Measurement with Quadrant Nozzles of Air Flow at Low Reynolds Numbers

The accurate measurement of air discharge at low Reynolds numbers is important in many cases for chemical engineering researches. The quadrant nozzle is recommended by Koennecke as one of the most suitable fluid meters for low Reynolds numbers, because the coefficient of discharge can be maintained constant with low Reynolds numbers.He gave the coefficient of discharge for quadrant nozzles having optimum values of the ratios r/d and m as shown in Fig. 6, as a result of his extensive experiments. However, owing to the fact that he used a steel pipe 40mm in diameter and incompressible fluid such as water or oil, it is questionable whether the results obtained by him are valid for the measurement of air flow through a pipe other than 40mm in diameter, because the effect of pipe diameter on the discharge coefficient may not be negligible. Furthermore, at present, no information is available on the expansion factors for air through quadrant nozzles.Hence, the authors made a series of experiments on the quadrant nozzles with 1-in, and 2-in. steel pipes.First, the discharge coefficient for a certain quadrant nozzle, No.1-St, was determined directly yb substituting water for air flowing through the nozzle, and the expansion factor was evaluated indirectly from tests with three air nozzles as shown in Fig. 2.Finally, others as shown in Table 1 were calibrated individually with No.1-St.From the experimental results, it may be concluded that: -i) The coefficient of discharge for quadrant nozzles increases with an increase of the ratios m and r/d, but appears to decrease when r/d exceeds a certain limiting value.ii) The agreement of the discharge coefficient with Koennecke's data is to some extent satisfactory with both the quadrant nozzles, No.1-5 and No.2-0, but the coefficient, as pointed out by Jorrisen et al., can not be maintained constant with Reynolds numbers quite as low as those asserted to have been reached by Koennecke.iii) The expansion factor for air, although under the influence of m, is almost independent of r/d.iv) The size of pipe diameter, as observed by Koennecke, affects the coefficient of discharge more or less, and at the same time changes the expansion factor.v) Values of the discharge coefficient and the expansion factor for these devices are between the values for standard orifices and those for standard nozzles under identical conditions.vi) A deviation from the prescribed values of m and r/d, which is due to the manufacturing procedure, causes changes within 0.4% in the discharge coefficient.Furthermore, another experiment was conducted as follows. Two quadrant nozzles were installed in such a manner that the flat surface of the nozzle plate might face upstream, unlike in normal installation, and the authors succeeded in determining, as the result, the values of the discharge coefficient and the expansion factor.