E1C10 09/14/2010
13:4:39 Page 445
Example 10.10
An ASME long radius nozzle ðb ¼ 0:5Þ is to be installed into a horizontal section of 12-in. (ANSI
schedule 40) diameter (304.8 mm) pipe. A long, straight length of pipe exists just downstream of a
fully open gate valve but upstream of an in-plane 90-degree elbow. Determine the minimum lengths
of straight unobstructed piping that should exist upstream and downstream of the meter.
KNOWN d 1 ¼ 11:938 in: ð303:28 mmÞ
b ¼ 0:5
Installation layout
FIND Meter placement
SOLUTION From Figure 10.13, the meter should be placed a minimum of eight pipe diameters
ðA ¼ 8Þ downstream of the valve and a minimum of three pipe diameters ðB ¼ 3Þ upstream of any
flow fitting. Note that since a typical flow nozzle has a length of about 1.5 pipe diameters, this
installation requires a straight pipe section of at least 8 þ 3 þ 1.5 ¼ 12.5 pipe diameters.
COMMENT A 12-in. diameter (Schedule 40) pipe has an inside diameter of 11.938 in. and an
outside diameter of 12.75 in. The equivalent metric pipe is DN 300 with outside diameter of
323.9 mm and inside diameter of 303.3 mm.
Laminar Flow Elements
Laminar flow meters take advantage of the linear relationship between volume flow rate and the
pressure drop over a length for laminar pipe flow (Re d < 2000). For a pipe of diameter d
with pressure drop over a length L, the governing equations of motion lead to
Q ¼
pd
4
128 m
p 1 À p 2
L
where Re d < 2000
ð10:19Þ
This relation was first demonstrated by Jean Poiseulle (1799–1869), who conducted meticulous tests
documenting the resistance of flow through capillary tubes.
The simplest type of laminar flow meter consists of two pressure taps separated by a length of
piping.
1 However, because the Reynolds number must remain low, this restricts either the pipe
diameter or the flow rate to which Equation 10.19 applies for a given fluid. This limitation is
overcome in commercial units by using bundles of small-diameter tubes or passages placed in
parallel and called laminar flow elements (Figure 10.14). The strategy of a laminar flow element is to
divide the flow by passing it through the tube bundle so as to reduce the flow rate in each tube such
that Re < 2000. Pressure drop is measured between the entrance and the exit of the laminar flow
element, and a flow coefficient is used to account for inefficiency, such that
Q ¼ K 1 Dp
ð10:20Þ
where coefficient K 1 is the meter static sensitivity and is called its K-factor. Commercial units come
calibrated with K 1 a constant over the useful meter range.
A laminar flow element has an upper limit on usable flow rate. Various meter sizes and designs
are available to accommodate user needs. Turndowns of up to 100:1 are available.
1 Alternately, if flow rate can be measured or is known, Equation 10.19 provides the basis for a capillary tube viscometer.
The method also achieves a linear resistance.
10.5 Pressure Differential Meters 445
13:4:39 Page 445
Example 10.10
An ASME long radius nozzle ðb ¼ 0:5Þ is to be installed into a horizontal section of 12-in. (ANSI
schedule 40) diameter (304.8 mm) pipe. A long, straight length of pipe exists just downstream of a
fully open gate valve but upstream of an in-plane 90-degree elbow. Determine the minimum lengths
of straight unobstructed piping that should exist upstream and downstream of the meter.
KNOWN d 1 ¼ 11:938 in: ð303:28 mmÞ
b ¼ 0:5
Installation layout
FIND Meter placement
SOLUTION From Figure 10.13, the meter should be placed a minimum of eight pipe diameters
ðA ¼ 8Þ downstream of the valve and a minimum of three pipe diameters ðB ¼ 3Þ upstream of any
flow fitting. Note that since a typical flow nozzle has a length of about 1.5 pipe diameters, this
installation requires a straight pipe section of at least 8 þ 3 þ 1.5 ¼ 12.5 pipe diameters.
COMMENT A 12-in. diameter (Schedule 40) pipe has an inside diameter of 11.938 in. and an
outside diameter of 12.75 in. The equivalent metric pipe is DN 300 with outside diameter of
323.9 mm and inside diameter of 303.3 mm.
Laminar Flow Elements
Laminar flow meters take advantage of the linear relationship between volume flow rate and the
pressure drop over a length for laminar pipe flow (Re d < 2000). For a pipe of diameter d
with pressure drop over a length L, the governing equations of motion lead to
Q ¼
pd
4
128 m
p 1 À p 2
L
where Re d < 2000
ð10:19Þ
This relation was first demonstrated by Jean Poiseulle (1799–1869), who conducted meticulous tests
documenting the resistance of flow through capillary tubes.
The simplest type of laminar flow meter consists of two pressure taps separated by a length of
piping.
1 However, because the Reynolds number must remain low, this restricts either the pipe
diameter or the flow rate to which Equation 10.19 applies for a given fluid. This limitation is
overcome in commercial units by using bundles of small-diameter tubes or passages placed in
parallel and called laminar flow elements (Figure 10.14). The strategy of a laminar flow element is to
divide the flow by passing it through the tube bundle so as to reduce the flow rate in each tube such
that Re < 2000. Pressure drop is measured between the entrance and the exit of the laminar flow
element, and a flow coefficient is used to account for inefficiency, such that
Q ¼ K 1 Dp
ð10:20Þ
where coefficient K 1 is the meter static sensitivity and is called its K-factor. Commercial units come
calibrated with K 1 a constant over the useful meter range.
A laminar flow element has an upper limit on usable flow rate. Various meter sizes and designs
are available to accommodate user needs. Turndowns of up to 100:1 are available.
1 Alternately, if flow rate can be measured or is known, Equation 10.19 provides the basis for a capillary tube viscometer.
The method also achieves a linear resistance.
10.5 Pressure Differential Meters 445