E1C10 09/14/2010
13:4:39 Page 444
Example 10.8
For the orifice meter in Example 10.3 with b ¼ 0:5 and a pressure drop of 50 cm Hg, calculate the
permanent pressure loss due to the meter that must be overcome by a pump.
KNOWN H ¼ 50 cm Hg
b ¼ 0:5
ASSUMPTION Steady flow
FIND Dp loss
SOLUTION For a properly designed and installed orifice meter, the permanent pressure loss of
the meter is about 75% of the pressure drop across the meter (Fig. 10.7). Hence,
Dp loss ¼ 0:75 Â g Hg H ¼ 49:9 kPa or H loss ¼ 38 cm Hg
ð
Þ
COMMENT In comparison, for Q ¼ 0:053 m
3 /s a typical venturi (say a 15-degree outlet) with
a b ¼ 0:5 would provide a pressure drop equivalent to 19.6 cm Hg with a permanent loss of only
3.1 cm Hg. Since the pump needs to supply enough power to create the flow rate and to overcome
losses, a smaller pump could be used with the venturi.
Example 10.9
For the orifice of Example 10.8, estimate the operating costs required to overcome these permanent
losses if electricity is available at $0.08/kW-h, the pump is used 6000 h/year, and the pump-motor
efficiency is 60%.
KNOWN Water at 16
C
Q ¼ 0:053 m
3 /s
Dp loss ¼ 49:9 kPa h ¼ 0:60
ASSUMPTIONS Meter installed according to standards (1)
FIND Annual cost due to Dp loss alone
SOLUTION The pump power required to overcome the orifice meter permanent pressure loss
is estimated from Equation 10.18,
_
W ¼ Q
Dp loss
h
¼
0:55 m
3 /s
ð
Þ49; 900 Pa
ð
Þ3600 s/h
ð
Þ1 N/m
2 /Pa
ð
Þ1 W/N-m/s
ð
Þ
0:6
¼ 4530 W ¼ 4:53 kW
The additional annual pump operating cost required to overcome this is
Cost ¼ ð4:53 kWÞð6000 h/yearÞð$0:08/kW-hÞ ¼ $2175/year
COMMENT In comparison, the venturi discussed in the Comment to Example 10.7 would cost
about $180/year to operate. If installation space allows, the venturi meter may be the less expensive
long-term solution.
444 Chapter 10 Flow Measurements
13:4:39 Page 444
Example 10.8
For the orifice meter in Example 10.3 with b ¼ 0:5 and a pressure drop of 50 cm Hg, calculate the
permanent pressure loss due to the meter that must be overcome by a pump.
KNOWN H ¼ 50 cm Hg
b ¼ 0:5
ASSUMPTION Steady flow
FIND Dp loss
SOLUTION For a properly designed and installed orifice meter, the permanent pressure loss of
the meter is about 75% of the pressure drop across the meter (Fig. 10.7). Hence,
Dp loss ¼ 0:75 Â g Hg H ¼ 49:9 kPa or H loss ¼ 38 cm Hg
ð
Þ
COMMENT In comparison, for Q ¼ 0:053 m
3 /s a typical venturi (say a 15-degree outlet) with
a b ¼ 0:5 would provide a pressure drop equivalent to 19.6 cm Hg with a permanent loss of only
3.1 cm Hg. Since the pump needs to supply enough power to create the flow rate and to overcome
losses, a smaller pump could be used with the venturi.
Example 10.9
For the orifice of Example 10.8, estimate the operating costs required to overcome these permanent
losses if electricity is available at $0.08/kW-h, the pump is used 6000 h/year, and the pump-motor
efficiency is 60%.
KNOWN Water at 16
C
Q ¼ 0:053 m
3 /s
Dp loss ¼ 49:9 kPa h ¼ 0:60
ASSUMPTIONS Meter installed according to standards (1)
FIND Annual cost due to Dp loss alone
SOLUTION The pump power required to overcome the orifice meter permanent pressure loss
is estimated from Equation 10.18,
_
W ¼ Q
Dp loss
h
¼
0:55 m
3 /s
ð
Þ49; 900 Pa
ð
Þ3600 s/h
ð
Þ1 N/m
2 /Pa
ð
Þ1 W/N-m/s
ð
Þ
0:6
¼ 4530 W ¼ 4:53 kW
The additional annual pump operating cost required to overcome this is
Cost ¼ ð4:53 kWÞð6000 h/yearÞð$0:08/kW-hÞ ¼ $2175/year
COMMENT In comparison, the venturi discussed in the Comment to Example 10.7 would cost
about $180/year to operate. If installation space allows, the venturi meter may be the less expensive
long-term solution.
444 Chapter 10 Flow Measurements