Experiment of Comparing Flow Rates for Different Meters - Assignment Example

Flow rates This experiment aimed at comparing flow rates for different meters with those obtained by direct measurement tank and stop watch. The flow rates were varied such that in each case a total six different flow rates were obtained. This flow rates are designated flow rate 1flow rate 2 up to flow rate 6. Flow rates using tank and stop watch The flow rates using tank are calculated by converting the volume of water in litres into m3 and diving by the time taken in seconds for the volume to be collected. The volume in litres is multiplied by 0.001 in order to covert into m3. The flow rates in m3/s is obtained by dividing the volume in m3 by the time in seconds taken for the volume to be collected From the experiment the following six flow rates were recorded by direct measurements Flow rate 1 Volume in L = 15L Time in s = 48.20  Q =  = 0.000311m3/s Flow rate 2 Volume in L = 10L Time in s = 35.67  Q =  = 0.00028m3/s Flow rate 3 Volume in L = 10L Time in s = 40.23  Q =  = 0.00025m3/s Flow rate 4 Volume in L = 10L Time in s = 55.25  Q =  = 0.00018m3/s Flow rate 5 Volume in L = 6L Time in s = 43.50  Q =  = 0.00014m3/s Flow rate 6 Volume in L = 6L Time in s = 62.80  Q =  = 0.000096m3/s Flow rates obtained for venturi The flow rates for venturi has been obtained using the discharge formula Q = x Where  (0.98)is the discharge coefficient; is the area at the narrowest point of constriction and  is the area upstream of constriction  and  gives the pressure at points A and B respectively. In the experiment the venturi has upstream diameter as 31.75mm and throat diameter is 15.0mm From Area =  Upstream area is calculated as =  = 0.00079m2 Similarly throat area =  = 0.000177m2 The value of s obtained from P =  where h is the difference in water heads at points A and B in metres obtained by multiplying the difference in millimeters by 0.001 Also for ease of calculation the part  of the equation can be taken to be a constant say U and its value calculated  =  = 0.000174x1.03 = 0.000179 Thus the expression for flow rate for the venture can be given as Q = Ux=  Flow rate 1  = 9.81x(200x0.001) = 1.962 Q =  = 0.00036m3/s Flow rate 2  = 9.81x(140x0.001) = 1.373 Q =  = 0.000297m3/s Flow rate 3  )/1000= 9.81x(105x0.001) = 1.0305 Q =  = 0.000257m3/s Flow rate 4  = 9.81x (70x0.001) =  Q =  = 0.00022m3/s Flow rate 5  = 9.81x (45x0.001) = 0.44145 Q =  = 0.00017m3/s Flow rate 6 )/1000= 9.81x (25x0.001) = 0.24525 Q =  = 0.000125m3/s Comparison of venturi flow versus tank and stop watch measurements The table and figure 1 it can be seen that the venturi flow rate higher in all the 6 flow measurements that were made. It can also be seen that the variation appear to be uniform at both low and high flow rates. Table 1: Comparison of venturi flow versus tank and stop watch measurements Tank 0.000311 0.00028 0.00025 0.00018 0.00014 0.000096 Venturi 0.00036 0.000297 0.000257 0.00022 0.000056 0.000125 Figure 1 Flow rates obtained for orifice plate The flow rates for orifice plate has been obtained using the discharge formula Q = x Where  (0.63)is the discharge coefficient; is the area at the narrowest point of constriction and  is the area upstream of constriction  and  gives the pressure at points A and B respectively. In the experiment the orifice plate has upstream diameter as 31.75mm and throat diameter is 20.0mm From Area =  Upstream area is calculated as =  = 0.00079m2 Similarly throat area =  = 0.000314m2 The value of s obtained from P =  where h is the difference in water heads at points A and B in metres obtained by multiplying the difference in millimeters by 0.001 Also for ease of calculation the part  of the equation can be taken to be a constant say U and its value calculated  =  = 0.000198x1.09 = 0.000216 Thus the expression for flow rate for the venture can be given as Q = Ux=  Flow rate 1  = 9.81x (134x0.001) = 1.31454 Q =  = 0.00035m3/s Flow rate 2  = 9.81x(100x0.001) =0. 981N/m2 Q =  = 0.0003m3/s Flow rate 3  = 9.81x(65x0.001) = 0.63765N/m2 Q =  = 0.00024m3/s Flow rate 4  = 9.81x(45x0.001) = 0.44145N/m2 Q =  = 0.0002m3/s Flow rate 5  = 9.81x(20x0.001) = 0.1962N/m2 Q =  = 0.00014m3/s Flow rate 6  = 9.81x (10x0.001) = 0.0981N/m2 Q =  = 0.000096m3/s Comparison of orifice flow versus tank and stop watch measurements The table 2 and figure 2 it can be seen that the orifice flow rate are higher in at the high flow rates but appear to coincide with the tank and stop watch measurements as the flow rate reduces. This could be an indication that at very high flow rates the orifice is not a reliable metre in measurement of flow. Table 1: Comparison of venturi flow versus tank and stop watch measurements Tank 0.000311 0.00028 0.00025 0.00018 0.00014 0.000096 Orifice plate 0.00035 0.0003 0.00024 0.00020 0.00014 0.000096 Figure 2 Flow rates by rotameter The flow rates by rotameter are given in L/min and they can be converted to m3/s by converting the litres into m3 and the minute into seconds. Thus the L/min is multiplied by 0.001/60 Flow rate 1 20L/min = 20x0.001/60 = 0.000333m3/s Flow rate 2 20L/min = 17x0.001/60 = 0.00028m3/s Flow rate 3 14L/min = 14x0.001/60 = 0.00023m3/s Flow rate 4 10L/min = 10x0.001/60 = 0.000167m3/s Flow rate 5 7L/min = 7x0.001/60 = 0.000117m3/s Flow rate 6 5L/min = 5x0.001/60 = 0.000083m3/s Comparison of ratometer flow versus tank and stop watch measurements The table 3and figure 3 it can be seen that the ratometer flow rate are higher than the actual flow rate made from the tank and stop watch measurements. The variation appears to be reducing as the flow rate reduces. This is a clear indication a ratometer is a very unreliable meter in measurement of flow rate. If the ratometer is to be used for approximation it would be advisable if the flow rates are low. Table 3: Comparison of ratometer flow versus tank and stop watch measurements Tank 0.000311 0.00028 0.00025 0.00018 0.00014 0.000096 Ratometer 0.000333 0.00028 0.00023 0.000167 0.000117 0.000083 Figure 3 Head loss and flow rate comparison for different metres In this section there has been comparison of the head loss for different flow rates for the three types of meters. Comparison of flow rate and head loss in ratometer From table 4 and figure 4 it can be seen that at high discharge the head loss is small in a rator meter. This could be attributed to increased friction resistance when the ratometer is moving at lower speed and the friction reducing at high speeds. Table 4: Comparison of flow rate and head loss in ratometer Head loss 0.08 0.0.07 0.07 0.07 0.09 0.065 Ratometer 0.000333 0.00028 0.00023 0.000167 0.000117 0.000083 Figure 4 Comparison of flow rate and head loss in orifice From table 5 and figure 5 it can be seen that at high discharge the head loss is high in the orifice. This could be attributed to increased turbulence around the orifice as the water speed increases thus leading to high head loss. Table 5 Head loss 0.09 0.07 0.045 0.030 0.01 0.005 Orifice plate 0.00035 0.0003 0.00024 0.00020 0.00014 0.000096 Figure 5 Comparison of flow rate and head loss in venturi From table 6 and figure 6 it can be seen that at high discharge the head loss is high in the venture just like in the orifice. However, the head loss appears to be lower for the venture as compared to the orifice. This could be the results of having a gradual reduction in the cross section which ensures there is low turbulence loss around the constriction. Table 6 Head loss 0.06 0.04 0.04 0.03 0.02 0.01 Venturi 0.00036 0.000297 0.000257 0.00022 0.000056 0.000125 Figure 6 Conclusion From this test it can be concluded that all the metres have errors in when used in measuring rate of flow in pipes but ratometres have highest discrepancy from the actual flow rate. The head loss in a rotameter reduces with increased rate of discharge in a pipe while for both venture and orifice the head loss increases with increases discharge. References Herschel, Clemens. (1898). Measuring Water. Providence, RI:Builders Iron Foundry. Adrian, R. J., editor (1993); Selected on Laser Doppler Velocimetry, S.P.I.E. Milestone Series, ISBN 978-0-8194-1297-3 Read More