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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) 2 H110 Engineering Bulletin 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. H110 Engineering Bulletin 3 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) 4 H110 Engineering Bulletin 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. H110 Engineering Bulletin 5 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 6 H110 Engineering Bulletin 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 H110 Engineering Bulletin 7 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. 8 H110 Engineering Bulletin 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 H110 Engineering Bulletin 9 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. 10 H110 Engineering Bulletin 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. H110 Engineering Bulletin 11 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. 12 H110 Engineering Bulletin 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. H110 Engineering Bulletin 13 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 Controls Group 507 E. Michigan Street P.O. Box 423 Milwaukee, WI 53201 16 H110 Engineering Bulletin Printed in U.S.A.