If I understand correctly, through one of the branches of the T junction enters hot water, through a second branch enters cold water, and through the third branch exits the mixed water. I suppose that you want to specify the momentum ratio for the two inlet branches. As far as I know, it is not possible to specify that ratio directly. However, it is possible to specify the flow rates and, as long as you impose one flow rate and you know the geometry of the T junction and the variation of water density with temperature, I think that you can calculate the other flow rate based on the following relationship: (rho1 x Q12 / S1) / (rho2 x Q22 / S2) = kH, where rho denotes water density, Q denotes volume flow rate, S denotes the cross-sectional area of an inlet branch, kH denotes the desired momentum ratio, and indices 1 and 2 denote the two inlet branches.
If I understand correctly, through one of the branches of the T junction enters hot water, through a second branch enters cold water, and through the third branch exits the mixed water. I suppose that you want to specify the momentum ratio for the two inlet branches. As far as I know, it is not possible to specify that ratio directly. However, it is possible to specify the flow rates and, as long as you impose one flow rate and you know the geometry of the T junction and the variation of water density with temperature, I think that you can calculate the other flow rate based on the following relationship: (rho1 x Q12 / S1) / (rho2 x Q22 / S2) = kH, where rho denotes water density, Q denotes volume flow rate, S denotes the cross-sectional area of an inlet branch, kH denotes the desired momentum ratio, and indices 1 and 2 denote the two inlet branches.