Approximate solution for discharge coefficient of the sonic nozzle with surface roughness

Sonic nozzle is widely used in the flow measurement and control. Nowadays, it has been applied to higher Reynolds number flow increasingly. The effect of surface roughness on discharge coefficient of the sonic nozzle should be discussed. An approximate analytic solution for discharge coefficient of the sonic nozzle with surface roughness was proposed in detail. The determination of this coefficient was based on universal logarithmic velocity-distribution law and the principle of equivalent velocity profile. Although there are some apparently approximations, this algebraic method accurately predicts the discharge coefficient of the sonic nozzle with surface roughness in Reynolds number range from 104 to 109, a relative equivalent roughness range of 10−6 to 10−2. Some experiments of sonic nozzle conducted by others showed agreement with present algebraic method. Besides, the agreement between this method and the corresponding exact numerical calculation is also good. The present method provides an excellent tool to deeply investigate the roughness effect and promote further improvement of the standard.