Page 92 - Fluid mechanics, heat transfer, and mass transfer

FLOW MEASUREMENT 69

. What is a critical flow nozzle? . On what factors do the recommended minimum dis-
& For a given set of upstream conditions, rate of tances upstream and downstream of orifice and venturi
discharge of a gas from a nozzle will increase for meters depend?
& The main consideration for accurate is that the flow
a decrease in absolute pressure ratio, P nozzle /P upstream
(say, P 2 /P 1 ), until linear velocity in the throat reaches should be fully developed before entry into the meter.
sonic velocity at that location. In other words, sufficient straight section of the
& Value of P 2 /P 1 for which acoustic velocity is just upstream pipe is required.
attained is called critical pressure ratio, r c . & On the downstream side, disturbance created in flow
& Actual pressure in the throat will not fall below P 1 r c , by the meter must be removed for maximum recovery
even if much lower pressure exists downstream. of pressure to minimize energy losses.
. What is a sonic nozzle? . Illustrate, graphically, permanent pressure losses with
respect to orifice meter, venturi meter, and flow nozzles.
& Sonic nozzle is used to measure and to control the
flow rate of compressible gases. It may take the form & From Figure 4.13, it is evident that venturi meter
of any of the previously described obstruction me- involves lowest permanent pressure losses compared
ters. If the gas flow rate through and obstruction to orifice meter or flow nozzle, the later having
meter becomes sufficiently high, the sonic condition marginally higher losses.
will be achieved at the meter throat. & Losses decrease with increased diameter ratios in all
& At the sonic condition, the gas velocity will equal the three cases. The decrease is uniformly steeper
the acoustic wave speed (speed of sound) of the with increased diameter ratios for both flow nozzle
gas. At that point, the throat is considered to be and orifice where as for the venturi, it is steeper at low
choked and the mass flow rate through the throat diameter ratios and becomes marginal at increased
will be at a maximum for the given inlet conditions ratios.
regardless of any further increase in pressure drop & For an area ratio of 0.5, the pressure loss is about
across the meter. 65–70% of the orifice pressure differential.

Pressure losses for different head flow meters as function of b-ratio.
FIGURE 4.13