Abstract:
Controlling the velocity of a jet of foamed furnish leaving the slice of a pressurized headbox of a paper or a tissue making machine by measuring the density and pressure of a flow of foamed furnish provided by a pump to estimate an atmospheric pressure air content, measuring the pressure of the foamed furnish in the headbox, using the estimated atmospheric pressure air content and the measured pressure in the headbox to estimate the current velocity of said jet of foamed furnish, comparing the estimated current velocity with a target velocity and controlling the pump to move the estimated and target velocities closer to each other. An alternate embodiment controls jet velocity on the basis of comparing estimated and target headbox pressures.

Description:
This application is a continuation of application Ser. No. 07/607,509 filed on Nov. 1, 1990, now abandoned. 
    
    
     BACKGROUND AND SUMMARY OF THE INVENTION 
     The invention relates to the manufacture of fibrous webs in which a foamed fiber-containing slurry is deposited on a moving support to form a continuous web that is further treated to form a product such as tissue paper. 
     In a common method of manufacturing a paper web, an aqueous slurry (furnish) of wood and/or other fibers is discharged through the outlet (slice or slice opening) of a distributor (headbox) onto a continuously moving foraminous support (Fourdrinier wire) or between facing surfaces of two such moving supports in the form of a continuous fibrous web. This web is dried and subjected to subsequent treatments to form the final paper product. The headbox can provide a single jet, or several jets of the same or different furnishes which may or may not merge into a single jet by the time they reach the moving support. 
     One of the important factors in this process is control over the slurry jet or jets discharged from the slice or slices, including control over the jet velocity. Such control can influence significantly important properties of the resulting paper product such as the orientation of the fibers in the web and, consequently, properties such as the tensile ratio of the paper product (longitudinal vs. transverse tensile strength). Such control can be important both in the case of single slice headboxes used to make paper products such as tissue as well as in the case of multiple slice headboxes used to make similar products or stratified products such as webs having a bulk-providing central stratum sandwiched between thinner but stronger outer strata. 
     When a simple slurry of fibers in a liquid is used, control over the jet can be easier than in the case of a foamed slurry where the vehicle in which the fibers are dispersed contains both liquid and gas phases, e.g., when the vehicle is a dispersion of air bubbles in water containing a suitable surfactant. See U.S. Pat. Nos. 4,764,253, 4,086,130 and 3,716,449, which are hereby incorporated by reference. See, also, an advertisement by the Beloit Corporation of Wisconsin in TAPPI, February, 1990 for a headbox producing a jet in the form of multiple thin converging layers. A foamed slurry can be advantageous, e.g., when the slurry contains fibers which have been rendered anfractuous (kinked) by a process such as milling in order to enhance properties of the final product such as bulk and softness. A conventional water furnish tends to relax the fiber kinks at too high a rate but a foamed furnish tends to reduce the exposure of the fibers to water and to maintain their desired anfractuous properties. 
     The unique properties of foamed furnish with respect to fluid parameters such as density, viscosity, compressibility and effects of temperature and pressure, can introduce significant difficulties in the control over the headbox jet or jets. Because relevant properties of foamed furnish are so dependent on parameters such as air content and temperature, strategies for controlling jet velocity that may be suitable for a conventional slurry of fibers in a liquid may not be appropriate for foamed furnishes. One type of control suitable for foamed furnishes is discussed in said U.S. Pat. No. 4,764,253 and uses the output of a magnetic flowmeter and knowledge of the headbox and the slice cross-sectional areas to calculate a control signal for a pump delivering the furnish to the headbox. Properties of frothy liquids are discussed in Van Dyke, M., et al., Annual Review of Fluid Mechanics, Vol.  4 , pp.369-396, 1972 (see, in particular, page 384), but not in the context of paper making. Accordingly, it is believed that a need still remains for a simpler, less expensive and more reliable and effective control, and this invention is directed to meeting such a need. 
     In one non-limiting example, the invention is embodied in system which uses only measurements of the pressure and density of the furnish using neither direct measurement of flow velocity nor direct measurement of volume flow rate of the furnish jet, which are easily and reliably obtained, to calculate the jet velocity and to control the delivery of furnish to the headbox so as to move the calculated jet velocity toward a target velocity. This can be done in accordance with the invention on the basis of comparing the calculated and target jet velocities or on the basis of comparing a calculated headbox pressure with a target headbox pressure. 
     In particular, an exemplary embodiment of the invention periodically measures the density of the foamed furnish fed to the headbox, for example with a radioactive mass sensor, and the pressure of the furnish at two points, one before the headbox and another in the headbox. A computing circuit uses these measurements to estimate. (e.g., calculate) the current velocity of the jet emitted from the headbox. The system then compares the estimated current jet velocity with a target velocity which typically is selected on the basis of the machine or wire speeds. The result of this comparison controls the feeding of furnish to the headbox to reduce the difference between the estimated and target jet velocities. In the alternative, the system can use the measurements to estimate (e.g., calculate) a target headbox pressure and can control the feeding of furnish to bring the current measured headbox pressure closer to the estimated target headbox pressure. 
     The invented system recognizes the influence of the air content and headbox pressure on jet velocity and can optionally use at least one empirical correction factor to enhance the control over jet velocity or headbox pressure. The relationships between measurements and controlled parameters which the invention uses are believed to be particularly efficacious in accounting for the unique properties of foamed furnish in paper making. The invention is believed to be useful for single jet systems, for systems using multiple jets of the same furnish and for systems using stratified jets of different furnishes. One preferred use of the invention is in a paper making line using foam forming and surfactant recovery techniques discussed in copending commonly owned patent applications Ser. No. 07/599,149 filed on Oct. 17, 1990 in the name of John H. Dwiggins and Dinesh M. Bhat and entitled Foam Forming Method and Apparatus, now abandoned and Ser. No. 07/598,995 filed on Oct. 17, 1990 in the name of Dinesh M. Bhat and entitled Recovery of Surfactant From Paper Making Process, now abandoned. However, the invention is not limited to use in such a paper making line. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a simplified schematic illustration of an exemplary embodiment of the invention controlling jet velocity on the basis of a comparison of a currently calculated jet velocity and a target velocity. 
     FIG. 2 illustrates a relationship between the density of a foamed furnish and the furnish pressure at different air content fractions of the furnish in an exemplary process embodying the invention. 
     FIG. 3 illustrates a relationship between the air volume fraction in the furnish at pressure and the furnish pressure at different air content fractions at atmospheric pressure in an exemplary process embodying the invention. 
     FIG. 4 is a flow chart of main steps in the process illustrated in FIG.  1 . 
     FIG. 5 a simplified schematic illustration of another exemplary embodiment of the invention controlling jet velocity on the basis of a comparison of a currently calculated target headbox pressure and a currently measured headbox pressure. 
     FIG. 6 is a flow chart of main steps in the alternate process illustrated in FIG.  5 . 
    
    
     DETAILED DESCRIPTION 
     Referring to FIG. 1, an exemplary embodiment of the invention comprises a headbox  10  which has an inlet  12  for receiving foamed furnish  11  and a slice  14  for emitting a jet  16  of foamed furnish onto a continuously moving support (wire)  18 . The source of furnish  11  comprises a silo  20  which supplies furnish to a fan pump  22  via a suitable conduit. Pump  22  via a suitable conduit delivers furnish under pressure to a pressure screen  24 , which in turn delivers screened furnish via a suitable conduit to inlet  12  of headbox  10 . A density transmitter  26 , which can comprise a radioactive mass sensor and a suitable circuit for generating and transmitting a measurement signal in a form suitable for use in a computer calculation, measures the density of furnish  11  at pressure as pumped by fan pump  22 , at a point between pressure screen  24  and headbox  10 . The radioactive mass sensor can be of the type which measures the attenuation that penetrating radiation suffers in passing through the material of interest (foamed furnish) as a measure of the mass density of the material. A first pressure transmitter  28  measures the pressure of the furnish pumped by fan pump  22 . Pressure transmitter  28  can comprise a pressure gauge and a suitable circuit for generating and transmitting a measurement signal suitable for use in a computer calculation. Transmitters  26  and  28  preferably are within a few feet downstream from pump  22  and pressure screen  24 , but could be at other locations. A second pressure transmitter  30 , which can be similar to transmitter  28 , measures the pressure of the furnish in headbox  10 , at a location downstream from tube bank  10   a  but in the wider part of the converging portion, where the velocity of furnish  11  is relatively low. The density and pressure measured by transmitters  26  and  28  are supplied to a calculating circuit  32  which calculates the volumetric air content fraction of the furnish at atmospheric pressure (α atm ), using for the purpose a relationship which is discussed in greater detail below. A jet velocity calculator circuit  34  uses the atmospheric pressure air content fraction α atm  calculated by circuit  32  and the pressure of the furnish in the headbox as measured by transmitter  30  to calculate an ideal current jet velocity (V J(I) ) and then corrects V J(I)  with an empirically derived correction factor (C 1 ) which is specific to the installation, e.g., to a particular headbox or a class of headboxes, to derive a calculated current velocity (V J ) of jet  16 , using for the purpose other relationships which are discussed in greater detail below. A comparator circuit  40  compares the current calculated jet velocity V J  with a target jet velocity V J(T)  provided from a source  36  and outputs a comparison result which is used as an input to a pump RPM control  38  which controls fan pump  22 . In response to this control signal from control  38 , pump  22  increases or decreases the rate at which it delivers furnish to headbox  10  as needed to reduce the difference between the calculated and target jet velocities V J  and V J(T) . The calculations and control discussed above are carried out at frequent intervals (e.g., at intervals in the range of 1 to 30 seconds. preferably once per second), to keep the calculated and target velocities close to each other. Calculating circuits  32  and  34  and comparator  48  can be implemented in the form of a general purpose digital computer programmed to carry out the steps described in this specification, or partly or fully in the form of special purpose circuits or ASICs (application-specific integrated circuits) carrying out the specified calculations. 
     Circuit  32  calculates the current volumetric air content fraction at atmospheric pressure α atm  in accordance with the invention from the relationship: 
      ρ=ρ liq {[(1−α atm ) p   abs ]/[(1−α atm ) p   abs +α atm   p   atm ]}  (1) 
     where 
     ρis the density of the furnish as measured by transmitter  26 ; 
     ρ liq  is the density of the liquid phase of the furnish, which is known or can be measured once or periodically and can be stored as a constant in circuit  32 ; 
     p abs  is the absolute pressure of the furnish downstream from pump  22 . It equals the sum of the pressure (p) as measured by first pressure transmitter  28  relative to the atmospheric pressure and p atm  defined below; 
     α atm  is the current volumetric air content fraction at atmospheric pressure of the furnish leaving pump  22 , expressed as a fraction of unity, as calculated by circuit  32 ; 
     p atm  is the absolute atmospheric pressure, which can be stored as a constant in circuit  32 . This constant can be updated from time to time, e.g., once or several times a day or week as needed. As an alternative, the output of an atmospheric pressure transmitter can be provided to circuit  32  for use in calculating the current α atm . 
     The variables and constants in expression (1) as well in the expressions discussed below, can be in any self-consistent system of units. 
     FIGS. 2 and 3 illustrate exemplary relationships between the relative pressure (p) as measured by transmitter  28  and the density (ρ) of foamed furnish  11  and the air volume fraction at pressure for different atmospheric pressure air volume fractions α atm  for an exemplary embodiment of the invention. 
     After circuit  32  calculates the current volumetric air content fraction at atmospheric pressure α atm  as discussed above, circuit  36  calculates the current ideal jet velocity V J(l)  in accordance with the relationship 
     
       
         ( V   J(I) ) 2 =2{( p   HB(abs)   −p   atm )/ρliq +gΔh+ [(α atm   p   atm )/ρ liq (1−α atm )][ln (p HB(abs)   /p   atm )}/[1−(ρ 2   2   A   2   2 )/(ρ 1   2   A   1   2 )]  (2) 
       
     
     where 
     p HB  is the pressure relative to the atmospheric pressure in headbox  10  as measured by second pressure transmitter  30 ; 
     p HB(abs)  is the absolute pressure in headbox  10 , derived in circuit  34  as the sum (p HB +p atm ); 
     p atm  is the absolute atmospheric pressure, derived as earlier noted in circuit  32  and supplied thereby to circuit  34 ; 
     ρ liq  is the density of the liquid phase of the furnish, which is known or can be measured once or periodically and can be stored as a constant in circuit  34 ; 
     g is acceleration due to gravity; 
     Δh is the elevation difference between pressure transmitter  30  and jet  16  (&gt;0 when jet  16  is at a lower elevation than pressure transmitter  30 ); 
     α atm  is the current volumetric air content fraction at atmospheric pressure of the furnish downstream from pump  22 , in volume fraction of unity, as provided from circuit  32 ; 
     ρ 1  is the density of furnish  11  at the entrance to the converging part of headbox  10 , which can be calculated from a special case of equation 1 for which p abs =p HB(abs)  and 
     
       
         ρ 1 =ρ liq {[(1−α atm ) p   HB(abs) ]/[(1−α atm ) p   HB(abs) +α atm   p   atm ]}; 
       
     
     ρ 2  is the density of the furnish leaving the slice (i.e., at atmospheric pressure), which also can be calculated from a special case of equation 1 for which p abs =p atm  and ρ 2 =ρ liq (1−α atm ); 
     A 1  is the known area at the entrance to the converging part of headbox  10 , which can be stored as a constant in circuit  34 ; and 
     A 2  is the area of the slice of headbox  10 , which can be measured and stored as a constant in circuit  34 . 
     The last term in square brackets of expression (2) for V J(I)  is close to unity and usually may be omitted in practicing the invention. Then, expression (2) reduces to 
     
       
         ( V   J(I) ) 2 =2{( p   HB(abs)   −p   atm )/ρ liq   +Δh+[ (α atm   p   atm )/ρ liq (1−α atm )][ln ( p   HB(abs)   /p   atm )}  (3) 
       
     
     However, expression (2) can be used instead of expression (3) in case the last term in square brackets of expression (2) proves to be significantly different from unity in a particular implementation of the invention. 
     Circuit  34  then converts the current ideal jet velocity V J(I)  calculated as described above to a current calculated jet velocity V J  in accordance with the relationship 
     
       
           V   J   =C   1   V   J(I)   (5) 
       
     
     where C 1  is a correction factor. 
     The correction factor C 1  is determined empirically for a particular implementation of the invented system (or at least for a particular headbox or class of headboxes). In a particular experimental system of the assignee embodying the invention 
     
       
           C   1   =a+b ( V   J(I)   −c )  (5) 
       
     
     where a, b and c are coefficients which for a particular experimental embodiment of the invention have such values that expression (5) becomes 
     
       
           C   1 =1.000+0.000246( V   J(I) −1510)  (6) 
       
     
     Note that units of meters/min are used for V J(I)  in equation 6. 
     This relationship was determined empirically by plotting the actual jet velocity determined in an experimental system of the assignee embodying the invention versus the calculated ideal jet velocity V J(I)  and curve-fitting expression (6) to the plot. Of course, a number of actual velocities and corresponding terms V J(I)  were used to construct the plot. Each actual velocity was determined as the ratio of the volumetric flow rate at the slice of the headbox and the measured flow area of the slice. The volumetric flow rate at the slice was determined by using a magnetic flow meter to measure the volumetric flow rate in the headbox approach pipe (i.e., near the location of pressure transmitter  28  in FIG. 1) and then correcting (using Equation 1) for the density change that occurs during transit through the headbox to the slice, at steady state conditions. The magnetic flow meter used for this purpose was of the type discussed in said U.S. Pat. No. 4,764,253. The correction factor C 1  need be found only once for a particular installation (except for possible infrequent recalibrations) and could be different for different installations. However, it is believed that it could be the same or substantially similar for installations using the same model headbox or headboxes which have similar properties. 
     Comparator  40  compares the current calculated jet velocity V J  which has been derived as discussed above, with a target jet velocity V J(T)  provided from source  36 . Target velocity V J(T)  typically is set by the operator and typically is related to the velocity of wire  18 . As a non-limiting example, if the wire velocity is 1600 m/min, the operator may set V J(T)  to 1500 m/min. In general, by definition 
     
       
           V   J(T)   =V   w   +ΔV   (7) 
       
     
     where 
     V W  is the wire velocity; and 
     ΔV is a positive or negative increment which the operator sets as the desired difference between the target jet velocity and the wire velocity (e.g., ΔV=(−100) in this example. 
     The output of comparator  40  thus depends on the difference between the current calculated jet velocity V J  and the target jet velocity V J(T) , and in this embodiment this difference signal is the control signal delivered to pump RPM control  38  in order to reduce the difference between the compared velocities. Typically, pump  22  is a positive displacement pump and the flowrate at its output tends to be close to directly proportional to the pump RPM. 
     The system carries out control cycles of calculating the current velocity V J , comparing it with the target velocity V J(T)  and providing a corresponding control signal to pump RPM control  38 , sufficiently frequently to maintain the actual jet velocity steady and close to the target velocity. Control cycles which take place at intervals from about 1 to about 30 seconds are believed to be suitable for typical embodiments of the invention. The currently preferred frequency is once per second. Factors such as the properties of a particular installation and the preference of the operator can determine the particular cycle frequency, and could suggest even more frequent or less frequent control cycles. 
     The main steps of the invented process are illustrated in the flow chart of FIG.  4 . At step  50  the system of FIG. 1 stores the indicated constants. However, as earlier noted, some of these values can be measured and supplied as variables rather than as constants. At step  52  the system measures the furnish pressure downstream from pump  22 , the density of this furnish and the furnish pressure in the headbox, for example by using transmitters  26 ,  28  and  30 . At step  54  the system calculates α atm  the current volumetric air content fraction at atmospheric pressure of the furnish downstream from pump  22 , for example in accordance with equation 1 above. At step  56  the system calculates V J(J) , the current ideal jet velocity, for example in accordance with equation 3 above. At step  58  the system calculates C 1 , the empirical correction factor, for example in accordance with equation 6 above. At step  60  the system calculates V J , the current jet velocity, for example in accordance with equation 4 above. At step  62  the system compares the calculated current jet velocity and the target jet velocity, and at step  64  generates a pump control signal based on the result of the comparison. At step  66  the control signal is applied to pump  22 , to change its RPM such that the calculated jet velocity would move closer to the target jet velocity. After step  66 , the process returns to step  52  to start another control cycle, and the control cycles repeat as long as control over the jet velocity is desired or until there is some reason to discontinue the process. 
     The process steps can be implemented in the form of the circuits illustrated in FIG.  1 . However, it is preferred to carry out the calculations discussed above by means of a general purpose computer or, preferably, an industrial process control computer which usually is a part of a paper making installation, through programming such a general purpose or industrial computer to carry out the calculations discussed above and to provide a control signal which can be used as an input to pump RPM control  38  either directly or after suitable conditioning. 
     In an alternative embodiment of the invention, illustrated in FIG. 5, the process is similar in principle but derives the control signal by comparing, e.g., in a comparator  44 , the actual pressure p HB  in headbox  10 , as measured by transmitter  30 , with a current target pressure p HB(T)  calculated in circuit  42  in accordance with relationships developed as a part of the invention. The target jet velocity is provided by a source  46  which, in the alternative, can provide the wire speed V W  and the increment ΔV. Components of FIG. 5 which serve the same function as in FIG. 1 are designated by the same reference numerals. Note that the headbox pressure measurement p HB  in this case is supplied to both of circuits  34  and  42 , and that the calculated value α atm  in this case also is supplied to both of circuits  34  and  42 . 
     The alternate embodiment illustrated in FIG. 5 carries out a process whose main steps are illustrated in the flow chart of FIG.  6 . The following notation is used in the description below of FIG. 6, where the units assumed for each variable are stated. Other units can be used if care is taken to appropriately alter the numerical constants: 
     V J  is the calculated current calculated velocity of jet  16 , e.g., in m/min; 
     V J(T)  is the target velocity of jet  16 , e.g., in m/min; 
     ΔV is an operator-specified velocity difference, defined as the difference (V J −V W ), e.g., in m/min; 
     V W  is the velocity of the support (wire)  18 , e.g., in m/min, supplied in the same manner as in FIG. 1; 
     p HB  is the current pressure relative to the atmospheric pressure in headbox  10 , e.g., in bar, supplied as in Fig. 1; 
     p HB(abs)  is the current absolute pressure in headbox  10 , e.g., in bar, derived in circuit  42  as the sum (p HB +p atm ); 
     p HB(T)  is the target pressure in headbox  10 , e.g., in bar, derived in circuit  42 ; 
     p atm  is the atmospheric pressure, e.g., in bar (e.g., 1.01325 bar), supplied as in FIG. 1; 
     ρliq is the density of the liquid phase of furnish  11 , e.g., in kg/m 3  (e.g., approx. 1000 kg/m 3  when the liquid phase is water), supplied as in FIG. 1; 
     V J(I)  is the current calculated ideal velocity of furnish jet  16 , e.g., in m/min (V J =C 1 V J(I) ), calculated as in FIG. 1; 
     g is acceleration due to gravity, e.g., in m/sec 2 ; 
     Δh is the elevation difference, e.g., in meters, between pressure transmitter  30  and jet  16  (&gt;0 when jet  16  is at a lower elevation than pressure transmitter  30 ); 
     α atm  is the volumetric air fraction of the furnish at atmospheric pressure (i.e., if the air content of furnish  11  at atmospheric pressure is 62% by volume, α atm  is 0.62), calculated as in FIG. 1; 
     C 1  is a first empirically derived correction factor, derived as in FIG. 1, e.g., for a particular experimental installation of the assignee is, as in equation (6) above, C 1 =1.000+0.000246(V J(I) −1510); 
     C 2  is a second empirically derived correction factor, derived in a manner similar to that for C 1 , e.g., the general expression used in the curve-fitting process is 
     
       
           C   2   =a′+b′ ( V   J(T)   −c′ )  (8) 
       
     
      and, for the assignee&#39;s particular experimental installation 
     
       
           C   2 =1.000+0.0001887( V   J(T) −1510);  (9) 
       
     
     S is the slope of the V J   2  vs. p HB  curve (i.e., (dV J   2 )/dp HB ), derived in circuit  42  as a numerical approximation of the indicated derivative, e.g., in (m 2 /min 2 )/bar. 
     Referring to FIG.  6 : 
     At step  100  the system provides the indicated constants. Note that either the target jet velocity can be stored as a constant or there can be stored the constants ΔV and V W . 
     At step  102 , calculator  34  calculates 
     
       
           p   HB(abs)   =p   HB+   p   atm   (10) 
       
     
     where, p atm  can be 1.01325 bar. 
     Unless the target jet velocity has already been provided at step  100 , at step  104  source  46  calculates the target jet velocity in accordance with expression (7) above, i.e., V J(T) =V W +ΔV, where ΔV is provided to step  100  by the operator and V W  is either specified by the operator or is measured by a suitable transducer and supplied to step  100 . 
     At step  106  calculator  32  calculates αatm, e.g., in accordance with expression 1 as in FIG.  1 . 
     At step  108 , calculator  34  calculates the current ideal jet velocity V J(I) , e.g., in accordance with 
     
       
           V   J(I)   2 =7200{(10 5   p   HB )/ρliq +gΔh+[ (10 5 α atm   p   atm )/ρ liq (1−α atm )][ln (p HB(abs)   /p   atm )}  (11) 
       
     
     using in this step the current value of α atm  calculated in step  106 . Note that equation 11 is a special case of equation 3, in that additional numerical factors are included (7200, 10 5 ) for use with units of m/min for V J(I) ; bar for p HB , p atm  and p HB(abs) ; and kg/m 3  for ρ liq . 
     At step  110  calculator  42  calculates the correction factor C 1 , e.g. in accordance with expression (6) above as in FIG. 1, i.e., in accordance with C 1 =1.000+0.000246(V J(I) −1510), and calculates the second correction factor C 2  in accordance with expression (9) above. 
     At step  112 , calculator  42  calculates the current jet velocity V J , e.g., in accordance with expression (4) above. 
     At step  114 , calculator  42  calculates the slope S in accordance with 
     
       
           S=[ 7.2(10) 8   C   2   2 /ρliq]{1+[α atm   p   atm ]/[(1−α atm ) p   HB(abs) ]}  (12) 
       
     
     At step  116  calculator  42  calculates the current target (setpoint) pressure p HB(T)  in headbox  10  in accordance with 
     
       
           p   HB(T)   =p   HB +( V   J(T)   2   −V   J   2 )/ S   (13) 
       
     
     At step  118 , comparator  44  compares the current calculated target pressure p HB(T)  with the measured headbox pressure p HB . 
     At step  120 , comparator  44  generates a pump control signal as a function of the comparison at step  118 . 
     At step  122 , control  38  controls pump  22  to bring the calculated target pressure closer to the measured pressure in the headbox, thereby bringing the calculated jet velocity closer to the target velocity. 
     After step  122 , the process returns to step  102  to start another control cycle, and the control cycles repeat as long as control over the jet velocity is desired or until there is some reason to discontinue the process. The cycles repeat at a suitable frequency, e.g., repeat after an interval in the range of about 1-30 seconds, preferably once per second. 
     The FIG. 6 process steps can be implemented in the form of the circuits illustrated in FIG.  5 . However, as in the case of FIG. 1, it is preferred to carry out the calculations discussed above by means of a general purpose computer or, preferably, an industrial process control computer which usually is a part of a paper making installation, through programming such a general purpose or industrial computer to carry out the calculations discussed above and to provide a control signal which can be used as an. input to pump RPM control  38  either directly or after suitable conditioning. 
     Each of the processes illustrated in FIGS. 4 and 6 is a preferred embodiment of the invention. Both have been implemented on experimental basis, and both are believed to provide unexpectedly superior results as compared with the known prior art. Of course, many variations of the particular examples discussed above are possible in accordance within the principles of the invention, the scope of which is defined by the appended claims. 
     The following components are believed to be suitable for the exemplary embodiments discussed above: 
       10  Headbox: Beloit Low convergence Concept III Stratified Headbox; 
       18  Wire: Appleton Wire—84M; 
       20  Silo: Vented fiberglass tank; 4 ft. diameter×10 ft. high (active foam depth about 6 ft.); 
       22  Fan Pump: Dresser External Screw—Twin Screw Positive Displacement Pump (NJHP); 
       24  Pressure Screen: Black-Clawson P24; 
       26  Density Transmitter: Kay-Ray Model No. 3680AAE200C2, calibrated 0 to 1.0 SGU; 
       28  First Pressure Transmitter: PMC Model No. PT-EL, calibrated 0-100 PSIG; 
       30  Second Pressure Transmitter: Rosemount Model No. 3051CG4A22AlAB4, calibrated 0-60 PSIG; 
       32  Calculator: Microprocessor-based distributed process control system Measurex Model 2002ET programmed to carry out the processes discussed above; 
       34  Same as  32 ; 
       36  Same as  32 ; 
       38  Same as  32 , but adds A-C Variable Speed Drive, Reliance 250HP; 
       40  Same as  32 . 
     It is noted that the parameter α atm  derived in each process cycle by calculator  32  can be used in another control loop, where a comparator (not shown) compares the current value of α atm  with a target value which can be stored as an operator-selected constant, and in response produces a control signal to control the feeding of surfactant to the furnish delivered to pump  22  to move the calculated value of α atm  closer to the target value. 
     The invention is sufficiently broad to be implemented in ways which are different from the examples set forth above but still are within the scope of the invention defined by the appended claims.