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Critical flow Venturi nozzles (toroidal, cylindrical, convergent–divergent, or C–D) nozzles) have discharge coefficients predicted through numerical and experimental investigations. Unfortunately, the imprecision of the critical-flow Venturi nozzle design makes it impossible to study the influence of inlet curvature Rc on the discharge coefficient in the laminar boundary layer area. This study examines how the inlet curvature affects the discharge coefficient, or Cd, in the laminar boundary layer area of a critical-flow Venturi nozzle with a cylindrical throat and toroidal shape. The inlet curvature has a range from one throat diameter to three and a half throat diameters. This range of inlet curvatures was obtained by throat the inlet of a high-precision nozzle that was primarily compliant with ISO 9300. The C-D nozzle showed the impact of the convergence angle on the discharge coefficient. The results showed that the highest discharge coefficient occurs at Rc= 2dth for a throat diameter of 0.5588 mm, whereas for dth= 3.175 mm, it occurs at Rc= 2.5dth for toroidal nozzle. For this C-D nozzle, the highest discharge coefficient was observed to occur at a curvature of angle of 10°. Moreover, Cd increases significantly with increase of inlet stagnation pressure but with a small throat diameter.