About density and pressure

Dear friends,
I am modeling Laplace drop test by a Multicomponent SC code. In this test, a heavy fluid is immersed in a lighter flow and the calculated pressure jump between inside and outside the drop is measured. Based on Laplace law, pressure jump should be prpoportional to 1/R which R is the radius of the drop. Boundary condition of all sides of the domain is periodic. In my code, tau, physical viscosity (vr) and physical delta x are inputs. physical delta t is calculted from:
vr=1/3*(tau-1/2)*delta x^2/delta t
and C=delta x/delta t is physical lattice speed.

In the code, LB units formulation is applied and at the end of the calculation cycles, results are given in physical units based on the following relations:

for velocity (u) -------> ur=uLC
for pressure ยง------> Pr=rho/3

Now when I choose tow different values of tau while all other conditions is the same, the code calculate two different values of delta t and accordingly two different pressure values which rationally is wrong. Can anyone help me?