Worked Example on Venturi-meter The Table below contains data obtained during the laboratory calibration of a horizontal venturi meter with an inlet diameter of 50mm and a throat diameter of 25mm (see Figure below). Water is flowing through the pipeline and the head difference values recorded are in mm head of water. Calculate the discharge coefficient for the meter. Theoretical discharge: Qtheoretical a1ª2 2 gH Ma? - a? Head difference h1-h2 (mm) 10 Measured Flow Rate (lmin -1 ) 13.2 30 23.1 50 28.5 70 34.6 90 39.7 h1- h2
Solution Theoretical discharge: Qtheoretical a1ª2 (a2 -a3) 2 gH Inlet area: a1 = 2 (0.05)2 =1.96×10-3m2 Throat area: a2 =(0.025)2 =0.491×10-3m2 H = h1 - h2: Pressure difference expressed as head of liquid flowing in the meter. If the tubes are filled with water then: Then the theoretical discharge will be given by: Q = 1.96× 10-3×0.491×10-3 2 X 2x 9.81x H v(1.96×10-3)2 -(0.491×10-3) =5.072×10-419.62Hm3s-1 Coefficient of Discharge, Cd = Qactual /Qtheoretical Head difference h1-h2 (mm) Head difference H = h1-h2 (m) Measured Flow Rate (lmin -1 ) Theoretical Flow Rate (lmin -1 ) 10 0.01 13.2 13.48 30 0.03 23.1 23.35 50 0.05 28.5 30.14 70 0.07 34.6 35.66 90 0.09 39.7 40.44 Coefficient of Discharge 0.98 0.99 0.95 0.97 0.98 In the table above, one may choose to work in m 3s -1 but working in lmin -1 gives sensible numbers to plot. Candidate should produce a linear plot of measured and theoretical flow rates.
y = 0.9721x R2 = 0.9991 Coefficient of discharge, Cd: From the Cd values presented in table above, Cd = Average of individual Cds = 0.97 In addition, from the above plot, Cd can be found as the gradient of the straight line. Cd = gradient of line = 0.97