This figure is for square edged orifices with flange

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This figure is for square-edged orifices with flange taps that are spaced one inch in front of and one inch behind the orifice plate. The Reynolds number, Re d1 , is based on the duct diameter. Unlike the earlier unrecoverable pressure drop equation, this equation accounts for both recoverable and unrecoverable effects. Alternatively, the following equation can be used for determining volumetric flow rate and follows a more generalized form. Discharge coefficient can be determined from Figure 2b. 4 1 / 2 air o d p A C Q Flow Development Whenever the velocity profile in a duct is perturbed, it will eventually recover to a steady profile as it traverses the duct. This is called flow development . When the duct flow goes through the orifice, it forms a high velocity jet downstream. The pressure in this jet is lower than the upstream pressure, because of unrecoverable viscous effects (recirculating eddies) and recoverable effects (increased velocity). The duct diameter is the same, both upstream and downstream of the orifice, so we expect that the jet downstream of the orifice will eventually expand. After some distance, the velocity profile in the duct will look just like the upstream profile. At this point, the recoverable component of pressure drop will have recovered, because velocity is restored. As the jet is expanding, the flow is called a developing flow. In this region the profile is changing along the duct and there is a radial velocity component. It can be difficult to take measurements in developing flows. Once the velocity profile has stabilized, and no longer changes with distance along the duct, the flow is fully developed . Environmental Effects The accuracies of both the Pitot-static probe velocity measurement and the orifice flow measurement are directly related to the accuracy with which the density of the fluid in the duct is known. Since air can be treated as an ideal gas at atmospheric pressures, its density is directly proportional to its pressure and inversely proportional to its temperature as defined by the ideal gas law. The ideal gas law states that: T R v p or T R p where p is the gas pressure; v is the gas specific volume, which is the reciprocal of the gas density ; R is the gas constant for air; and T is the gas temperature. Both the pressure and temperature are required in absolute scales. Thus, the density of dry air is:
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ME 4600:483 Lab Notes Revised 11/16/2015 Flow Measurement Page 6 of 18 air air air air T R p The pressure of the air in the laboratory will be measured with a barometer, while temperature is measured with a thermometer. We are also at a latitude of 41 degrees, so the acceleration due to gravity in Akron is approximately 9.79 m/s 2 . A further complication is the slight effect of humidity on the density of air. Water vapor is less dense than air, so humid air is less dense than dry air as represented by the ideal gas equation.
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