E1C10 09/14/2010
13:4:39 Page 441
The sonic nozzle provides a very convenient method to meter and regulate a gas flow. The
judicious selection of throat diameter can establish any desired fluid flow rate provided that the flow
is sonic at the throat. This capability makes the sonic nozzle attractive as a local calibration standard
for gases. Special orifice plate designs exist for metering at very low flow rates (1). Both large
pressure drops and system pressure losses must be tolerated with the technique (1).
Example 10.7
A flow nozzle is to be used at choked conditions to regulate the flow of nitrogen N 2 at 1.3 kg/s
through a 6-cm-i.d. pipe. The pipe is pressurized at 690 kPa abs and gas flows at 20
C. Determine the
maximum b ratio nozzle that can be used. R N 2 ¼ 297 N-m/kg-K.
KNOWN N 2 k ¼ 1:4
ð
Þ p 1 ¼ 690 kPa abs
_
m ¼ 1:3 kg/s
d 1 ¼ 6 cm
T 1 ¼ 293 K
r ¼ 7:93 kg/m
3
ASSUMPTIONS Perfect gas (ideal gas with constant specific heats)
Steady, choked flow
FIND Find b max ¼ d 0 max =d 1
SOLUTION Equation 10.17 can be rewritten in terms of nozzle throat area, A:
A max ¼
_
m
r 1
ffiffiffiffiffiffiffiffi ffi
2RT
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k=ðk þ 1Þ
½
2=ðk þ 1Þ
½
2=ðkÀ1Þ
q
¼ 8:12 Â 10
À4 m
2
Since A o ¼ pd
2
0 =4, this yields a maximum nozzle throat diameter, d 0 :
d 0 max ¼ 3:22 cm
Hence, b ¼ d 0 =d 1 0:536 is required to maintain the specified mass flow rate.
Obstruction Meter Selection
Selecting between obstruction meter types depends on a number of factors and engineering
compromises. Primary considerations include meter placement, overall pressure loss, overall
(capital and operating) costs, accuracy, and operating range (turndown).
Placement
It is important to provide sufficient straight pipe lengths on each side of a flow meter to allow for
proper flow development. The flow development dissipates swirl, promotes a symmetric velocity
distribution, and allows for proper pressure recovery downstream of the meter so as to reduce
systematic error. Installation effects can be minimized by placing the flow meter outlined in Figure
10.13. However, the engineer needs to be wary that installation effects are difficult to predict,
particularly downstream of elbows (out-of-plane double elbow turns are notoriously difficult), and
Figure 10.13 is a guide for best practice (3, 7). Even with recommended lengths, an additional 0.5%
10.5 Pressure Differential Meters 441
13:4:39 Page 441
The sonic nozzle provides a very convenient method to meter and regulate a gas flow. The
judicious selection of throat diameter can establish any desired fluid flow rate provided that the flow
is sonic at the throat. This capability makes the sonic nozzle attractive as a local calibration standard
for gases. Special orifice plate designs exist for metering at very low flow rates (1). Both large
pressure drops and system pressure losses must be tolerated with the technique (1).
Example 10.7
A flow nozzle is to be used at choked conditions to regulate the flow of nitrogen N 2 at 1.3 kg/s
through a 6-cm-i.d. pipe. The pipe is pressurized at 690 kPa abs and gas flows at 20
C. Determine the
maximum b ratio nozzle that can be used. R N 2 ¼ 297 N-m/kg-K.
KNOWN N 2 k ¼ 1:4
ð
Þ p 1 ¼ 690 kPa abs
_
m ¼ 1:3 kg/s
d 1 ¼ 6 cm
T 1 ¼ 293 K
r ¼ 7:93 kg/m
3
ASSUMPTIONS Perfect gas (ideal gas with constant specific heats)
Steady, choked flow
FIND Find b max ¼ d 0 max =d 1
SOLUTION Equation 10.17 can be rewritten in terms of nozzle throat area, A:
A max ¼
_
m
r 1
ffiffiffiffiffiffiffiffi ffi
2RT
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k=ðk þ 1Þ
½
2=ðk þ 1Þ
½
2=ðkÀ1Þ
q
¼ 8:12 Â 10
À4 m
2
Since A o ¼ pd
2
0 =4, this yields a maximum nozzle throat diameter, d 0 :
d 0 max ¼ 3:22 cm
Hence, b ¼ d 0 =d 1 0:536 is required to maintain the specified mass flow rate.
Obstruction Meter Selection
Selecting between obstruction meter types depends on a number of factors and engineering
compromises. Primary considerations include meter placement, overall pressure loss, overall
(capital and operating) costs, accuracy, and operating range (turndown).
Placement
It is important to provide sufficient straight pipe lengths on each side of a flow meter to allow for
proper flow development. The flow development dissipates swirl, promotes a symmetric velocity
distribution, and allows for proper pressure recovery downstream of the meter so as to reduce
systematic error. Installation effects can be minimized by placing the flow meter outlined in Figure
10.13. However, the engineer needs to be wary that installation effects are difficult to predict,
particularly downstream of elbows (out-of-plane double elbow turns are notoriously difficult), and
Figure 10.13 is a guide for best practice (3, 7). Even with recommended lengths, an additional 0.5%
10.5 Pressure Differential Meters 441