# Calculation Methods - Inline Nozzle

The user can choose from two pressure loss models in FluidFlow, the method as set out in ISO 5167-3 and the "Long Radius Model". The pressure loss is determined from the following equation: ΔP = Δw [(1 - β 4)0.5 - C1 β 2] / [(1 - β 4)0.5 + C1 β 2]. where: β is the nozzle diameter "beta" ratio (β = d/D where "d" is the nozzle bore diameter and "D" is the upstream internal pipe diameter). As a reference guide, a beta ratio of 0.45 indicates that the nozzle bore diameter is 45% of the pipe inside diameter. Guidelines on design beta ratios are available in ISO 5167 & Perry's Chemical Engineering Handbook. Published literature makes reference to keeping the design beta ratio to within the range of 0.15 to 0.68 to develop the best performance from the nozzle. If an inline nozzle is solved in FluidFlow and the calculated beta ratio is outside of this range, a warning message is enunciated to prompt the designer into reviewing the design conditions. Beta ratios outside of this range are noted to introduce flow system errors and other potential flow problems. When sizing inline nozzles, ensure the right pressure drop range, maximum flow and optimum beta ratio for best performance of the nozzle. Note, beta ratio and pressure drop for an inline nozzle are related and as such, altering one affects the other. Δw is the differential pressure. C1 is the discharge coefficient. The actual mass flow rate through the nozzle is diminished from the theoretical value by the existence of a fluid boundary layer. Therefore, a "discharge coefficient" (C1) is applied to the theoretical value required to obtain the actual flow rate. The discharge coefficient (C1) for ISA 1932 nozzles is determined from the following equation: C1 = 0.99 - 0.2262 β4.1 - (0.00175 β2 - 0.0033 β4.15) (106/Re)1.15. For long radius nozzles, the discharge coefficient (C1) is determined from the following equation: C1 = 0.9965 - 0.006653 * β0.5 * (106/Re)0.5. FluidFlow automatically calculates the losses at corner tap points and the gas expansibility correction factor as part of the solution routines.