Download Fluid Flow in Piping Systems

Valve and Actuator Manual
Hydronic System Basics Section
Engineering Bulletin
Issue Date
977
H110
0989
Fluid Flow in Piping Systems
The relationship between the many factors which influence the pressure
and flow rate within a hydronic system can sometimes seem very
confusing. This report provides a simple systematic approach for
analyzing basic hydronic systems. These concepts can later be applied to
more complicated systems like those discussed in Engineering Reports
H111 and H112. For the purpose of this report the “fluid” discussed will
always be water.
Head
The term head is frequently utilized in discussions of hydronic systems. It
is often used interchangeably with pressure. For example, pump curves
depict the relationship between the head developed by a pump and its flow
rate. Piping friction-factors are also normally expressed in terms of head
loss per unit length of pipe.
Head has the dimension of length, usually expressed in terms of feet. If all
of the system variables are expressed in terms of head, it is possible to
relate the different forms of energy transport with a common dimension.
Therefore, energy transport caused by changes in pressure, elevation,
velocity, pumping and friction losses within a system can simply be added
or subtracted from each other which greatly simplifies calculations. There
are six different types of head which are typically utilized in the analysis
of hydronic systems. These are pressure head, elevation head, velocity
head, pump head, head losses due to piping friction and head losses due to
control valves.
Pressure Head
The amount of energy stored in a unit of fluid by virtue of its pressure is
called pressure head. In other words, it is the static pressure which exerts
itself against the walls of the piping system. Its magnitude can be
measured with a pressure gauge.
Pressure head can be defined by the following equation:
Pressure head (Hp) = p ÷ γ
Where: p = pressure (lb/ft2)
γ = specific gravity (for water this is 62.4 lb/ft3)
© 1989 Johnson Controls, Inc.
Code No. LIT-351H110
1
Elevation Head
The potential energy stored in a unit of fluid is called the
elevation head. This represents the energy contributed to a
given point in the system due to the height of the water column
above the referenced point.
It is defined by the following equation:
Elevation head (He) = z
Where: z = elevation of unit of fluid above the reference point (feet)
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Velocity Head
The kinetic energy stored in a unit of fluid is called velocity head.
Velocity head is measured with a pitot tube.
It is defined by the following equation:
Velocity head (Hv) = V2 ÷ 64.4
Where: V = Average velocity of the fluid (ft/sec)
64.4 = 2 × Acceleration of Gravity (32.2 ft/sec2)
Pump Head (Hpump)
The relationship between the flow and pressure (head) developed by a
pump is graphically represented by a pump curve. A pump curve shows
all of the operating points of a constant speed pump as its discharge is
throttled between zero and full flow. Values of Hpump can be obtained
from the y-axis of a pump curve. Figure 4 shows a pump curve for a
centrifugal pump.
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The magnitude of the Hpump, therefore, depends on the flow rate through
the pump and the curvature of the pump curve.
Head Losses Due
To Piping Friction
(HLpf)
When water flows through a section of pipe the friction between the fluid
and the inside surface of the piping creates a pressure drop (head loss).
This head loss is related to:
1.
2.
3.
4.
5.
The viscosity of the fluid.
The velocity of the fluid.
The inside diameter of the pipe.
The roughness of the inside of the pipe.
The length of the section of piping.
There are two methods which can be utilized to determine the actual head
loss in a section of pipe. The first method involves calculating a
dimensionless number called the Reynolds Number (Nr). This number is
applied to a Moody Chart from which another term called the pipe
friction factor (Ff) is determined. After Ff is determined, the HLpf for a
length of pipe can be calculated as follows:
HLpf = Ff × (L ÷ 100)
Where: HLpf = Piping Friction Loss (feet)
Ff = Piping Friction Factor (from Moody Chart)
L
= Length Of Section Of Pipe (feet)
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Calculating Reynolds Numbers and applying them to a Moody chart to
find Ff is a rather laborious task. Therefore, a second method of
calculating head loss due to friction within the pipe was formulated which
is much simpler than the first. This method allows the user to read the
pipe friction factor (Ff) directly from a chart. A separate chart must be
used for each type of pipe because the roughness of the interior will vary
with the different materials and manufacturing processes. Charts for
several common types of pipe are available in the A.S.H.R.A.E.
Fundamentals Handbook. The actual head loss in a section of pipe can
then be determined as follows:
HLpf = Ff × (L ÷ 100)
Where:
HLpf = Piping Friction Loss (feet)
= Piping Friction Factor (from A.S.H.R.A.E. Chart)
Ff
L
= Length Of Section Of Pipe (feet)
Figure 5 shows this relationship in a graphic format.
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Head Losses In
Control Valves
(HLCV)
A control valve is essentially a variable restriction installed in the piping
system. As water flows through the valve (restriction) a head loss
(pressure drop) occurs. The magnitude of the head loss is related to the
flow rate through the valve and the open area between the valve plug and
the orifice through which the plug moves.
For a fully open control valve:
HLcv
Where: HLcv
= 2.31 x (Flow Rate ÷ CV)2
= Head Loss In Control Valve (feet)
Flow Rate = Flow Rate (gallons per minute [gpm])
CV
= Valve Flow Coefficient (from Valve
Manufacturer)
How is This
Information
Utilized?
If a simple energy balance is applied to the various types of head
described above, the following relationship may be ascertained. This
relationship assumes there is no heat loss or gain in the system and is valid
for any incompressible fluid.
Equation 1
Hp(1) + Hv(1) + He(1) + Hpump = Hp(2) + Hv(2) + He(2) + HLpf(1-2) + HLcv
Where: Point "1" is Upstream Of Point "2"
And:
Hp(1)
= Pressure Head At Point 1
Hv(1)
= Velocity Head At Point 1
He(1)
= Elevation Head At Point 1
Hp(2)
= Pressure Head At Point 2
Hv(2)
= Velocity Head At Point 2
He(2)
= Elevation Head At Point 2
HLpf(1-2) = Head Loss Due to Pipe Friction Losses
Between Point 1 & 2 (feet)
* Hpump
= Head developed By Pump (feet)
* HLcv
= Head Loss Of Control Valve (feet)
* Appropriate if located between points 1 and 2
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It may not be obvious, but this is a very powerful relationship. It shows
how the pressure head, elevation head, velocity head, pump head and head
losses due to piping friction and control valve head losses are related for
any two points within a hydronic system (see Figure 6).
Since the pressure and elevation are known at point "A", it is possible to
determine the system pressure (head) at any other point within the system.
In Figure 6 the reading of the pressure gage located at point "B" can be
determined as follows:
First calculate components of Equation 1. Figures 1 through 3 illustrate
how to make the calculations.
For Point # A:
Point # B:
Hp(A) = 50 feet
Hp(B) = ?
Hv(A) = 1.62 feet
Hv(B) = 1.62 feet
He(A) = 0 feet
He(B) = 50 feet
And:
Hpump
= 40 feet (From Pump Curve In Figure 4)
HLpf(A-B)
= 4 x (325 ÷ 100) = 13 feet
HLcv
= 2.31 x (1600 ÷ 544)2 = 20 feet
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Inserting these components into Equation 1 yields the following result:
50 + 1.62 + 0 + 40 = Hp(2) + 1.62 + 50 + 13 + 20
Solving for Hp(2) yields:
Hp(2) = 7ft ∴ PB = 7 ft x 0.433 psig/ft = 3.03 psig
Effect of
Reduced
System Flow
Rates
Figure 7 is similar to Figure 6 except the control valve is no longer wide
open. It is now positioned such that the system flow rate is 1/2 of its
original value.
Equation 1 can also be used to evaluate partial flow conditions. A partial
flow analysis is very useful for determining how well a particular system
component will function through its total range of operation. In the case
of a control valve, it is useful to know the magnitude of the variation in
head loss at the control valve (HLcv) as a function of the system flow rate.
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Equation 1 can be rewritten into the form shown below:
(Hp(1) - Hp(2)) + (Hv(1) + Hv(2)) + (He(1) - He(2)) = HLpf(1-2) + HLcv - Hpump
This time the piping system between points B and C will be analyzed with
point B as the upstream point. Because points B and C, in Figure 7, are
located next to one another; the difference is pressure head, velocity head
and elevation head between them is negligible. Therefore, the sum of all
of the terms on the left side of the equal sign in the rewritten form of
Equation 1 is equal to 0, leaving:
HLcv = Hpump - HLpf(1-2)
Since this hydronic system does not have either a system bypass or a
variable speed pump to perform pressure control, the value of Hpump will
increase as the flow rate is reduced. The amount of this increase can be
determined by referring to the pump curve shown in Figure 4.
The lower system flow rate will also reduce the value of the Ff and will
consequently lower HLpf(1-2). The new pipe friction factor can be
determined by one of two methods. The first method involves applying
the new reduced flow rate to the appropriate charts in the A.S.H.R.A.E.
Fundamentals Handbook. The second method involves applying the
following simple relationship to obtain the same result.
Ff(new) = Ff(old) x (Qnew ÷ Qold)2
Where: Ff(old) = Pipe Friction Factor With Valve Fully Open
Qnew = Current Flow Rate in gpm
Qold
= Flow Rate With Valve Fully Open
For the hydronic system depicted in Figure 7 the new
pipe friction factor is calculated as shown below:
Ff(new) = 4 x (800 ÷ 1600)2 = 1
The head loss across the control valve at the reduced flow rate can now be
calculated as follows:
HLcv = Hpump - HLpf
HLcv = 55 - [1 x 500 ÷ 100)]
HLcv = 50 feet
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System
Resistance
Curves
A graphic representation of the relationship between the head losses within
a system to the system flow rate is called a system resistance curve. A
particular system resistance curve is only valid for a fixed system. In other
words, if the orifice area of any component within the system changes, the
curvature of the system resistance curve will also change.
If the system resistance curve is overlaid onto a pump curve, the point
where the two curves intersect will determine the operating point of the
pump. In Figure 8 the intersection of system resistance curve #1 and the
pump curve is the design operating point of the pump. The intersection of
system resistance curve #2 and the pump curve represents the operating
point of the pump at 1/2 of the design flow rate. Notice that the pump is
developing more head at a lower flow rate.
The components of the system resistance curve shown in Figure 9 are
slightly different from those utilized in the system curves shown in
Figure 8. In Figure 9 the system curve represents only HLpf as a function
of system flow. It does not consider HLcv. Since the piping system
(excluding the control valve) is a fixed system, the system curve shown in
Figure 9 will not change.
Note that at 1/2 of the design system flow rate the head loss within the
piping is 1/4 of the value associated with the design flow rate. Based on
the previous discussion concerning the relationship between Ff and
changes in the system flow rate, this should have been expected.
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Figure 9 also illustrates another interesting relationship. The length of the
vertical line between the system resistance curve and the pump curve
represents HLcv. Notice how dramatically the head loss across the control
valve increases as the system flow rate is decreased. For the control valve
shown in this example, HLcv will increase by 2.5 times when the flow rate
is reduced to 1/2 of its original value (value of "Y" ÷ value of "X" = 2.5).
Pressure shifts of this magnitude can cause unacceptable changes in the
operating characteristics of a control valve. These problems are discussed
in detail in Engineering Report H111.
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Relationships
Derived From
Equation 1
By manipulating Equation 1 several simple relationships manifest
themselves. For example, a relationship describing the factors which
influence pump selection can be easily determined. It is also possible to
determine which factors influence actuator sizing requirements for 2-way
control valves. These equations can be applied to both circulating and
non-circulating systems.
A circulating system is a system in which the water leaves the pump via
supply piping and returns to the pump piping (see Figure 10). In contrast,
in a non-circulating system the water which leaves the pump does not
return to the pump. The pump obtains water from a different source such
as a tank or city water (see Figure 11). Sprinkler systems and domestic
water systems are examples of non-circulating systems. Chilled, hot and
condenser water systems are typical circulating systems.
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The following relationships were derived from Equation 1:
For Circulating Systems:
1. Hpump = HLpf + HLcv
Where:
Hpump = Head developed by pump (feet)
HLpf
HLcv
= Pipe friction head loss in water circuit between
pump and the control valve (feet)
= Control valve head loss (feet)
Hp, Hv, and He have no effect on Hpump. Therefore, the height of a
building will have no effect on sizing a pump. The pump must only be
sized to overcome the sum of the friction losses within the piping and
the pressure drop through a wide open control valve at design flow.
HLpf should be calculated at design flow for the longest water circuit,
assuming all piping was selected for the same Ff.
2. HLcv = Hpump - HLpf
It is desirable for the magnitude of HLcv to be held constant regardless
of the system flow rate. Unfortunately, in systems without pressure
control the value of HLcv is affected by Hpump and HLpf as shown.
Both Hpump and HLpf will change with the system flow rate.
Fortunately, many times hydronic systems have some means of
pressure control in the system. These can take the form of a variable
speed drive or a system bypass with its associated controls. Either of
these two schemes will reduce the possible variation in the magnitude
of HLcv. Pressure control can negate the effect of Hpump increasing at
lower system flow rates. Pressure control schemes, however, do not
affect HLpf. These concepts are discussed in detail in Engineering
Reports H111 and H112.
3.
∆Hcv = Hpump - HLpf
Where:
∆Hcv
= Head 2-way control valve must close off
against (feet)
Hpump = Head developed by pump (feet)
HLpf
= Pipe friction head loss in water circuit
between pump and the control valve (feet)
Once again Hp, Hv, and He have no effect on the actuator force
required to modulate the plug within a 2-way control valve. To
determine the worst case shut-off condition, Hpump should be set equal
to the shut-off head of the pump and HLpf should equal 0. These
conditions will occur at extremely low system flow rates in systems
without pressure control. This equation is not applicable to 3-way
control valves. The head against which a 3-way control valve must
close off will vary significantly based on the piping configuration.
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For Non-Circulating Systems:
4. Hpump = (He - Hp(ps)) + HLpf(p-cv) + HLcv
Where: Hpump
= Head developed by the pump (feet)
He
= Elevation of highest point in the system (feet)
Hp(ps)
= Pressure head at pump suction (feet)
HLpf(p-cv) = Piping friction losses between pump discharge
and worst case control valve (feet)
HLcv
= Control valve head loss (feet)
In the case of a non-circulating system the height of a building can
have a significant impact on pump selection. To determine pump
sizing criteria, HLcv and HLpf(p-cv) should also be calculated at the
design flow rate. HLpf(p-cv) should be calculated for the longest piping
run assuming all piping was sized for the same Ff.
5. HLcv = Hpump + Hp(ps) - He(cv) - HLpf(p-cv)
Where: HLcv
= Control valve head loss (feet)
Hpump
= Head developed by the pump (feet)
Hp(ps)
= Pressure head at pump suction (feet)
He(cv)
= Elevation of control valve above pump (feet)
HLpf(p-cv) = Piping friction losses between pump discharge
and control valve (feet)
Once again it is desirable for the magnitude of HLcv to be held as
constant as possible regardless of the system flow rate. In systems
without pressure control the value of HLcv will be affected by Hpump
and HLpf(p-cv). Hpump and HLpf(p-cv) both change with the system flow
rate. If a variable speed drive is utilized for pressure control, it can
negate the effect of the Hpump increasing at lower system flow rates.
Unfortunately, changes in HLpf(p-cv).will still cause the value of HLcv to
vary.
∆Hcv = Hpump + Hp(ps) - He(cv) - HLpf(p-cv)
6.
Where: ∆Hcv
= Head control valve must close off against (feet)
Hpump
= Head developed by the pump (feet)
Hp(ps)
= Pressure head at pump suction (feet)
He(cv)
= Elevation of control valve above pump (feet)
HLpf(p-cv) = Piping friction losses between pump discharge and
control valve (feet)
To determine the worst case shut-off condition for a particular valve,
the value of Hpump should be equal to the pump shut-off head and the
value of HLpf(p-cv) should be set equal to 0.
14 H110 Engineering Bulletin
Notes
H110 Engineering Bulletin
15
Notes
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16 H110 Engineering Bulletin
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