{"id":4652,"date":"2016-05-01T01:07:48","date_gmt":"2016-05-01T01:07:48","guid":{"rendered":"https:\/\/inst-tools.rdkaijf1-liquidwebsites.com\/?p=4652"},"modified":"2019-03-21T23:24:07","modified_gmt":"2019-03-21T17:54:07","slug":"control-valves-basic-theory","status":"publish","type":"post","link":"https:\/\/instrumentationtools.com\/control-valves-basic-theory\/","title":{"rendered":"Control Valves Theory"},"content":{"rendered":"<p style=\"text-align: justify;\">The flow regulation \u00a0in a valve\u00a0 is accomplished \u00a0by the varying \u00a0resistance as the valve \u00a0is stroked, i.e. its effective cross sectional area is changed. As the fluid moves from the piping into\u00a0 the \u00a0smaller \u00a0diameter \u00a0orifice \u00a0of the\u00a0 valve, \u00a0its velocity \u00a0increases \u00a0to enable \u00a0mass \u00a0flow through the valve.<\/p>\n<p style=\"text-align: justify;\">The energy needed to increase the velocity comes at the expense of the pressure, so the point of highest velocity is also the point of lowest pressure (smallest cross section).<\/p>\n<p style=\"text-align: justify;\">The point where the pressure is at the lowest is called \u201c<em><u>vena contracta\u201d<\/u><\/em>. To display the general behavior of flow through a control valve, the valve is simplified to an orifice in a pipeline as shown in the figure below:<\/p>\n<h2>Control Valves Theory<\/h2>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4653 size-full\" title=\"Fundamentals of Control Valves\" src=\"https:\/\/instrumentationtools.com\/wp-content\/uploads\/2016\/05\/instrumentationtools.com_fundamentals-of-control-valves.png\" alt=\"Fundamentals of Control Valves\" width=\"1040\" height=\"260\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4654 size-full\" title=\"Control Valve Vena-Contracta\" src=\"https:\/\/instrumentationtools.com\/wp-content\/uploads\/2016\/05\/instrumentationtools.com_control-valve-vena-contracta.png\" alt=\"Control Valve Vena-Contracta\" width=\"561\" height=\"386\" \/><\/p>\n<p style=\"text-align: justify;\">As the liquid passes the point of greatest restriction (vena contracta); its velocity reaches a maximum and its pressure falls to a minimum.<\/p>\n<p style=\"text-align: justify;\">Hence we would expect the highest velocity at the internal to the valve than on upstream and downstream. Beyond the vena contracta, the fluid\u2019s \u00a0velocity \u00a0will \u00a0decrease \u00a0as\u00a0 the \u00a0diameter \u00a0of\u00a0 piping \u00a0increases.<\/p>\n<p style=\"text-align: justify;\">This \u00a0allows \u00a0for \u00a0some pressure \u00a0recovery \u00a0as the energy\u00a0 that was imparted \u00a0as velocity \u00a0is now partially \u00a0converted back into pressure (refer pressure-velocity profile below).<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4655 size-full\" title=\"Control Valve Pressure and Velocity Relationship\" src=\"https:\/\/instrumentationtools.com\/wp-content\/uploads\/2016\/05\/instrumentationtools.com_control-valve-pressure-and-velocity-relationship.png\" alt=\"Control Valve Pressure and Velocity Relationship\" width=\"561\" height=\"261\" \/><\/p>\n<p style=\"text-align: justify;\">It is important to understand how the pressure-velocity conditions change as the fluid passes through the restriction. This is best described by the continuity equation:<\/p>\n<h4 style=\"text-align: justify;\">V1 * A1 = V2 * A2<\/h4>\n<p style=\"text-align: justify;\">Where:<\/p>\n<ul style=\"text-align: justify;\">\n<li>V = mean velocity and<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>A = flow area.<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>Subscript 1 refers to upstream conditions<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>Subscript 2 refer to downstream conditions<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">The equation shows that the velocity and hence the pressure can be changed by adjusting the valve opening (area). With this introduction, we will jump straight to control valve basics and the readers interested in further reading should read the basic principles of hydraulics.<\/p>\n<h2 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">Control Valve Capacity &#8211; Cv:<\/span><\/h2>\n<p style=\"text-align: justify;\">For sizing a control valve we are interested in knowing how much flow we can get through the valve for any given opening\u00a0 of the valve and for any given pressure \u00a0differential.<\/p>\n<p style=\"text-align: justify;\">The relationship between pressure drop and flow rate through a valve is conveniently expressed by a flow coefficient (Cv).<\/p>\n<h2 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">What is Flow Coefficient (Cv)?<\/span><\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/instrumentationtools.com\/calculate-flow-coefficient-kv-of-solenoid-valve\/\" target=\"_blank\" rel=\"noopener\">Flow coefficient<\/a> (Cv) is defined as the number of gallons per minute (gpm) at 60\u00b0F that will pass through a full open valve with a pressure drop of 1 psi.<\/p>\n<p style=\"text-align: justify;\">Simply stated, a control valve which has a Cv of 12 has an effective port area in the full open position such that it passes<\/p>\n<p style=\"text-align: justify;\">12gpm \u00a0of \u00a0water \u00a0with \u00a01 \u00a0psi \u00a0pressure\u00a0\u00a0 drop. \u00a0The \u00a0Cv \u00a0for \u00a0water \u00a0is \u00a0usually \u00a0determined experimentally by measuring the flow through a valve with 1 psi applied pressure to the valve inlet and have a 0 psi pressure at the outlet.<\/p>\n<p style=\"text-align: justify;\">For incompressible \u00a0fluids like water, a close approximation \u00a0can be found mathematically \u00a0by the following equation;<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4656 size-full\" title=\"What is Flow Coefficient\" src=\"https:\/\/instrumentationtools.com\/wp-content\/uploads\/2016\/05\/instrumentationtools.com_what-is-flow-coefficient.png\" alt=\"What is Flow Coefficient\" width=\"158\" height=\"42\" \/><\/p>\n<p style=\"text-align: justify;\">Where,<\/p>\n<ul style=\"text-align: justify;\">\n<li>Cv = Valve flow coefficient<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>Q = Fluid flow, (also given by Area of pipe x mean velocity)<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>S = Specific gravity of fluid relative to water @ 60\u00baF<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>\u2206P = Pressure drop (P1 \u2013 P2) across the control valve at maximum flow, psi<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">The equation shows that the flow rate varies as the square root of the differential pressure across the control valve. Greater the pressure drop, higher will be the flow rate.<\/p>\n<p style=\"text-align: justify;\">Pressure drop across a valve is highly influenced by the area, shape, path and roughness of the valve.<\/p>\n<h2 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">Choked Flow<\/span><\/h2>\n<p style=\"text-align: justify;\">The flow coefficient (Cv) equation illustrates that the flow rate through a valve (Q) increases with the pressure differential (\u2206P).<\/p>\n<p style=\"text-align: justify;\">Simply stated, as the pressure drop across the valve gets larger, more flow will be forced through the restriction due to the higher flow velocities.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4657 size-full\" title=\"Choked Flow Formula\" src=\"https:\/\/instrumentationtools.com\/wp-content\/uploads\/2016\/05\/instrumentationtools.com_choked-flow-formula.png\" alt=\"Choked Flow Formula\" width=\"170\" height=\"42\" \/><\/p>\n<p style=\"text-align: justify;\">In reality, the above relationship only holds true over a limited range. As the pressure drop across the valve is increased, it reaches a point where the increase in flow rate is less than expected.<\/p>\n<p style=\"text-align: justify;\">This continues until no additional flow can be passed through the valve regardless of the increase in pressure drop. This condition is known as choked flow.<\/p>\n<p style=\"text-align: justify;\"><strong><a href=\"https:\/\/instrumentationforum.com\/t\/what-is-choked-flow\/701\" target=\"_blank\" rel=\"noopener\">Choked flow<\/a> (otherwise known as critical flow) takes place:<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>When an increase in pressure drop across the valve no longer has any effect on the flow rate through the valve.<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>When the velocity of the gas or vapor reaches sonic velocity (Mach 1) at the vena contracta.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">To understand \u00a0more about what is occurring, it is necessary\u00a0 to return to the basics again. Recall that as a liquid passes through a restriction, the velocity increases to a maximum and the pressure decreases to a minimum.<\/p>\n<p style=\"text-align: justify;\">As the flow exits, velocity is restored to its previous value, \u00a0while\u00a0 the pressure \u00a0never \u00a0completely \u00a0recovers, \u00a0thus creating \u00a0a pressure \u00a0differential across the valve.<\/p>\n<p style=\"text-align: justify;\">If the pressure differential is sufficiently large, the pressure may, at some point, decrease \u00a0to less than the vapor pressure\u00a0 of the liquid. When this occurs, the liquid partially vaporizes and is no longer incompressible.<\/p>\n<p style=\"text-align: justify;\">It\u00a0 is \u00a0necessary \u00a0to \u00a0account \u00a0for \u00a0choked \u00a0flow \u00a0during \u00a0the \u00a0sizing \u00a0process \u00a0to \u00a0ensure \u00a0against undersizing \u00a0a valve. In other words, it is necessary\u00a0 to know the maximum flow rate that a valve can handle under a given set of conditions.<\/p>\n<p style=\"text-align: justify;\">When selecting a valve, it is important to check the pressure recovery characteristics of valves for the thermodynamic properties of the fluid. High recovery valves, such as ball and butterfly, will become choked at lower pressure drops than low recovery valves such as globe which offer a more restricted flow path when fully open.<\/p>\n<h2 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">Flashing<\/span><\/h2>\n<p style=\"text-align: justify;\">As previously mentioned, at the point where the fluid\u2019s velocity is at its highest, the pressure is at its lowest.<\/p>\n<p style=\"text-align: justify;\">Assuming the fluid is incompressible\u00a0 (liquid), if the pressure falls below the liquid\u2019s vapor pressure, vapor bubbles form within the valve and collapse into themselves as the pressure increases downstream.<\/p>\n<p style=\"text-align: justify;\">This leads to massive shock waves that are noisy and will certainly ruin the equipment.<\/p>\n<p><img loading=\"lazy\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4663 size-full\" title=\"Flashing in Control Valve\" src=\"https:\/\/instrumentationtools.com\/wp-content\/uploads\/2016\/05\/instrumentationtools.com_flashing-in-control-valve.png\" alt=\"Flashing in Control Valve\" width=\"679\" height=\"348\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">Requirements for occurrence of flashing:<\/span><\/h3>\n<ul style=\"text-align: justify;\">\n<li>The fluid at the inlet must be in all-liquid condition, but some vapor must be present at the valve outlet;<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>The fluid at the inlet may be in either a saturated or a subcooled condition; and<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>The valve outlet pressure must be either at or below the vapor pressure of the liquid.<\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">Flashing effects:<\/span><\/h3>\n<ul style=\"text-align: justify;\">\n<li>Material damage is associated with the formation of sand-blasted surfaces;<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>Decreased efficiency \u00a0&#8211; valve ability to convert \u00a0pressure \u00a0drop across \u00a0the valve into mass flowrate is compromised.<\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">How can flash damage be contained:<\/span><\/h3>\n<p style=\"text-align: justify;\">Under \u00a0such \u00a0scenario, \u00a0there \u00a0are two\u00a0 phases \u00a0flowing \u00a0downstream \u00a0of the valve: \u00a0liquid \u00a0and vapor. Flashing cannot be eliminated in the valve if the downstream pressure is less than the vapor pressure of liquid.<\/p>\n<p style=\"text-align: justify;\">However, the damage can be minimized by:<\/p>\n<ul style=\"text-align: justify;\">\n<li>Hard face trim (using hard facing materials \u00a0such as Stellite \u00a0or Tungsten \u00a0Carbide), more erosion resistant body material.<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>Increasing size of the valve, therefore reducing the velocity<\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li>Using angle valve \u2013 flow over plug<\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">Cavitation:<\/span><\/h3>\n<p style=\"text-align: justify;\">Cavitation \u00a0is similar to flashing \u00a0in a way that the liquid pressure \u00a0drops to value below its vapor pressure, causing a liquid to vaporize into vapor bubbles.<\/p>\n<p style=\"text-align: justify;\">Both <a href=\"https:\/\/instrumentationtools.com\/control-valve-cavitation-and-flashing\/\" target=\"_blank\" rel=\"noopener\">cavitation and flashing<\/a> occurs \u00a0because \u00a0the pressure \u00a0energy \u00a0in a fluid\u00a0 is converted \u00a0to kinetic \u00a0energy \u00a0due to the contraction at the valve closure member, causing an increase in velocity.<\/p>\n<p style=\"text-align: justify;\">In addition, as the temperature of the liquid increases, the likelihood of cavitation becomes more likely because of\u00a0 the \u00a0increased \u00a0vapor \u00a0pressure. \u00a0The \u00a0extent \u00a0of \u00a0the \u00a0cavitation \u00a0depends \u00a0mainly \u00a0on \u00a0the downstream pressure and the differential pressure across the valve.<\/p>\n<p><img loading=\"lazy\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4664 size-full\" title=\"Cavitation in Control Valves\" src=\"https:\/\/instrumentationtools.com\/wp-content\/uploads\/2016\/05\/instrumentationtools.com_cavitation-in-control-valves.png\" alt=\"Cavitation in Control Valves\" width=\"702\" height=\"352\" \/><\/p>\n<p style=\"text-align: justify;\">The difference is that with the cavitation phenomenon, the liquid pressure increases over its vapor pressure during pressure recovery and turns back into liquid state while during flashing the liquid pressure <u>remains below<\/u> the vapor pressure throughout.<\/p>\n<p style=\"text-align: justify;\">The key differences are:<\/p>\n<p><img loading=\"lazy\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4665 size-full\" title=\"Difference between cavitation and flashing in control valve\" src=\"https:\/\/instrumentationtools.com\/wp-content\/uploads\/2016\/05\/instrumentationtools.com_difference-between-cavitation-and-flashing-in-control-valve.png\" alt=\"Difference between cavitation and flashing in control valve\" width=\"699\" height=\"430\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">How to avoid Cavitation:<\/span><\/h3>\n<p style=\"text-align: justify;\">If cavitation is ever encountered, consider the following corrective actions:<\/p>\n<ol style=\"text-align: justify;\">\n<li>The first is to equip the control valve with special trim and ensure that the plug and seat are made of a hard facing material that can resist both the onset and effect of cavitation (e.g. stellite hard facing).<\/li>\n<\/ol>\n<ol style=\"text-align: justify;\" start=\"2\">\n<li>The second is to use a valve with a low recovery coefficient (see below).<\/li>\n<\/ol>\n<ol style=\"text-align: justify;\" start=\"3\">\n<li>The \u00a0third \u00a0is\u00a0 to increase \u00a0the \u00a0downstream \u00a0pressure \u00a0by\u00a0 installing \u00a0a flow \u00a0restrictor \u00a0if possible or reducing the pipe size of a short piece downstream.<\/li>\n<\/ol>\n<h3 style=\"text-align: justify;\"><span style=\"color: #ff0000;\">Valve Recovery Coefficient:<\/span><\/h3>\n<p style=\"text-align: justify;\">Valve recovery refers to the pressure recovery from the low pressure at vena contracta to the valve outlet. The term &#8220;valve recovery&#8221; \u00a0is usually applied\u00a0 when a valve is employed \u00a0as a restriction.<\/p>\n<p style=\"text-align: justify;\">\u00a0It is a given that any valve could cause cavitation \u00a0to a differing\u00a0 degree and in different closure positions. If using a valve to cause a pressure drop as compared to control the flow of volume, it is safe to say that a low recovery valve will resist causing cavitation more than a high recovery type.<\/p>\n<p style=\"text-align: justify;\">The valve recovery coefficient is a dimensionless, \u00a0numerical factor that represents a valve&#8217;s flow vs. liquid pressure curve, and thus the valve&#8217;s tendency to cavitate. If this factor is higher than \u00a0desired, \u00a0cavitation \u00a0might \u00a0develop.<\/p>\n<p style=\"text-align: justify;\">The \u00a0valve \u00a0coefficient \u00a0is\u00a0 affected \u00a0by \u00a0the \u00a0internal geometry of the valve, valve size, pressure, and the presence or absence of piping reducers adjacent to the valve.<\/p>\n<p style=\"text-align: justify;\"><strong>Also Read: <span style=\"color: #ff0000;\"><a style=\"color: #ff0000;\" href=\"https:\/\/instrumentationtools.com\/summary-of-valve-types-characteristics\/\" target=\"_blank\" rel=\"noopener\">Valves Characteristics<\/a><\/span><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The flow regulation \u00a0in a valve\u00a0 is accomplished \u00a0by the varying \u00a0resistance as the valve \u00a0is stroked, i.e. its effective cross sectional area is changed. As the fluid moves from the piping into\u00a0 the \u00a0smaller \u00a0diameter \u00a0orifice \u00a0of the\u00a0 valve, \u00a0its velocity \u00a0increases \u00a0to enable \u00a0mass \u00a0flow through the valve. The energy needed to increase [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":4659,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":"","footnotes":""},"categories":[4],"tags":[23554,23541,23542,23543,4374,4368,4366,4362,23530,23531,4363,4364,5652,23536,4187,4360,23534,23551,23550,23544,23545,23546,23547,23548,516,23539,23540,4369,22539,22452,23537,4371,4372,4367,23533,23549,4359,4373,4375,23532,23553,23535,23538,1942,4370,23552,4376,4361,4365],"class_list":{"0":"post-4652","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-control-valves","8":"tag-5-2-directional-control-valve-theory","9":"tag-basics-of-control-valves","10":"tag-basics-of-control-valves-pdf","11":"tag-basics-of-control-valves-ppt","12":"tag-cavitation","13":"tag-cavitation-in-control-valves","14":"tag-choked-flow","15":"tag-choked-flow-formula","16":"tag-control-valve-basics-ppt","17":"tag-control-valve-basics-theory","18":"tag-control-valve-capacity","19":"tag-control-valve-capacity-cv","20":"tag-control-valve-characteristics-theory","21":"tag-control-valve-positioner-basics","22":"tag-control-valve-positioner-theory","23":"tag-control-valve-pressure-and-velocity-relationship","24":"tag-control-valve-sizing-basics","25":"tag-control-valve-sizing-calculation-theory","26":"tag-control-valve-sizing-theory","27":"tag-control-valve-theory","28":"tag-control-valve-theory-of-operation","29":"tag-control-valve-theory-pdf","30":"tag-control-valve-theory-ppt","31":"tag-control-valve-theory-wiki","32":"tag-control-valves","33":"tag-control-valves-basics","34":"tag-control-valves-basics-pdf","35":"tag-difference-between-cavitation-and-flashing-in-control-valve","36":"tag-directional-control-valve-theory","37":"tag-directional-control-valves-basics","38":"tag-fisher-control-valve-basics","39":"tag-flashing","40":"tag-flashing-effects","41":"tag-flashing-in-control-valve","42":"tag-flow-control-valves-basics","43":"tag-flow-control-valves-theory","44":"tag-fundamentals-of-control-valves","45":"tag-how-can-flash-damage-be-contained","46":"tag-how-to-avoid-cavitation","47":"tag-hydraulic-control-valves-basics","48":"tag-introduction-to-control-valve-theory","49":"tag-pneumatic-control-valve-basics","50":"tag-pressure-control-valve-basics","51":"tag-pressure-control-valve-theory","52":"tag-requirements-for-occurrence-of-flashing","53":"tag-theory-of-control-valves","54":"tag-valve-recovery-coefficient","55":"tag-what-is-flow-coefficient","56":"tag-what-is-flow-coefficient-cv"},"yoast_head":"<!-- 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