I want to clarify the back wash flow rate when specified as volume per minute per square area is totally the same as speed (length/time). 10 gallons/min-ft2 comes out to 1.336 ft/min, or 0.41 m/min.
You have to have the effective size (d10 screen size) and the uniformity coefficient (d60/d10) to calculate the flow rate required for fluidization. You also need to know how much freeboard you have above the top of your filter media. Assuming you want to expand the bed 30% (the generally accepted percent expansion that reflects adequate fluidization) then you need to know you have enough freeboard in the tank to allow for this expansion percentage without discharging filter media out the backwash outlet line.
Depending on the grain size of the used filter media, the back wash flow rates are different. Just let me know what grain sizes you use and I can support you in this issue.
Rule of thumb for anthracite media: 10 gpm/ft2 cold water, up to 15 gpm/ft2, hot water (lower viscosity. Sand filters may be back-washed at the higher of the two numbers. In your case, use the lower of the two back-wash rates, expand the anthracite portion about 30-40%. Your filter probably is designed with 100% free-board (half the vessel is just water) to allow for expansion during back-wash.
gallons per minute per square foot, SI equivalence: 1 gpm/ft2 = (velocity) 0.1337 ft/min, thus we have 0.0407 m/min. Good velocity for typical media will be 0.41 m/min.