 7 tons of ice = 7 tons liquid water. When the water reaches down to 0 degrees C. or 32 F the freezing point at sea level, you need extra btu's to remove the latent heat and form ice. You need to know the temperature of the water you would be starting out with to deal with time required.

Answer 2

There might be the Tons R = 12,000 btu/hr is 1 ton of refrigeration is the amount of refrigeration needed to produce a ton 2000 lbs of ice in a 24 hr day.

I wouldn't use a formula to select a compressor. First I would look at the operating conditions. The ice maker has conditions for suction pressure/temperature where it needs to operate. You also need a condenser section which will determine your condensing temperature.

Most compressor manufacturers have charts for their machines which tell you which machine produces the required tonnage at a given suction pressure and condensing temperature/pressure.

These charts are more certain than any rule of thumb you could use.