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<br />25 <br /> <br />emphasized. Model calculations will now be done in the J and K domains rather <br /> <br />than the mass scales in which the particulate equations have been previously <br /> <br />expressed. <br /> <br />This transformation is accomplished via the density function transform <br />'" <br /> <br />f(J)dJ = f(x) dx (eq. 26) <br /> <br />Substituting into the expressions for x(J) and y(K) yields the following <br /> <br />relations between particulate number density functions in the J, K, and mass scales. <br /> <br />f(J) = 3 x(J) f(x) <br />Jo <br /> <br />(eq. 27) <br /> <br />f(K) = 3 y(K) f(y) <br />Ko <br /> <br />(eq. 28) <br /> <br />From here the conversion of particulate continuity equations to the J and K scales <br /> <br />is straightforward. For example, the transformed conservation equation for liquid <br /> <br />hydrometers is: <br /> <br />~-M. = - [W + V(J)] ~f(J). _ f(J) afpv(J)] <br />d t OZ P OZ <br /> <br />8 K J <br />+ 1.. rK f(J)] _ P f(J) + 0 <br />az l p z 7 3x(J) <br /> <br />~ [xf(J)] <br />a J <br /> <br />+ A f (J) + C 1 - R 1 + B 1 + B 2 - F 1 <br /> <br />(eq. 29) <br />