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Rotational velocityFigure 3 shows the effect of flow rate, nozzle diameter and number of nozzles on the rotational velocity of water in a circular tank. The results indicate that the rotational velocity increases with increasing flow rates and deceasing nozzle diameter. It could be seen that, the rotational velocity decreased from 10.1 to 5.0 cm s−1, when the nozzle diameter increased from 10 to 20 mm, respectively for 5 nozzles used, and it decreased from 5.1 to 4.0 cm s−1, when the nozzle diameter increased from 10 to 15 mm, respectively, for 10 nozzles used with 5 m3 h−1 flow rate. At 15 m3 h−1, the rotational velocity was decreased from 23.5 to 17.5, 12.0 to 7.5, 10.0 to 6.9, 7.6 to 4.7 and 5.9 to 4.0 cm s−1 when the nozzle diameter increased from 10 to 20 mm, respectively, for 5, 10, 15, 20 and 25 nozzles, respectively. The results also indicate that when the nozzle diameter increased from 20 to 25 mm, the rotational velocity decreased from 19.0 to 16.5, 12.0 to 10.0 and 7.1 to 5.5 cm s−1 for 3, 6 and 9 nozzles, respectively, with 15 m3 h−1 flow rate.Figure 3Effect of flow rate, nozzle diameter and number of nozzles on the rotational velocity of water in a circular tank.Full size imageAt 30 m3 h−1 flow rate, the highest value of the rotational velocity was 33.5 cm s−1 was found for 5 nozzles and 10 mm nozzle diameter. While, the lowest value of the rotational velocity was 7.3 cm s−1 was found for 25 nozzles and 25 mm nozzle diameter. At 45 m3 h−1 flow rate, the rotational velocity ranged from 11.0 to 49.9 cm s−1 for all treatments under study.At 60 m3 h−1 flow rate, the rotational velocity deceased from 61.0 to 50.1, 47.7 to 34.0, 36.3 to 23.0, 23.5 to 17.5, 21.0 to 15.0 and 17.0 to 11.5 cm s−1 when the nozzle diameter increased from 10 to 20 mm, respectively at 5, 10, 15, 20, 25 and 30 number of nozzles. The results also indicate that, when the nozzle diameter increased from 20 to 25 mm, the rotational velocity decreased from 56.0 to 47.0, 43.0 to 33.0, 27.0 to 22.0 and 19.0 to 16.5 cm s−1 at 3, 6, 9 and 12 nozzles, respectively.At 75 m3 h−1 flow rate, the rotational velocity deceased from 60.9 to 49.1, 48.4 to 38.0, 39.0 to 30, 31.8 to 23.0, 23.5 to 17.5 and 22.0 to 15.0 cm s−1 when the nozzle diameter increased from 10 to 20 mm, respectively for 5, 10, 15, 20, 25 and 30 nozzles, respectively. The results also indicate that, when the nozzle diameter increased from 20 to 25 mm, the rotational velocity decreased from 50.48 to 43.0 to 38.5, 33.0 to 27.5 and 23.5 to 22.0 cm s−1 for 3, 6, 9 and 12 nozzles, respectively.The results also indicate that the highest values of the rotational velocities were 10.1, 23.5, 33.5, 49.9, 60.9 and 61.0 cm s−1 were found for 5 nozzles and 10 mm nozzle diameter at 5, 15, 30, 45, 60 and 75 m3 h−1 flow rate, respectively. While, the lowest values of the rotational velocities were 4.0, 7.5 and 11.5 cm s−1 for 25 nozzles and 15 mm nozzle diameter at 5, 15 and 30 m3 h−1 flow rate, respectively. They were 11.5 and 15 cm s−1 were found for 30 nozzles and 15 mm nozzle diameter at 60 and 75 m3 h−1 flow rate, respectively. The velocity of water obtained seemed to be in the recommended range of safe and proper velocity for fish according to12. Due to it is effective compromise to allow heavy solids settle rapidly, yet sufficiently fast to create “good” hydraulics. Timmons and Youngs18 mentioned that the water velocity needed to maintain self-cleaning properties ranges from 3 to 40 cm s−1 varying greatly according to the physical properties of the biosolids. When fish swims at lower speed than its optimal, a large amount of energy will be used for higher spontaneous activity such as aggression. In contrast, when fish swim at higher speed than optimal, they become stressful, unstable, increase lactate production and fatigue6.Multiple regression analysis was carried out to obtain a relationship between the rotational velocity of water as dependent variable and different both of flow rate and nozzle diameter as independent variables. The best fit for this relationship with coefficient of determination of 0.95 and an error of 1.06% is in the following form:-$$ RV = 6.97 + 0.41Q – 0.19Dquad {text{R}}^{{2}} = 0.95 $$
(3)
where RV is the rotational velocity of water, cm s−1, Q is the water flow rate, m3 h−1, D is the nozzle diameter, mm.This equation could be applied in the range of 5 to 75 m3 h−1 water flow rate and from 10 to 25 mm of nozzle diameter.Impulse force of waterFigure 4 shows the effect of flow rate, diameter and number of nozzles on the impulse force of water in a circular tank. The results indicate that the impulse force of water increases with increasing flow rates and deceasing nozzle diameter and number of nozzles. It could be seen that, the impulse force of water decreased from 5.1 to 1.7 N, when the number of nozzles increased from 5 to 15, respectively at 10 nozzle diameter, and it decreased from 2.3 to 1.2 N, when the number of nozzles increased from 5 to 10, respectively, at 15 diameter nozzle with 5 m3 h−1 flow rate. At 15 m3 h−1, the impulse force of water was decreased from 84.7 to 9.4 N when the number of nozzles increased from 5 to 30, respectively 10 mm diameter nozzle. The results also indicate that when the number of nozzles increased from 5 to 25, the impulse force of water decreased from 14.8 to 1.4 N at 15 mm nozzle diameter, respectively, and it decreased from 9.5 to 1.9 and 5.3 to 1.3 N at 20 and 25 mm, respectively, when the number of nozzles increased from 3 to 9.Figure 4Effect of flow rate, nozzle diameter and number of nozzles on the impulse force of water in a circular tank.Full size imageAt 30 m3 h−1 flow rate, the impulse force of water deceased from 84.7 to 46.9, 56.9 to 14.8, 28.5 to 5.3, 14.9 to 3.0 and 11.8 to 2.2 N when the nozzle diameter increased from 10 to 15 mm, respectively at 5, 10, 15, 20 and 25 nozzles. The results also indicate that, when the nozzle diameter increased from 20 to 25 mm, the impulse force of water decreased from 21.4 to 14.9, 14.8 to 5.4, 5.3 to 2.2 and 2.3 to 1.9 N for 3, 6, 9 and 12 nozzles, respectively.At 45 m3 h−1 flow rate, the impulse force of water was ranged from 2.1 to 111.2 N for all treatments under this study. Also, at 60 m3 h−1 flow rate, the impulse force of water ranged from 5.1 to 151.3 N for all treatments under this study. At 75 m3 h−1 flow rate, the highest value of the impulse force of water 211.2 N was found for 5 numbers of nozzles and 10 mm nozzle diameter, respectively. While, the lowest value of the impulse force of water was 9.1 N was found for 12 nozzles and 25 mm nozzle diameter, respectively.The results also indicate that the highest value of the impulse force of water 211.2 N was found for 5 nozzles and 10 mm nozzle diameter at 75 m3 h−1 flow rate, respectively. While, the lowest value of the impulse force of water was 1.2 N was found for 10 nozzles and 15 mm nozzle diameter at 5 m3 h−1 flow rate, respectively.The results indicated that, the relationship between the rotational velocity and impulse force of water is linear relationship at the same treatments. When the rotational velocity increased from 10.7 to 37.6, 8.1 to 28.8, 10.2 to 36.0 and 11.0 to 31.9 cm s−1, the impulse force of water increased from 3.1 to 106.6, 1.8 to 31.1, 1.3 to 32.5 and 1.4 to 22.8 N, respectively, at the same treatments. The trend of these results agreed with those obtained by19.Multiple regression analysis was carried out to obtain a relationship between the impulse force of water as dependent variable and different both of flow rate and nozzle diameter as independent variables. The best fit for this relationship with coefficient of determination of 0.88 and an error of 2.13% is in the following form:-$$ F_{i} = 38.18 + 0.67Q – 2.35Dquad {text{R}}^{{2}} = 0.88 $$
(4)
This equation could be applied in the range of 5 to 75 m3 h−1 water flow rate and from 10 to 25 mm of nozzle diameter.Average velocity of waterFigure 5 shows the effect of flow rate, diameter and number of nozzles on the average velocity of water in a circular tank. The results indicate that the average velocity of water increases with increasing flow rates and deceasing nozzle diameter and number of nozzles. It could be seen that, the average velocity of water decreased from 3.32 to 1.59 cm s−1, when the number of nozzles increased from 5 to 15, respectively at 10 nozzle diameter, and it decreased from 1.13 to 1.07 cm s−1, when the number of nozzles increased from 5 to 10, respectively, at 15 diameter nozzle with 5 m3 h−1 flow rate. At 15 m3 h−1, the average velocity of water was decreased from 12.03 to 4.33 cm s−1 when the number of nozzles increased from 5 to 30, respectively 10 mm diameter nozzle. The results also indicate that when the number of nozzles increased from 5 to 25, the average velocity of water decreased from 6.93 to 2.89 cm s−1 at 15 mm nozzle diameter, respectively, and it decreased from 7.55 to 4.00 and 4.89 to 2.95 cm s−1 at 20 and 25 mm, respectively, when the number of nozzles increased from 3 to 9.Figure 5Effect of flow rate, nozzle diameter and number of nozzles on the average velocity of water in a circular tank.Full size imageAt 30 m3 h−1 flow rate, the highest value of the average velocity of water 18.51 cm s−1 was found for 5 nozzles and 10 mm nozzle diameter. While, the lowest value of the average velocity of water was 4.65 cm s−1 was found for 12 nozzles and 25 mm nozzle diameter. At 45 m3 h−1 flow rate, the average velocity of water ranged from 6.66 to 23.26 for all treatments under study, also, at 60 m3 h−1 flow rate, the average velocity of water ranged from 9.23 to 34.82 for all treatments under study. At 75 m3 h−1 flow rate, the average velocity of water ranged from 10.00 to 48.76 for all treatment of this study.The results also indicate that the highest value of the average velocity of water 48.76 cm s−1 was found for 5 nozzles and 10 mm nozzle diameter at 75 m3 h−1 flow rate, respectively. While, the lowest value of the average velocity of water was 1.07 cm s−1 was found for 10 nozzles and 15 mm nozzle diameter at 5 m3 h−1 flow rate, respectively. These results agreed with those obtained by18,20. Fish distribution in the circular tank is influenced by the heterogeneity of water velocity in the area between inlet flow and the center of the tank9. Fish distribution in the circular tank is mostly concentrated in the area between high and low velocity area. The high velocity area will be avoided by most fishes as it requires high swimming energy, while dead volumes (low velocity area) are unfavorable condition for fish (low DO and higher metabolites accumulation)21.Multiple regression analysis was carried out to obtain a relationship between the average velocity of water as dependent variable and different both of flow rate and nozzle diameter as independent variables. The best fit for this relationship with coefficient of determination of 0.91 and an error of 1.48% is in the following form:$$ V_{avg} = 6.53 + 0.26Q – 0.37Dquad {text{R}}^{{2}} = 0.91 $$
(5)
This equation could be applied in the range of 5 to 75 m3 h−1 water flow rate and from 10 to 25 mm of nozzle diameter. More

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