FlowMeasLab_and_Worksheet.pdf

# Low enough turbulence intensities that the effect of

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low enough turbulence intensities that the effect of turbulence can be neglected, but disturbed regions of flow near sharp edges or area changes can prevent good readings. Orifice Plates and Unrecoverable Losses Unlike the pitot tube, which uses local recoverable pressure to find velocity at points in the duct, many processes apply obstruction flow meters to measure volumetric flow rate for the entire duct. Obstruction flow meters effectively block part of the duct area, causing an increase in velocity and therefore a change in recoverable pressure according to the Bernoulli equation. Volumetric flow is evaluated by measuring the pressure difference between the upstream and downstream sides of the obstruction, which is an orifice in our experiment. If we try to use the Bernoulli equation here, however, we will be disappointed. The flow through an orifice is not inviscid and the pressure difference is only partially recoverable. Downstream of the orifice flow separation occurs, creating recirculating eddies that affect the downstream pressure. We need a different equation to account for these unrecoverable losses. A general equation for unrecoverable pressure drop is ) 2 v ( k + ) 2 v ( D L f = P 2 r 2 ble unrecovera where f is an empirical term called a friction factor that accounts for wall friction losses over a duct of length L and diameter D , and k is a term called a form loss coefficient that accounts for losses caused by a change in duct configuration like the orifice plate. The velocity v r is calculated at the smallest area where the form loss occurs, the orifice diameter in this case. Both k and f depend on a characteristic called the Reynolds number, D v = Re where is the fluid viscosity. Reynolds number is an important scaling parameter for fluid flows. It is often used to predict, whether flow is laminar, with Re less than about 5000, or turbulent when Re is greater than about 5000. The friction factor can be evaluated using a table like that shown in Figure 5 given Reynolds number. The form loss must be empirically estimated for specific objects. Because orifice plates are used often for flow measurement, engineers have, over time, developed very detailed instructions, called standards , on how to make plates that give repeatable results. If these instructions are followed, as they are for the orifice in this experiment, the volumetric flow is given by the orifice flow equation,

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ME 4600:483 Lab Notes Revised 11/16/2015 Flow Measurement Page 5 of 18 air o o P 2 A K = Q where Q is the volumetric flow rate of air, A o is the orifice cross-sectional area and K o is the orifice flow coefficient. Note that this is nearly the inverse of the unrecoverable pressure drop equation given before, and K o is related to but not the same as k . The orifice flow coefficient is a function of the ratio of the orifice diameter to the duct diameter, = d/D , and the Reynolds number for flow in the duct. A graph of values for K o for different Reynolds numbers is shown in Figure 2a.
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