Viscous fluid flow measurement using a differential pressure measurement and a SONAR measured velocity

An apparatus for determining a parameter of fluid flow within a piping system, comprising:

• a fluid flow meter operable to determine the velocity of the fluid flow within the piping system;
• a differential pressure meter operable to determine a measured difference in pressure within the fluid flow within the piping system;
• a processor adapted to receive input including an estimated Reynolds number of the fluid flow, and to determine a calculated difference in pressure value using a model which relates the calculated difference in pressure value to a measured fluid flow velocity and the estimated Reynolds number of the fluid flow, and to determine a degree of inaccuracy of the estimated Reynolds number using the measured difference in pressure and the calculated difference in pressure, and to iteratively adjust the estimated Reynolds number, determine the calculated difference in pressure, and determine the degree of inaccuracy until the degree of inaccuracy is within an acceptable range, and to determine the parameter of the fluid flow within the piping system using the adjusted Reynolds number.