The orifice meter consists of an accurately machined and drilled plate concentrically mounted between two flanges. The position of the pressure taps is somewhat arbitrary. The orifice meter has several practical advantages when compared to venturi meters. • Lower cost • Smaller physical size • Flexibility to change throat to pipe diameter ratio to measure a larger range of flow rates Disadvantage: • Large power consumption in the form of irrecoverable pressure loss The development of the orifice meter equation is similar to that of the venturi meter and gives: V 2 pa pb C0 1 4 q V S0 where: –= ratio of orifice diameter to pipe diameter ≈ 0.5 usually S0 = cross sectional area of orifice V = bulk velocity through the orifice C0 = orifice coefficient ≈ 0.61 for Re > 30,000 There is a large pressure drop much of which is not recoverable. This can be a severe limitation when considering use of an orifice meter. Fluid Meters: Their Theory and Applications, 6th ed., American Society of Mechanical Engineers, New York, 1971 pp. 58-65. Rotameters fall into the category of flow measurement devices called variable area meters. These devices have nearly constant pressure and depend on changing cross sectional area to indicate flow rate. Rotameters are extremely simple, robust devices that can measure flow rates of both liquids and gasses. Fluid flows up through the tapered tube and suspends a ‘float’ in the column of fluid. The position of the float indicates the flow rate on a marked scale. Three types of forces must be accounted for when analyzing rotameter performance: • Flow • Gravity • Buoyancy Buoyancy Gravity For our analysis neglect drag effect Flow Mass Balance Assume Gradual Taper V1S V2 S Q V1 V2 S Flow Between Float and Tube Q S V3 V1 S S f S3 S3 is annular flow area at plane 3 Momentum Balance Note: • p3 = p2 • Must account for force due to float QV3 V1 p1 p2 S gzS Vf f gVf p Q gz S 2 S gV f b 1 S S3 Mechanical Energy Balance 1 2 p 2 ˆ W0 V3 V1 gz hf 2 2 V Assume: h f K R 3 2 (Base velocity head on smallest flow area) 2 2 p 1 2 S S 2 2 gz V1 V1 K RV1 2 S3 S3 Combining Momentum and Mechanical Energy Balance 2 S S gVf b 1 Q Q 1 1 K R 1 2 S S3 S S3 S 2 2 After Some Manipulation Q S3 S Sf 1 K R S S f 2 2 gVf f Sf Assuming Sf ≈ S a discharge coefficient can be defined 1 2 CR 1 K R Q S3C R 2 gV f f Sf CR must be determined experimentally. As Q increases the float rides higher, the assumption that Sf = S is poorer, and the previous expression is more nearly correct. Measure by determining RPM of turbine (3) via sensor (6). Turbine meters are accurate but fragile. When fluid is passed through a U-bend, it imposes a force on the tube wall perpendicular to the flow direction (Coriolis force). The deformation of the U-tube is proportional to the flow rate. Coriolis meters are expensive but highly accurate. A 2 in. Schedule 40 pipe carries 35º API distillate at 50° F (SG=0.85). The flow rate is measured by an orifice meter which has a diameter of 1.5 in. The pressure drop across the orifice plate is measured by a water manometer connected to the flange taps. If the manometer reading is 20 in. of H2O, what is the flow rate of the oil in GPM ? Uo Co 2( Pa Pb ) 1 4 do 1.5 in 0.726 d p 2.067 in P g h ( Pa Pb ) Assum e: Co 0.61 N Re 30,000 P (1 0.85) 62.4 Uo 0.61 1 (0.726) 4 lbm lbm ft 20 32 . 2 ft 502 . 3 ft 3 s 2 12 ft s 2 lb 2 502.3 m 2 ft s ft 3.120 lb s 53.04 m3 ft . 2 1.5 ft 2 d o ft 7.48 gal 60s 12 Q U o 3.120 17.2 GPM 4 4 s ft 3 min . N RE 1.5 3.120 ft 53.04 lbm ft s ft 3 d o U o 12 6840 30,000 4 lbm 6.719710 ft s 4.5 cP cP Now what ???