Apparatus for treating a surface of a workpiece with a blasting medium, comprising: a blasting chamber with a blasting device for accelerating the blasting medium onto the workpiece received in the blasting chamber, an air classifying device for separating dust and a blasting medium fine fraction, a second dust discharge line leading away from the air classifying device for discharging the dust and the blasting medium fine fraction, a main hopper arranged downstream of the air classifying device for receiving the blasting medium, a dosing hopper connected to the main hopper for replenishing unused blasting medium, a blasting medium supply line connecting the main hopper to the blasting device for supplying the blasting medium to the blasting device, wherein a computer is set up to determine an average blasting medium consumption V m according to the following formula: V m = G n / T s, where G n is the weight and/or volume added in a predetermined time interval from the dosing hopper or another parameter from which the weight and/or volume of blasting medium present in the dosing hopper can be inferred, and T s is the blasting duration in the predetermined time interval, characterized in that a first dust discharge line leading away from the blasting chamber is provided for discharging dust, that at least one first measuring device for measuring the wind speed or a parameter physically related to the wind speed is provided in the second dust discharge line, that the first measuring device is connected or connectable to a computer for the transmission of measured values, and that the computer is set up for the time-correlated display of the following measured values or a parameter corresponding thereto in each case: Wind speed and average blasting medium consumption V m. a blasting chamber with a blasting device for accelerating the blasting medium onto the workpiece received in the blasting chamber, an air classifying device for separating dust and a blasting medium fine fraction, a second dust discharge line leading away from the air classifying device for discharging the dust and the blasting medium fine fraction, a main hopper arranged downstream of the air classifying device for receiving the blasting medium, a dosing hopper connected to the main hopper for replenishing unused blasting medium, a blasting medium supply line connecting the main hopper to the blasting device for supplying the blasting medium to the blasting device, wherein a computer is set up to determine an average blasting medium consumption V m according to the following formula: V m = G n / T s, G n is the weight and/or volume added in a predetermined time interval from the dosing hopper or another parameter from which the weight and/or volume of blasting medium present in the dosing hopper can be inferred, and T s is the blasting duration in the predetermined time interval, characterized in that a first dust discharge line leading away from the blasting chamber is provided for discharging dust, that at least one first measuring device for measuring the wind speed or a parameter physically related to the wind speed is provided in the second dust discharge line, that the first measuring device is connected or connectable to a computer for the transmission of measured values, and that the computer is set up for the time-correlated display of the following measured values or a parameter corresponding thereto in each case: Wind speed and average blasting medium consumption V m.