Before a rotameter can be used to measure an unknown flow rate, a calibration curve of flow rate versus rotameter reading must be prepared. A calibration technique for liquids is illustrated below. A flow rate is set by adjusting the pump speed; the rotameter reading is recorded, and the effluent from the rotameter is collected in a graduated cylinder for a timed interval. The procedure is carried out twice for each of several pump settings. 

(a) Assuming the liquid is water at 25°C, draw a calibration curve of mass flow rate, m_ (kg/min), versus rotameter reading, R, and use it to estimate the mass flow rate of a water stream for which the rotameter reading is 5.3. 

(b) The mean difference between duplicates, D̅_i , provides an estimate of the standard deviation of a single measurement, which was given the symbol s_x in Eq. 2.5-4: 

Moreover, confidence limits on measured values can be estimated to a good approximation using the mean difference between duplicates. For example, if a single measurement of Y yields a value Y_measured, then there is a 95% probability that the true value of Y falls within the 95% confidence limits (Y_measured - 1.74D̅_i) and (Y_measured + 1.74D̅_i). For a measured flow rate of 610 g/min, estimate the 95% confidence limits on the true flow rate.

Transcribed Image Text:

Rotameter Collection Volume Reading Time (min) Collected (cm) 2 1 297 1 301 4 1 454 4 1 448 ROTAMETER 6 0.5 300 6. 0.5 298 STOPWATCH 8 0.5 371 8 0.5 377 GRADUATED VARIABLE- 10 0.5 440 CYLINDER SPEED 10 0.5 453 PUMP