Chapter 8 Water-side System Pipe Sizing And Control Valve .

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Chapter 88.1Water-side System Pipe Sizing and Control Valve SelectionDesign process for the water-side systemBased on the estimated design cooling loads of air-conditioned spaces in a building, wecan determine the requirements on the cooling capacity, supply air flow rate and chilledwater flow rate of individual air-handling equipment serving those spaces. Rather thansumming up the chilled water flow rate requirements of all the air-handling equipment,the total chilled water supply flow rate that the central chiller plant should be able todeliver should be determined from the estimated design block cooling load of thebuilding. As explained in Chapter 3, the diversity in occurrence of peak cooling demandsof the spaces is accounted for in estimation of the block cooling load. It, therefore, is amore realistic basis for determination of the central plant capacity.Following design cooling load estimation, design decisions would need to be maderegarding the type of heat rejection system, the type of chilled water pumping system,the number of chillers and pumps and, where required, other chiller plant equipment,e.g. seawater pumps, condenser water pumps and cooling towers, to be adopted.Decisions would need to be made also on the locations of the air-handling equipment,e.g. in AHU rooms preserved for their accommodation or within the air-conditionedspace, as well as the location of the chiller plant and, where applicable, the locations ofthe other major equipment, in the building.Multiple chiller units would typically be adopted to allow adjustment of cooling capacityto meet the varying cooling load by turning chillers on and off, which will help upholdthe operating efficiency of the chillers. The reliability of the chiller plant would also beenhanced with multiple units because a large percentage of the installed coolingcapacity would remain available when one of the chillers is out of order or needs to beset aside for maintenance. Each chiller would typically be equipped with a chilled waterpump or primary-loop pump of matching design water flow rate, and one more unitwould typically be added as standby. Similar consideration would be given to condenserwater pumps and cooling towers, which would ease operational control.When the above design work has been done, we may proceed to determining the piperouting for distribution of the chilled water supply from the chiller plant to individualair-handling equipment, and the chilled water flow rates to be carried by individualsupply and return pipe sections in the piping network. The required pipe routing isdependent on the locations of the main chiller plant room, the air-handling equipmentor their plant rooms, and locations of pipe ducts available for installation of riser pipes.Whilst the routing of chilled water pipes from the chiller plant to the air-handlingequipment would be the same, the pipe routing within the chiller plant room woulddepend on which chilled water pumping system is chosen for the building.The next step would then be determination of the required sizes of the pipes and thepressure drops that would be incurred by chilled water flowing through the pipesections at the estimated flow rates. With this result, we may proceed to selection ofcontrol valves for the air-handling equipment and then selection of chilled waterpumps. Besides the considerations to be given to pipe sizing and control valve selection,detailed explanation on why control valves would need to be selected before pump322

selection will be given in this chapter. Where applicable, similar considerations asoutlined above are to be given to the condenser and/or seawater circulation systems.Good planning would help avoid unnecessary pipe runs and bends, leading to optimaluse of pipe and insulation materials and minimum possible pressure losses andpumping energy use. Additionally, the architect should be made aware of the space andbuilding work requirements of the air-side and water-side systems at an early stage ofthe building design process to ensure the system can be installed as planned.8.2Pressure loss estimation and pipe sizingPipe sizing, i.e. selection of a pipe of a certain diameter for conveying a given water flowrate, involves a compromise between the first cost and the running cost of the system. Apipe of a larger diameter is more expensive than a smaller pipe but the pressure lossthat the water flow would incur is smaller with the larger pipe, which means lesspumping energy would be needed to drive water flow at the required flow rate. Pipesizing is typically guided by an allowable pressure drop per unit pipe length. Otherconsiderations include the flow generated noise which should be kept low by limitingthe flow velocity inside a pipe below a maximum tolerable level.To inform pipe sizing, we need to know the relation between flow rate or velocity insidea pipe of a given diameter and the corresponding pressure drop that would be incurred.The fundamental principles governing air flow through ducts and fittings, which arecovered in Chapter 5, apply equally to water flow through pipes and fittings. The majorfluid mechanics relations that we need to use for pipe sizing include:i)The Bernoulliโ€™s equation applicable to fluid flow along a pipeline:๐‘1 ๐œŒ๐‘ข122 ๐œŒ๐‘”๐‘ง1 ๐‘2 ๐œŒ๐‘ข222 ๐œŒ๐‘”๐‘ง2 ๐‘๐‘™(8.1)Where p is static pressure, fluid density, u flow velocity, g the gravitationalacceleration, z height above a datum level, and pl pressure loss. The subscripts1 & 2 denote two locations along the streamline over which the pressure loss isincurred.ii)The Darcyโ€“Weisbach equation for fluid flow inside a duct or pipe of uniforminternal diameter, for evaluation of the pressure loss term in the Bernoulliโ€™sequation:๐ฟ ๐‘๐‘™ ๐‘“ ๐ท ๐œŒ๐‘ข2(8.2)2Where f is the friction factor, L the pipe length and D the pipe diameter.iii)The Colebrookโ€™s equation, for evaluation of the friction factor in the DarcyWeisbach equation:1 ๐‘“๐‘˜ 2 log (3.7๐ท 2.51๐‘…๐‘’ ๐‘“)(8.3)323

Where Re is Reynoldโ€™s Number, defined as:๐‘…๐‘’ ๐œŒ ๐‘ข ๐ท(8.4)๐œ‡And k is the surface roughness of the internal pipe wall, and ยต the viscosity of thefluid.Friction factorEquation (8.3) is used mainly in calculation routines implemented in a computer but isseldom used in manual calculations because it is an implicit equation involving theunknown f on both sides which requires the use of an iterative procedure to solve.Alternatively, a graph showing how the friction factor will vary with surface roughnessand diameter of a pipe and with the Reynold number (proportional to the flow rate),typically called a Moody diagram as shown in Figure 8.1, can be used for evaluation ofthe friction factor.Figure 8.1Moody diagram (friction factor denoted as in this diagram)For a specific fluid, e.g. water, and a specific type of pipe, e.g. galvanized iron (GI) pipeor black steel pipe, graphs or tables showing the pressure loss per unit length and flowvelocity for pipes of different nominal sizes when applied to convey a given range offlow rate may be constructed to facilitate pipe sizing. Such graphs and tables may befound in handbooks, e.g. [1, 2], and textbooks, e.g. [3, 4], in the air-conditioning field.Figure 8.2 shows an example of pipe frictional loss chart for pipe sizing.324

Figure 8.2Pipe frictional loss chart for sizing steel pipes conveying waterThe recommended pipe sizing criteria [1] are that for pipe size 50mm, flow velocityshould not exceed 1.2m/s and, for larger pipes, the pressure drop should not exceed400 Pa/m. Pipes sized may have pressure drop per unit length ranging from 100 to 400Pa/m, averaged at around 250 Pa/m. These thresholds have been shown in Figure 8.2as lines for an upper limit and a lower limit and operating conditions between these twolines are considered adequate. For example, for a flow rate of 20m3/h, we may use apipe of 75mm diameter in which case the flow velocity would be slightly below 1.2m/s( 4 ft/s) and the pressure loss slightly lower than 200 Pa/m ( 2 mH2O/100m piperun) (Figure 8.2).For pipe fittings, such as bends, tees and joints, and other system components, such ascoils, valves, strainers, etc., local loss coefficient and velocity pressure are also used forquantification of pressure loss.1 ๐‘ ๐ถ 2 ๐œŒ๐‘ข2(8.5)Unlike air ducts, water pipes are typically circular in cross-section and, therefore, thereis no need for the concepts of hydraulic mean diameter and equivalent diameter inquantification of pipe pressure losses. Nevertheless, similar approach can be used todetermine the overall pressure drop of a piping system from the pressure losscharacteristics of components in the system, including components in series andparallel configurations. Tables and charts that provide pressure loss characteristics ofpipe fittings are also available in relevant handbooks and guides, such as the ASHRAEHandbook, Fundamentals [1] and CIBSE Guide C [2].An alternative method for quantification of the pressure loss characteristics of fittingsand system components is to express the loss of a fitting or system component in termsof the length of a straight pipe of the same material and diameter which will incur thesame pressure drop as the fitting or system component while passing the same fluid at325

the same flow rate. This measure is called equivalent length, which is a convenientmethod for pipe loss calculations: the equivalent lengths of the fittings and systemcomponents may simply be added to the physical lengths of the pipe run to get the totalequivalent length and this may be multiplied by an average pressure drop per unitlength to yield the overall pressure drop through a pipeline or an entire system.At an early stage of design development, a rule of thumb may be used for makingallowances for fitting pressure losses. A common practice is to assume that fittingpressure losses would be about 50 to 100% of the total loss of the pipes along the piperun. However, such results should be checked and corrected when more details of thedesign become available.8.3Control valvesAs highlighted in the discussion on chilled water pumping systems given in Chapter 7,the key functions of control valves, including two-way and three-way valves, are to: Modulate the output of a heating or cooling coil for maintaining the temperatureof the supply air or indoor space at the set point level. Keep the pressure difference across two points in a piping network at the setpoint level, e.g. in differential pressure bypass control for ensuring constantchilled water flows through chillers in a single-loop pumping system. Control water flow rate, e.g. in differential pressure bypass control for ensuringthe secondary loop pumps in a two-loop pumping system will not run into thesurge zone, and in minimum flow rate control for protecting chillers in a variableprimary flow (VPF) system.Control valves in air-conditioning systems may also be used to control watertemperature, through regulation of water flow rates from two streams that would mixwith each other, e.g. for cooling tower water leaving temperature low limit control, orthat would exchange heat via a heat exchanger, e.g. for control of leaving chilled watertemperature at the secondary-side of a heat exchanger that serve as a pressure break ina super-tall building.Properly functioning control valves are crucial to satisfactory performance of airconditioning systems. Unfortunately, the principles behind proper control valveselection are often not well understood, resulting in improper valve selection which isundesirable. Undersized control valves will give rise to degraded system output orexcessive pumping energy use whilst oversized control valves will lead to poor controlperformance, such as hunting.In the following, the key characteristics of control valves and proper selection criteriawill be elucidated. Problems with inadequate control valves will be explained anddiscussed. Common causes of confusion and misconceptions will also be highlighted.326

8.3.1 Control valve characteristicsA control valve is basically a flow restriction with variable flow resistance. Figure 8.3shows the internal parts of a two-way control valve. Its flow resistance can be adjustedby varying the degree of opening of the valve, quantified by the valve lift, Z, also calledvalve stroke or travel, which is the linear displacement of the valve plug measured fromthe fully closed position (Figure 8.4). Its flow resistance is the lowest when the valve isfully open and reaches an extremely high value when the valve is fully closed. Themovement of the valve plug is driven by a valve actuator, which may be a pneumaticactuator (Figure 8.3) or an electric actuator. Nowadays, pneumatic actuators are usedmainly for large valves and electric actuators are more commonly used in airconditioning systems in commercial buildings.Pneumatic actuatorFigure 8.3Cross-sectional views of a control valve and valve actuatorValve Plug PvVValve Lift orStroke, ZFigure 8.4The valve plug position, quantified by the lift or stroke (left), and typicalsymbol used to denote a control valve (right)327

i)Flow coefficient of control valveWhen an incompressible fluid is flowing steadily, under fully turbulent condition,through a flow restriction with a fixed resistance, such as a control valve with its valvelift fixed, the relation between the pressure drop across the flow restriction and the flowrate through it can be written, according to Equation (8.5), as:11๐‘‰ 2 ๐‘ƒ ๐‘˜ 2 ๐œŒ๐‘ข2 ๐‘˜ 2 ๐œŒ (๐ด)(8.6)Where P pressure drop across the flow restrictionk proportionality constant density of fluidV volume flow rate of fluidA flow cross-sectional area of flow restrictionFor a particular control valve at a given valve lift (Z), the above equation may be rearranged to: ๐‘ƒ๐‘ฃ ๐œŒ ๐‘˜ 2 ๐ด๐‘‰ ๐‘ƒ๐‘ฃ๐‘‰ ๐ถ (8.7)๐œŒwhere Pv is the differential pressure across the control valve (Figure 8.4).Since the flow resistance of a control valve will change with the valve lift, Z, the value ofthe coefficient, C, in the above equation is a function of Z. This implies that, for eachmodular size of control valve of a particular design, a set of C values corresponding to arange of Z values, or a curve or an equation relating the two, is needed to represent itscharacteristics, which is rather cumbersome.It is a conventional practice to specify the performance of a control valve separately forthe fully-open characteristic, which is related to its flow capacity, and the characteristicsat different degrees of valve opening, which affects its control performance. Thefollowing equation is commonly used to describe the relationship between the flow rateand pressure drop across a fully open control valve:๐‘‰ ๐ถ๐‘ฃ ๐‘ƒ๐‘ฃ(8.8)With the understanding that the fluid under concern is always water, the density termin the equation has been dropped. The coefficient Cv in the equation is called the โ€˜flowcoefficientโ€™, which is a measure of the valve capacity (or size), and thus a key parameterfor valve sizing.328

A closer look at this equation unveils that the flow coefficient (Cv) carries dimension,which is in the unit derived from the unit of flow rate divided by the square root of theunit of pressure. Its value, therefore, is dependent on the units used to quantify flowrate and pressure. Conventionally, flow rate and pressure are measured, respectively, in(UK or US) GPM (gallon per minute) and PSI (pounds per square inch). Correspondingto these units (but often not explicitly mentioned), Cv is used as the symbol for flowcoefficient, and referred to directly as โ€˜Cee-Veeโ€™.Alternative forms of the flow-pressure drop relationship (Equation (8.8)) for metric / SIunits include:The metric version:๐‘‰ ๐พ๐‘ฃ ๐‘ƒ๐‘ฃ ๐œŒ(8.9a)where Kv is the flow coefficient, and V is in m3/h, Pv in bar & in kg/m3.A simplified version commonly used (for water):๐‘‰ ๐พ๐‘ฃ ๐‘ƒ๐‘ฃ(8.9b)where Kv is the flow coefficient, and V is in m3/h & Pv in bar.The SI version adopted in BS4740:๐‘‰ ๐ด๐‘ฃ ๐‘ƒ๐‘ฃ ๐œŒ(8.9c)where Av is the flow coefficient, and V is in m3/s, Pv in Pa & in kg/m3.Multiplying factors for conversion of flow coefficient in one unit to another are assummarized in Table 8.1.Multiplying factors for conversion between flow coefficients ( 1000kg/m3)Table 8.1Cv (US)Cv (UK)Cv (US)1Cv (UK)From To KvKvAv0.8327(Eq. 8.9a)27.35(Eq. 8.9b)0.865024.03 x 10-61.201132.851.03928.86 x 10-6Kv (Eq. 8.9a)0.036560.0304410.031620.8784 x 10-6Kv (Eq. 8.9b)1.1560.962631.62127.78 x 10-641.62 x 10334.65 x 1031,138 x 10336.00 x 1031Av329

ii)Inherent characteristics of control valveWith the capacity of a fully-open control valve quantified by the flow coefficient, anormalized characteristic curve may then be used to show the change in flow rate withvalve lift, or vice versa, for a series of control valves designed to exhibit that flow-liftcharacteristic. Such a curve is called the โ€˜inherent characteristicโ€™ of a control valve,denoted by:๐‘ฃ ๐‘“(๐‘ง) or ๐‘ง ๐‘”(๐‘ฃ)(8.10)Where v and z are, respectively, normalized flow rate and normalized valve lift, definedas follows:๐‘ฃ ๐‘‰ ๐‘‰๐‘‚(8.11)๐‘ง ๐‘ ๐‘๐‘‚(8.12)In the above equations, V is the flow rate when the valve lift is Z and VO & ZO are thefully-open flow rate and maximum valve lift. Since, at a fixed valve lift, the flow rate willstill vary with the differential pressure ( Pv) across the control valve, an inherentcharacteristic curve can only be defined under a constant Pv across a control valvewhen the valve lift is varied. Figure 8.5 shows some inherent characteristic curves ofcontrol valves.Specific inherent characteristics can be achievedthrough varying valve plug design.Figure 8.5Inherent characteristics of typical types ofcontrol valve.Inherent characteristics of control valvesAs the inherent characteristic curves show (Figure 8.5):1)A quick opening valve will allow the flow rate to rise from zero to a highpercentage of the full-flow rate when the valve is opened from the fully closed330

position to a small valve lift. Such valves are suitable for equipment that areexpected to deliver a large output within a short duration after being put intooperation.2)For a linear valve, the change in flow rate would be directly proportional to thevalve lift, which should provide good control characteristic, but this would be thecase only if the differential pressure across the control valve would remainrelatively stable.3)For an equal percentage valve, the change in the flow rate per unit change in thevalve lift is proportional to the current flow rate (see equation below), i.e. thechange in flow rate will be large if the current flow rate is large, and vice versa:๐‘‘๐‘ฃ๐‘‘๐‘ง ๐พ ๐‘ฃ(8.13)where K is the proportionality constant. Note that Equation (8.13) is undefinedwhen v approaches zero, which can be clearly seen when it is integrated:๐‘‘๐‘ฃ๐‘ฃ ๐พ ๐‘‘๐‘งln ๐‘ฃ ๐พ ๐‘ง ๐ดwhere A is an integral constantThe boundary condition z 0 & v 0 should allow us to evaluate A but theresult is . This, however, is not a serious restriction to the application ofEquation (8.13) to equal percentage valves as long as it is not applied to a valvelift too close to zero.Using the boundary condition z 1 & v 1, we get0 ๐พ ๐ดor๐ด ๐พln ๐‘ฃ ๐พ(๐‘ง 1)or๐‘ฃ exp[๐พ(๐‘ง 1)]The value of K can be determined by curve fitting the inherent characteristiccurve of a given equal percentage valve.As will be shown in later discussions, equal percentage valves are preferred inmany applications to HVAC systems for the better overall control performancethat they can offer.iii)Installed characteristicsThe flow coefficient (Kv) in conjunction with the inherent characteristic curve (๐‘ฃ ๐‘“(๐‘ง)) will allow the flow rate (V) that the control valve will let pass at a particular valvelift (Z) and under a given differential pressure ( Pv) to be determined by following thecalculation steps given below:1)๐‘‰๐‘‚ ๐พ๐‘ฃ ๐‘ƒ๐‘ฃ331

2)๐‘ง ๐‘ ๐‘๐‘‚3)๐‘ฃ ๐‘“(๐‘ง)4)๐‘‰ ๐‘ฃ ๐‘‰๐‘‚Note that VO above denotes the flow rate when the control valve is fully open while thepressure difference across it is at the SAME Pv value as in the case being

Figure 8.2 Pipe frictional loss chart for sizing steel pipes conveying water The recommended pipe sizing criteria [1] are that for pipe size 50mm, flow velocity should not exceed 1.2m/s and, for larger pipes, the pressure drop should not exceed 400 Pa/m. Pipes sized may have pressure drop per unit length ranging from 100 to 400

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