Abstract:
A device used to measure the mass flow of a particulate transported with the aid of a gas. The device includes an arrangement which is used to create an electromagnetic field, with a measuring area being defined therein. An evaluation device for electromagnetic radiation which is reflected at least off of the solid(s) is connected to a detector. The evaluation device is provided with a differentiator which is connected to the detector for detecting reflected electromagnetic radiation. A rectifier is connected to the differentiator in order to determine an amount, whereby mass flow is obtained from the reflection amount. The reflection is measured, at least from the solid(s) within the measuring area of the magnetic field, whereupon the differential quotient is determined as a function of time from the chronological progression of the measuring signal and the amount is obtained therefrom. A measuring signal is obtained from the non-homogeneity of the electromagnetic field, forming the integral over time of the amount of the reflected power per time. The measuring signal is proportional to the mass flow.

Description:
BACKGROUND  
       [0001]     The invention relates to a method for measuring the mass flow of a particulate solid which is transported by means of a gas, a measuring region being defined in an electromagnetic field, and the electromagnetic radiation reflected by the solid(s) being evaluated. Moreover the invention relates to an arrangement for performing the method, which has a device for producing an electromagnetic field in which a measuring region is defined, and with an evaluation device, connected to a detector, for at least the electromagnetic radiation reflected from the solid(s).  
         [0002]     A series of different methods and devices are known for the determination of the mass flow (also termed “throughput”) of a solid which preferably passed through a tube with a transport gas, for example, air.  
         [0003]     “Mass flow” will always be understood hereinafter the transport of a weight unit of a material in a given time unit: for example, Kg/s or t/h.  
         [0004]     The solid is preferably comminuted or milled, so that as a rule it is present as a powder or dust. It can also, however, naturally have a granular appearance, such as is the case of cereals. As the electromagnetic waves, microwaves, visible light, or infrared can be used.  
         [0005]     In all the measurement methods known heretofore, which use electromagnetic waves for mass flow determination, on the one hand the concentration, and in addition the speed, of the solid are measured. For concentration measurements the damping of the amplitude of an electromagnetic wave is frequently determined; for speed measurements, the frequency shift due to the Doppler effect is frequently used. Both measurement results are then multiplied together to give the mass flow. These mass flow measuring devices thus consist in principle of two measuring devices.  
         [0006]     Methods and devices which operate according to this principle are known from, for example, WO90/03668, Patent Abstracts of Japan, Vol. 8, No. 109 (P-275), 22 May 1984, JP-A-59 019814, and U.S. Pat. No. 4,580,441.  
         [0007]     From U.S. Pat. No. 5,500,537, it is known to determine the concentration of the transported solid using the reflected energy or power. The flow speed measurement takes place by measurement of the frequency shift of the reflected radiation due to the Doppler effect.  
         [0008]     Here also, two measurements and two mutually separated evaluations are necessary. A corresponding cost for the measuring and evaluation devices, and also a doubled possibility of error, are present.  
       SUMMARY  
       [0009]     The object of the present invention is to provide a method and a device of the kind mentioned at the beginning, making possible a simplified substantially error-free measurement, with simultaneously reduced expense.  
         [0010]     To attain this object, it is proposed according to the method that the mass flow is determined from only the measure of reflection, that for this purpose the reflection is measured at least on the solid within the measuring region of the electromagnetic field, that from the time course of the measurement signal, the differential quotient according to time, or a derivative of higher order, and the sum thereof is determined. This signal available after sum formation is appropriately integrated for signal damping.  
         [0011]     Through this measurement method, only a single measurement effect is evaluated, in order to determine the mass flow. Due to the inhomogeneity of the electromagnetic field, a measurement signal results which is the integral formed over time of the amount of the reflected power, derived over time. This measurement signal is proportional to the mass flow.  
         [0012]     Expressed in a simplified manner, in this measurement method the particles are counted, since each particle produces the same signal independently of the concentration and speed at which it is forwarded. In addition, larger particles produce a larger signal than smaller particles of the same kind.  
         [0013]     In the measurement method according to the invention, the total reflected radiation can be measured. This is sufficient because in an intermediate step in signal generation the derivative of the reflected power is formed, so that constant fractions of reflected power cancel out of the calculation. Thereby power reflected from pipe walls and/or adhered deposits does not lead to a false result.  
         [0014]     Since the fraction of power reflected from pipe walls and/or deposits is often very much greater than that reflected from the solid, this can however lead to a poorer signal/noise ratio. In this case it is advantageous to measure only the radiation reflected from the solid, and for this purpose to measure the reflected radiation, frequency shifted due to the Doppler effect.  
         [0015]     It is furthermore possible to use, instead of the reflected power, only the ratio or the difference of irradiated and reflected power, when the irradiated power is constant or known, or undergoes a known variation with time.  
         [0016]     The device according to the invention for performing the method is in particular characterized in that the evaluation device has a differentiator connected to the detector for determining reflected, electromagnetic radiation, to which a rectifier is connected for amount formation. As already described in connection with the method according to the invention, the mass flow can then be determined, in that only a single measurement is evaluated. The cost of measurement technology is then correspondingly small, and the measurement device has a considerably reduced likelihood of error.  
         [0017]     An intermediate stage for null point displacement is advantageously connected between the differentiator and the rectifier, and preferably has a capacitor for blocking direct currents. The null point, which does not lie in the center after the derivation, can thereby be correspondingly displaced, and the constant direct current fraction can be separated with the capacitor.  
         [0018]     According to an embodiment of the invention, a portion of the signal preparation is provided by an analog circuit, and another portion of the signal preparation is provided by a digital circuit, in particular, an analog circuit for derivation with formation of differential quotients, and a digital circuit for sum formation and integration, are provided.  
         [0019]     Furthermore, the possibility exists that the output of the rectifier, with the output signal originating there if necessary after smoothing with a capacitor, is connected to a digital function unit with an A/D converter and a processor.  
         [0020]     Finally, a digital circuit can be provided for signal generation, the detector, if necessary after immediate matching, being directly connected to an A/D converter, and the latter to a processor. In the latter case, the processor first forms the derivative, then the sum of the derivatives, and finally performs the integration. The use of a digital processor has the advantage that it can also perform relatively simply the calibration or conversion of the signal into a suitable magnitude for the user.  
         [0021]     A laser can be provided for the production of an electromagnetic field.  
         [0022]     Alternatively, a microwave generator can be provided for the production of an electromagnetic wave when there is a high dust or particle density. Reflection is poorer of a microwave because of its greater wavelength, so that at higher particle concentrations, the saturation of the signal is reached substantially later. Thus it is preferred in coal power stations, in which large amounts of coal are milled, to use microwaves for mass flow determination.  
         [0023]     Additional embodiments of the invention are set out in the further dependent claims. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0024]     The invention with its essential details is explained in detail hereinafter using the drawings.  
         [0025]     In the drawings:  
         [0026]      FIG. 1  is a schematic diagram of a mass flow measuring device in connection with a flow channel,  
         [0027]      FIGS. 2-3  are two diagrams showing the power reflected by a particle being applied over time,  
         [0028]      FIG. 4  is a diagram generally corresponding to  FIG. 2 , with the reflected power of a particle over time,  
         [0029]      FIG. 5  is a diagram that represents the reflected power after forming the differential quotient according to time,  
         [0030]      FIG. 6  is a diagram with a representation of the sums of the derivative of the reflected power,  
         [0031]      FIGS. 7-10  are diagrams generally corresponding to  FIGS. 4 and 6 , at different conveying speeds,  
         [0032]      FIGS. 11-16  are schematic representations for comparison of the mass flow signals at different conveying speeds,  
         [0033]      FIGS. 17-22  are schematic representations for comparison of the mass flow signals at different concentrations of solids,  
         [0034]      FIG. 23  is a schematic diagram of a mass flow measurement device with microwaves coupled-in and coupled-out at different places of a flow channel,  
         [0035]      FIG. 24  is a side view of the arrangement shown in  FIG. 17 , and  
         [0036]      FIG. 25  is a diagram, generally corresponding to  FIG. 17 , of a mass flow measuring device in connection with a flow channel, using a laser for producing an electromagnetic field. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0037]     A device  1  shown in  FIG. 1  measures the mass flow of a particulate solid  2 , which is conveyed using a gas within a flow channel  3 . The solid  2  is indicated by a single particle. A measuring device  4  according to the invention is connected laterally to the flow channel  3 , and can measure the mass flow or throughput of the solid  2 .  
         [0038]     The measuring device  4  has a transmitter with an oscillator  5  for producing an electromagnetic field  6  and also a receiver with an evaluation device  7  for measuring the power reflected by the particles of the solid, or the like measure of reflection.  
         [0039]     This takes place, as described in more detail herein below, in that the mass flow is formed from the amount of reflection alone. For this purpose, the reflection is measured at least on the solid within the measurement region of the electromagnetic field, from the time course of the measurement signal of the differential quotient of according to time, and the sum formed therefrom.  
         [0040]     The measure of reflection can, as previously mentioned, be proportional to a function of the reflected power, or else proportional to a function of the reflected energy or a function of the reflected intensity or a function of the reflected radiation flow.  
         [0041]     A measurement region covering the cross section of the flow channel is defined within the electromagnetic field, in which the electromagnetic radiation reflected from the solid is evaluated.  
         [0042]     This takes place, as described in more detail hereinbelow, in that the mass flow is determined from the amount of reflection alone. For this purpose, the reflection is measured at least from the solid within the measurement region of the electromagnetic flow, from the time course of the measurement signal of the differential quotient according to time, and the sum formed therefrom.  
         [0043]     In the device  1  shown in  FIG. 1 , a microwave field is produced as the electromagnetic field by a Gunn oscillator  5  with a Gunn diode. The microwave field produced is conducted from the Gunn diode via a hollow conductor  10  to a horn antenna  15 , and from this is irradiated through a wall aperture  9  of the flow channel  3  into the flow channel  3 .  
         [0044]     The electromagnetic field irradiated into the flow channel  3  is indicated by dashed arrows.  
         [0045]     The hollow conductor as intermediate element is in particular advantageous when the flow channel and/or the solid is particularly hot.  
         [0046]     The waves reflected from the solid  2  and indicated by the arrows Pf  2  reach a detector  11 , which is formed by a Schottky diode as a reflection receiver in the exemplary embodiment according to  FIG. 1 .  
         [0047]     The sensor formed of transmitter and receiver is constructed here as a transceiver, i.e. the sensor transmits and receives simultaneously. The Gunn diode and the Schottky diode are built together into a housing. These microwave modules are obtainable as standard parts (e.g., Macon 86849-M01).  
         [0048]     The Schottky diode  12  converts the microwaves into an electrical voltage signal. This voltage from the Schottky diode  12  is not proportional to power over the whole measurement region. However, this is insignificant for the generation of the mass flow signals, since arbitrary functions of the power are suitable for this. The voltage at the Schottky diode results both from the irradiated power and also from the received power; therefore, in this embodiment, the mass flow signal is not determined using the common power, but from the ratio of irradiated power to received power. There is adjoined an intermediate stage  14  with a capacitor  26  by which a null point displacement is effected, by means of which and whereby a separation of this constant direct current portion takes place.  
         [0049]     The signal is then supplied to a rectifier stage  16  with a bridge rectifier and is rectified there. Mathematically, a sum formation is effected with the measurement signal derived with the differentiator  13 . The rectified signal is smoothed with a capacitor  18 . This signal represents the mass flow signal, and is the integral formed over time of the amount of the reflected power according to time.  
         [0050]     This signal can now be supplied to a digital unit, consisting of an A/D converter  19  and processor  20 . The processor can convert the signal to a magnitude which is reasonable for the user.  
         [0051]     The possibility also exists of placing the digital unit directly behind the circuit which differentiates the signal. In this case, the processor must continue the null point displacement and the rectification of the signal, which is possible in principle but requires processors with high computing power. It is likewise possible to set the processor directly on the Schottky diodes; A/D converters are then of course then required with a substantially higher precision, and processors with still more computing power.  
         [0052]     In  FIGS. 2-16 , the physical connections of the invention are shown.  FIGS. 2 and 3  show the power reflected from a solid particle over time at different conveying speeds. It is assumed for simplicity that the electromagnetic field just rises linearly up to a first position at P 0 , then runs constant to a second position, to then fall linearly again to zero.  
         [0053]     Corresponding to this assumed course of the field, the reflected power of a particle at a conveying speed V 1  is as shown in  FIG. 2 . If now the conveying speed is doubled to V 2 =2*V 1 , the course of the curve shown in  FIG. 3  results.  
         [0054]     The areas under the curves in  FIGS. 1 and 2  correspond to the energy which a particle reflects on passing through the field. It can be seen that at a doubled speed only half as much energy is reflected as at a single speed. However, since at double the speed and the same particle concentration, the overall reflected energy of all particles which are located exactly in the field is exactly as large as when the particles with single speed are transported (cf. U.S. Pat. No. 5,550,537). Lastly, the total reflected energy is thus a measure of the concentration and not of the mass flow.  
         [0055]      FIGS. 4-6  show how the mass flow can be determined from the measurement of the reflected power or the like reflection measurement.  
         [0056]      FIG. 4  shows the reflected power P(t) of a solid particle with a field geometry such as was used as the basis in  FIGS. 2 and 3 .  
         [0057]     If the field strength of the field increases linearly, the reflected power P(t) can be described by a*t with the simplification that the amount of the reflected power is constant, independently of the angle which the direction of light of the particle forms to the sensor.  
         [0058]     If the reflected power is constant, P 0 , then, 
 
 P ( t )= P   0    Equation 3: 
 
         [0059]     If the reflected power is linear, then: 
 
 P ( t )=− a+t+P   1    Equation 4: 
 
         [0060]     Taking the derivatives of these equations with respect to time, for the linearly rising portion: 
 
 dP ( t )/ dt=a    Equation 5: 
 
 for the Constant portion: 
 
 dP ( t ) /dt= 0   Equation 6: 
 
 and for the portion falling linearly: 
 
 dP ( t ) /dt=−a    Equation 7: 
 
         [0063]     Mathematically, as can be seen from  FIG. 5 , the area under the curve for the linearly falling portion is negative and for the linearly rising portion is positive. This is expressed in  FIG. 5  by a plus sign and minus sign in the hatched surfaces. However, the actual area under the curves is to be determined ( FIG. 6 ). The thus hatched surface is the integral formed over time of the amount of reflected power, derived over the time.  
         [0064]     The integral over the amount of the time derivative of the reflected power is thus proportional to the mass flow. Furthermore, the integral formed over time of the reflected power derived according to time is termed the mass flow signal.  
       Equation  8:       
         mass   ⁢           ⁢   flow   ⁢           ⁢   signal     =     ∫              (     ∂     P   ⁡     (   t   )         )       (     ∂   t     )            ⁢     ⅆ   t             
 
         [0065]     Here: P=reflected power 
        t=time        
 
         [0067]     The thus formed measurement result is proportional to the mass flow, since each particle produces an equally large mass flow signal, independent of speed. This is indicated in  FIGS. 7-10 , the speed being V=V 1 , while in  FIGS. 9 and 10  the speed V=V 2 =2*V 1 .  
         [0068]     The mass flow signal is equal at both speeds, since the area under the curve is equal at both speeds.  
         [0069]     For speed V=V 1 , the area is calculated as follows: 
 
mass flow signal  V   1   =a*t 1 +a* ( t   3 − t   2 )   Equation 9: 
 
 with (t 3 −t 2 )=t 1  gives 
 
mass flow signal  V   1 =2 a*t   1    Equation 10: 
 
 for a speed V=V 2 =2*V 1 , the area is calculated as follows: 
 
mass flow signal  V   2 =2 a* ( t   1 )/2+2 a *( t   3   −t   2 )/2   Equation 11: 
 
 with (t 3 −t 2 )=t 1 , there holds (cf.  FIG. 10 ): 
 
mass flow signal  V   2 =2 a*t   1    Equation 12: 
 
         [0073]     Thus on passing across the field, each particle produces, independently of its speed, an identical signal, provided that each particle has the same geometry and that their other material properties are identical. A comparison of  FIGS. 2 and 3  shows that only the reflected energy is considered there. In this case, a particle moving twice as fast produces only half as large a signal as a particle traversing the field half as fast.  
         [0074]     The consequence is clear in  FIGS. 11-16 . In  FIGS. 14-16 , a conveying state is shown in which the solid particles are passed through with twice the speed of those in the conveying state shown in  FIGS. 11-13 .  
         [0075]     The mass flow signal for the respective conveying state already mentioned is shown in  FIGS. 12 and 15 .  
         [0076]     It can be seen in  FIGS. 13 and 16  that in the conveying state shown on the right-hand side in which the mass flow is twice as large for that shown on the left-hand side, a mass flow signal twice as large can also be measured. The individual hatched surfaces present, as shown on the left-hand side in the time window are all of equal size, but on the right-hand conveying state there are twice as many hatched rectangles as for the conveying state on the left-hand side.  
         [0077]     In order to indicate that the mass flow signal produced according to the measures of this patent, it is shown in  FIGS. 17-22  that for two conveying states with the same speed but different concentration, the mass flow signal is likewise correlated with the mass flow and not with the speed.  
         [0078]     It can be seen in these Figures that with the conveying state shown on the left-hand side, the concentration is only half as great as for the conveying state shown on the right-hand side. Since both conveying states have the same speed, the mass flow signal of a particle is also identical for the two conveying states ( FIGS. 18 and 21 ). The conveying state shown on the left-hand side conveys with only half the throughput as that shown on the right-hand side; the mass flow signal behaves correspondingly. In the time window on the left-hand side corresponding to  FIG. 19 , only half as many hatched surfaces are present as on the right-hand side according to  FIG. 22 .  
         [0079]     Expressed illustratively, in this measurement method the particles are counted, because each particle produced independently of the concentration and the speed at which it is conveyed. Larger particles produce larger signals than smaller particles of the same kind. If a larger particle reflects k times more power that smaller, then:  
       Equation  13:       
         ∫              (     ∂     P2   ⁡     (   t   )         )       (     ∂   t     )            ⁢     ⅆ   t         =       ∫              ∂     (     k   *     P1   ⁡     (   t   )         )       )       (     ∂   t     )              =     k   ⁢     ∫              (     ∂     P1   ⁡     (   t   )         )       (     ∂   t     )            ⁢     ⅆ   t                 
 
         [0080]     Thus also the mass flow signal is k times greater, when a larger particle reflects k times more power. Thus not only can particles be counted but also the weight of an individual particle can be correctly determined.  
         [0081]     Thus it can finally be said that the integral over the sum of the reflected power derived according to time is very well correlated with the mass low.  
         [0082]     It is theoretically sufficient to measure only the total reflected power, since with signal generation in an intermediate stop the derivative of the reflected power is formed, with which constant fractions of reflected power likewise fall out of the calculation, so that reflected power from pipe wall and/or adherent deposits do not lead to a false result. Since the fraction of reflected power from pipe walls and/or adherent is often very much greater than that reflected from the solid, this however leads to a poor signal/noise ratio. It is therefore more favorable to measure only the power of the electromagnetic wave reflected at the solid. The Doppler effect can be used for this purpose, in that only the power of frequency-shifted electromagnetic waves is used to produce the mass flow signal. Particularly when the irradiated power is constant or undergoes a known time variation.  
         [0083]     The equivalence of the measurement of the ratio of reflected to irradiated power is a pure power measurement, may be explained briefly by the example of a constant irradiated power.  
       Equation  14:       
         ∫              (       ∂     (     Pr   ⁡     (   t   )       )       Pa     )       (     ∂   t     )            ⁢     ⅆ   t         =       1   Pa     ⁢     ∫              (     ∂     Pr   ⁡     (   t   )         )       (     ∂   t     )            ⁢     ⅆ   t               
 
 with P a =irradiated power=constant 
        P r (t)=reflected power.        
 
         [0086]     Since the constantly irradiated power or respectively the inverse ratio thereof, may mathematically be taken out before the integral, calibration into weight units per time unit must be solely by means of this constant factor, so that likewise the mass throughput can be determined. In the example shown here, the extent of the field has been taken as greater than the particle size; however, the measurement effect is independent of the ratio of field extent to particle size.  
         [0087]     Furthermore, the measurement effect was shown at only a few special fields and the further limitation is made that this reflected power is independent of the angle which the direction of flight makes to the sensor. However, this is only a simplification of the representation limitation and for given fields. It is decisive that the reflected power depends only on the particle geometry, the specific properties of the material, and the irradiated power of the sensor.  
         [0088]     Thus for the reflected power of two particles one of which moves twice as fast as the other, with a given field and taking into account the angle which the direction of flight of the particle makes with the sensor: 
 
 V   1 =2* V   2    Equation 15: 
 
 so that 
 
 P   1 ( t )= P   2 (2 t )   Equation 16: 
 
         [0090]     A voltage or a current is usually produced in an electrical measuring device, and is proportional to the quantity to be measured. However, there are cases where this is not possible, and the voltage or the current produced is only proportional to a function of the quantity to be measured. In this case, Equation 16 must be extended to: 
 
 f ( P   1 ( t ))= f ( P   2 ( t ))   Equation 17: 
        P 1 =reflected power from particle  1      P 2 =reflected power from particle  2      t=time     V 1 =speed of particle  1      V 2 =speed of particle  2      f=symbol for function        
 
         [0097]     It is to be noted that a particle which passes twice as fast through the field of a sensor than a second similar particle which produces the same signal. Expressed formally in Equation 18.  
       Equation  18:       
           ∫   0   To     ⁢              ∂     P1   ⁡     (   t   )           ∂   t            ⁢           ⁢     ⅆ   t         =       ∫   0       2   *     ⁢   To       ⁢              ∂     P2   ⁡     (   t   )           ∂   t            ⁢           ⁢     ⅆ   t             
 
         [0098]     This should be substantially more valid general case of  
       Equation  19:       
           ∫   0   T     ⁢              ∂     f   ⁡     (     P1   ⁡     (   t   )       )           ∂   t            ⁢           ⁢     ⅆ   t         =       ∑   0       2   *     ⁢   T       ⁢           ⁢              ∂     f   ⁡     (     P2   ⁡     (   t   )       )           ∂   t            ⁢     ⅆ   t             
 
         [0099]     This case is generally valid, because the constant T 0  is replaced with the variable T. T 0  is a special case of t. Furthermore the same function of the power is taken into account.  
         [0100]     For evaluation, Equation 17 is inserted into the left-hand position of Equation 19:  
       Equation  20:       
           ∫   0   T     ⁢              ∂     f   ⁡     (     P1   ⁡     (   t   )       )           ∂   t            ⁢           ⁢     ⅆ   t         =       ∫   0   T     ⁢              ∂     f   ⁡     (     P2   ⁡     (     2   ⁢   t     )       )           ∂   t            ⁢           ⁢     ⅆ   t             
 
 only u is substituted for 2t, resulting in 
 
 u= 2 t    Equation 21: 
 
 this is equivalent to  
       Equation  22:       
         u   2     =   t       
 
         [0103]     In equation 22, t is now differentiated in respect to time:  
       Equation  23:       
           ⅆ   u       ⅆ   t       =   2       
 
         [0104]     This is equivalent to  
       Equation  24:       
           ⅆ   u     2     =   ⅆ       
 
         [0105]     Hereinbelow, Equation 22 and Equation 24 are substituted in Equation 20. Furthermore, first the outer and then the inner derivative are formed within the summation signal:  
       Equation  25:       
           ∫   0   T     ⁢              ∂     f   ⁡     (     P2   ⁡     (     2   ⁢   t     )       )           ∂   t            ⁢           ⁢     ⅆ   t         =       ∫   0       2   *     ⁢   t       ⁢                ∂     f   ⁡     (     P2   ⁡     (   u   )       )           ∂   u       ⁢       ∂   u       ∂   t              ⁢           ⁢       ⅆ   u     2             
 
 with Equation 23 gives:  
       Equation  26:       
           ∂   u       ∂   t       =   2       
 
         [0107]     Equation 26 is now inserted into Equation 25, resulting in  
       Equation  27:       
           ∫   0       2   *     ⁢   t       ⁢                ∂     f   ⁡     (     P2   ⁡     (   u   )       )           ∂   u       ⁢           ⁢       ∂   u       ∂   t              ⁢           ⁢       ⅆ   u     2         =       ∫   0       2   *     ⁢   t       ⁢                ∂     f   ⁡     (     P2   ⁡     (   u   )       )           ∂   u       ⁢   2          ⁢       ⅆ   u     2             
 
         [0108]     Constants also have to be taken out of the sum and should therefore be abbreviated; thus there results from Equation 28  
       Equation  28:       
           ∫   0       2   *     ⁢   t       ⁢                ∂     f   ⁡     (     P2   ⁡     (   u   )       )           ∂   u       ⁢           ⁢   2          ⁢           ⁢       ⅆ   u     2         =       ∫   0       2   *     ⁢   t       ⁢              ∂     f   ⁡     (     P2   ⁡     (   u   )       )           ∂   u            ⁢     ⅆ   u             
 
         [0109]     Since the result of an integral does not depend on the sign of the variables and constraints, Equation 28 can be written as:  
       Equation  29:       
           ∫   0       2   *     ⁢   t       ⁢              ∂     f   ⁡     (     P2   ⁡     (   u   )       )           ∂   u            ⁢           ⁢     ⅆ   u         =       ∫   0       2   *     ⁢   t       ⁢              ∂     f   ⁡     (     P2   ⁡     (   t   )       )           ∂   t            ⁢     ⅆ   t             
 
         [0110]     The assertion is thus proved. The constant  2  can be replaced by another given constant without further proof, so that in the most general case as Equation 32:  
         [0111]     When Equation 30: V1=a*V 2  holds, then likewise Equation 31: P 1 (t)=P 2 (a*t) holds, so that To/a  
       Equation  32:       
           ∫   0       a   *     ⁢   To       ⁢              ∂     f   ⁡     (     P2   ⁡     (   t   )       )           ∂   t            ⁢           ⁢     ⅆ   t         =       ∫   0     To   /   a       ⁢              ∂     f   ⁡     (     P2   ⁡     (   t   )       )           ∂   t            ⁢     ⅆ   t             
 
         [0112]     This means the signal magnitude G as in Equation 33:  
       G   =     ∫              ∂     f   ⁡     (     P   ⁡     (   t   )       )           ∂   t            ⁢     ⅆ   t             
 
 is independent of the speed. Each particle of the same kind which passes through the field of a sensor which generates this measurement quantity produces the same signal G independent of its speed. Now only the sum of all these signals has to be formed and measured over a given time; then a signal is obtained which is proportional to the number of particles which were transported through the field in this given time. Since not only are particles counted, but simultaneously also larger particles produce more signal, the weight of the particles is also detected, so that finally the signal is proportional to the mass flow. 
 
         [0114]     As already mentioned, this kind also functions to determine the mass flow if not only the power can be directly determined, hereby a function of the power, for example p 2 .  
         [0115]     This can be seen if for P 1  and P 2  respectively P 1   2  and P 2   2  are respectively inserted in Equation 33:  
       Equation  34:       
         G   1     =       ∫   o   To     ⁢              ∂     (       P   1   2     ⁡     (   t   )       )         ∂   t            ⁢     ⅆ   t             
 
         [0116]     Equation 35:  
         [heading-0117]     If the outer derivative is formed respectively within the sum, these results:  
         [0118]     Equation 36:  
         [0119]     Equation 37: 
 
 With the respective Equation 18 or 19, there directly follows that G1=G2, since  
       Equation  36/37:       
         G   1     =       2   ⁢       ∫   o   To     ⁢              ∂     (     P1   ⁡     (   t   )       )         ∂   t            ⁢     ⅆ   t           =       G   2     =     2   ⁢       ∫   o       2   *     ⁢   To       ⁢              ∂     (     P2   ⁡     (   t   )       )         ∂   t            ⁢     ⅆ   t                   
 
         [0121]     This has a direct consequence if microwaves are used as the electromagnetic waves. For measuring the power of the reflected microwaves, relatively inexpensive diodes can be used. These however have the disadvantage that the output voltage is not proportional to the power. The Schottky diode shows a kind of saturation behavior at high powers, since the characteristic of the Schottky diode flattens out. Since however it is not the power which has to be determined with the signal magnitude, but the mass flows signal using only the characteristic, or the output voltage of the Schottky diode as a function of the power, this means that there is no disadvantage, and the inexpensive Schottky diodes can be used without the characteristic having to be linearized.  
         [0122]      FIGS. 23 and 24  show a measurement arrangement which is generally comparable to  FIG. 1 . The receiver transmitter however do not form a unit here, but are arranged separately. There are several receivers; it is to be indicated that the receivers can be installed above and below, and also right and left, of the transmitter.  
         [0123]     Exhaust air mostly contains only slight amounts of dust. It is often necessary to measure the amount of dust in order to maintain legal standards. This can take place using the devices according to the invention, corresponding for example to  FIG. 1  or  FIGS. 23 and 24 .  
         [0124]     For example, in  FIG. 25 a  laser  21  is installed on a chimney or exhaust air channel as the flow channel  3 . Plural reflectors are installed on the inner wall of the chimney or exhaust air channel, and reflect the laser back and forth so that the greatest possible region of the cross section is detected. The detector(s) which measure the reflective power can be installed laterally of, or above or below, the laser  21 . The receiver can have a condenser  23  which focuses the reflected light onto a photocell  24 . If the reflection is too weak, a photomultiplier  25  can be placed between the condenser  25  and the photocell  24 . The photocell generates, from the reflected power of the electromagnetic wave, a voltage or a current signal, which has to be differentiated in the next step. For this, and for the further steps, the measuring device according to  FIG. 1  can be used.  
         [0125]     The photocell  24  or a phototransistor can be used, instead of the Schottky diode  12  used as detector  12  there.  
         [0126]     Alternatively according to the arrangement, according to  FIG. 25 , the cross section of the flow channel  3  can be scanned using a laser, the laser being continuously or discontinuously sweeping over the cross section, so that this is detected as completely as possible.  
         [0127]     With a higher dust or particle density, it is advantageous to use a microwave as the electromagnetic wave. They are poorly reflected because of their greater wavelength, so that at high particle concentrations, the saturation of the signal is reached substantially later. For example, in coal power stations, in which large amounts of coal are comminuted, microwaves can therefore advantageously be used for mass flow determination.  
         [heading-0128]     Captions for the Figures  
         [0129]    
       FIG. 2 
       
         
           
              At speed V=V1  
              Ordinate: P(t) (reflected power)  
              Abscissa: t (time)  
           
         
       
     
         [0133]    
       FIG. 3 
       
         
           
              At speed V=V2=2×V1  
              Ordinate: P(t) (reflected power)  
              Abscissa: t (time)  
           
         
       
     
         [0137]    
       FIG. 4 
       
         
           
              P(t) (Power)  
           
         
       
     
         [0139]    
       FIG. 7 
       
         
           
              At speed V=V1  
              Ordinate: P(t) Power  
              Abscissa: t (time)  
           
         
       
     
         [0143]    
       FIG. 9 
       
         
           
              At speed V=V2=2×V1  
           
         
       
     
         [0145]    
       FIG. 11 
       
         
           
              Particle  
           
         
       
     
         [0147]    
       FIG. 12 
       
         
           
              Speed=V1; concentration=C1; reflected power=P(t); time (t).  
              At t=0, particle enters the field,  
              At t=T1, particle leaves the field  
           
         
       
     
         [0151]    
       FIG. 13 
       
         
           
              Particle N . . . Particle N+6  
           
         
       
     
         [0153]    
       FIG. 14 
       
         
           
              Particle  
           
         
       
     
         [0155]    
       FIG. 15 
       
         
           
              Speed=V2=2×V1  
              Concentration=C2=C1  
              Reflected power=P(t)  
              time=t  
              At t=0, particle enters the field  
              At t=(T1)/2, particle leaves the field  
           
         
       
     
         [0162]    
       FIG. 16 
       
         
           
              Time window  
           
         
       
     
         [0164]    
       FIG. 17 
       
         
           
              Particle  
           
         
       
     
         [0166]    
       FIG. 18 
       
         
           
              Speed=V1  
              Concentration=C1  
              Reflected power=P(t)  
              Time=t  
           
         
       
     
         [0171]    
       FIG. 19 
       
         
           
              Time window  
             
               FIG. 20 
             
              Particle  
             
               FIG. 21 
             
              Speed=V2=V1  
              Concentration=C2=2×C1  
              Reflected power=P(t)  
              Time=t  
              At t=0, particle enters field  
              At t=T1, particle leaves field  
           
         
       
     
         [0182]    
       FIG. 22 
       
         
           
              Particle N . . . N 43  
              Time window  
           
         
       
     
         [0185]    
       FIGS. 23-24 
       
         
           
              (7, 11)=receiver  
              (5)=microwave transmitter  
           
         
       
     
         [0188]    
       FIG. 25 
       
         
           
              (11, 24, 25, 23)=receiver  
              (21)=laser