{"id":2275,"date":"2016-03-13T16:02:44","date_gmt":"2016-03-13T16:02:44","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=2275"},"modified":"2016-03-13T16:02:44","modified_gmt":"2016-03-13T16:02:44","slug":"entropyisentropic-efficiencies-of-steady-flow-devices","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/entropyisentropic-efficiencies-of-steady-flow-devices\/","title":{"rendered":"ENTROPY:ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICES"},"content":{"rendered":"<div class=\"bjqno6a0dbe34ba535\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '61e5902552e2353963d8d2f1bd1f4a8f',\n\t\t'format' : 'iframe',\n\t\t'height' : 250,\n\t\t'width' : 300,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/61e5902552e2353963d8d2f1bd1f4a8f\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.bjqno6a0dbe34ba535 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.bjqno6a0dbe34ba535 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.bjqno6a0dbe34ba535 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.bjqno6a0dbe34ba535 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.bjqno6a0dbe34ba535 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<p align=\"justify\"><font size=\"5\">\u25a0 <b>ISENTROPI<\/b><b>C EFFICIENCIES<\/b><b> <\/b><b>O<\/b><b>F STEADY-FLOW DEVICES<\/b><\/font> <\/p>\n<p align=\"justify\">\n<p align=\"justify\"><font size=\"5\"><\/font><\/p>\n<p><font size=\"5\">We mentioned repeatedly that irreversibilities inherently accompany all actual processes and that their effect is always to downgrade the performance of devices. In engineering analysis, it would be very desirable to have some parameters that would enable us to quantify the degree of degradation of energy in these devices. In the last chapter we did this for cyclic devices, such as heat engines and refrigerators, by comparing the actual cycles to the idealized ones, such as the Carnot cycle. A cycle that was composed entirely of reversible processes served as the <i>mode<\/i><i>l cycle <\/i>to which the actual cycles could be compared. This idealized model cycle enabled us to determine the theoretical limits of performance for cyclic devices under specified conditions and to examine how the performance of actual devices suffered as a result of irreversibilities.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Now we extend the analysis to discrete engineering devices working under steady-flow conditions, such as turbines, compressors, and nozzles, and we examine the degree of degradation of energy in these devices as a result of irreversibilities. However, first we need to define an ideal process that will serve as a model for the actual processes.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Although some heat transfer between these devices and the surrounding medium is unavoidable, many steady-flow devices are intended to operate under adiabatic conditions. Therefore, the model process for these devices should be an adiabatic one. Furthermore, an ideal process should involve no irreversibilities since the effect of irreversibilities is always to downgrade the performance of engineering devices. Thus, the ideal process that can serve as a suitable model for adiabatic steady-flow devices is the <i>isentropic <\/i>process (Fig. 7\u201348).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0237.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0237\" border=\"0\" alt=\"ENTROPY-0237\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0237_thumb.jpg\" width=\"198\" height=\"176\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The more closely the actual process approximates the idealized isentropic <\/font><font size=\"5\">process, the better the device will perform. Thus, it would be desirable to have a parameter that expresses quantitatively how efficiently an actual device approximates an idealized one. This parameter is the <b>isentropic <\/b>or <b>adiabatic efficiency, <\/b>which is a measure of the deviation of actual processes from the corresponding idealized ones.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Isentropic efficiencies are defined differently for different devices since each device is set up to perform different tasks. Next we define the isentropic efficiencies of turbines, compressors, and nozzles by comparing the actual performance of these devices to their performance under isentropic conditions for the same inlet state and exit pressure.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>Isentropi<\/b><b>c Efficiency of Turbines<\/b><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">For a turbine under steady operation, the inlet state of the working fluid and <\/font><font size=\"5\">the exhaust pressure are fixed. Therefore, the ideal process for an adiabatic turbine is an isentropic process between the inlet state and the exhaust pressure. The desired output of a turbine is the work produced, and the <b>isentropic efficiency of a turbine <\/b>is defined as <i>the ratio of the actual work output of the turbine to the work output that would be achieved if the process between the inlet state and the exit pressure were isentropic:<\/i><\/font> <\/p>\n<p align=\"justify\"><em><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0238.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0238\" border=\"0\" alt=\"ENTROPY-0238\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0238_thumb.jpg\" width=\"251\" height=\"32\"><\/a><\/font><\/em> <\/p>\n<p align=\"justify\"><font size=\"5\">Usually the changes in kinetic and potential energies associated with a fluid stream flowing through a turbine are small relative to the change in enthalpy and can be neglected. Then the work output of an adiabatic turbine simply becomes the change in enthalpy, and Eq. 7\u201360 becomes<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0239.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0239\" border=\"0\" alt=\"ENTROPY-0239\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0239_thumb.jpg\" width=\"220\" height=\"31\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0240.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0240\" border=\"0\" alt=\"ENTROPY-0240\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0240_thumb.jpg\" width=\"172\" height=\"241\"><\/a><\/font> <\/p>\n<h6 align=\"justify\"><font size=\"5\">where <i>h<\/i>2<i>a <\/i>and <i>h<\/i>2<i>s <\/i>are the enthalpy values at the exit state for actual and isentropic processes, respectively (Fig. 7\u201349).<\/font><\/h6>\n<p align=\"justify\"><font size=\"5\">The value of h<i>T <\/i>greatly depends on the design of the individual components <\/font><font size=\"5\">that make up the turbine. Well-designed, large turbines have isentropic ef<\/font><font size=\"5\">ficiencies above 90 percent. For small turbines, however, it may drop even below 70 percent. The value of the isentropic efficiency of a turbine is deter- mined by measuring the actual work output of the turbine and by calculating the isentropic work output for the measured inlet conditions and the exit pressure. This value can then be used conveniently in the design of power plants.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0241.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0241\" border=\"0\" alt=\"ENTROPY-0241\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0241_thumb.jpg\" width=\"371\" height=\"164\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0242.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0242\" border=\"0\" alt=\"ENTROPY-0242\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0242_thumb.jpg\" width=\"408\" height=\"484\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>Isentropi<\/b><b>c Efficiencies of Compressors and Pumps<\/b><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>&nbsp;<\/b>The <b>isentropic efficiency of a compressor <\/b>is defined as <i>the ratio of the work input required to raise the pressure of a gas to a specified value in an isentropic manner to the actual work input:<\/i><\/font> <\/p>\n<p align=\"justify\"><em><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0243.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0243\" border=\"0\" alt=\"ENTROPY-0243\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0243_thumb.jpg\" width=\"302\" height=\"42\"><\/a><\/font><\/em> <\/p><div class=\"rhobr6a0dbe34ba7d5\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '0c1eb4c533eaedb7b996f49a5a4983a9',\n\t\t'format' : 'iframe',\n\t\t'height' : 300,\n\t\t'width' : 160,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/0c1eb4c533eaedb7b996f49a5a4983a9\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.rhobr6a0dbe34ba7d5 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.rhobr6a0dbe34ba7d5 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.rhobr6a0dbe34ba7d5 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.rhobr6a0dbe34ba7d5 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.rhobr6a0dbe34ba7d5 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"euigj6a0dbe34ba676\" ><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-0778475562755157\"\n     crossorigin=\"anonymous\"><\/script>\n<!-- 300x600 hydraulics-and-pneumatics -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:600px\"\n     data-ad-client=\"ca-pub-0778475562755157\"\n     data-ad-slot=\"3735577695\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.euigj6a0dbe34ba676 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.euigj6a0dbe34ba676 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.euigj6a0dbe34ba676 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.euigj6a0dbe34ba676 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.euigj6a0dbe34ba676 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<h6 align=\"justify\"><font size=\"5\">Notice that the isentropic compressor efficiency is defined with the <i>isent<\/i><i>r<\/i><i>opic wor<\/i><i>k input in the numerator <\/i>instead of in the denominator. This is because <i>w<\/i><i>s <\/i>is a smaller quantity than <i>w<\/i><i>a<\/i>, and this definition prevents h<i>C <\/i>from becoming greater than 100 percent, which would falsely imply that the actual compressors performed better than the isentropic ones. Also notice that the inlet conditions and the exit pressure of the gas are the same for both the actual and the isentropic compressor.<\/font><\/h6>\n<p align=\"justify\"><font size=\"5\">When the changes in kinetic and potential energies of the gas being com- pressed are negligible, the work input to an adiabatic compressor becomes<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0244.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0244\" border=\"0\" alt=\"ENTROPY-0244\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0244_thumb.jpg\" width=\"202\" height=\"34\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">where <i>h<\/i>2<i>a <\/i>and <i>h<\/i>2<i>s <\/i>are the enthalpy values at the exit state for actual and isentropic compression processes, respectively, as illustrated in Fig. 7\u201351.<\/font> <\/p>\n<p align=\"justify\">\n<h6 align=\"justify\"><font size=\"5\"><\/font><\/h6>\n<p><font size=\"5\">Again, the value of h<i>C <\/i>greatly depends on the design of the compressor. Well- <\/font><font size=\"5\">designed compressors have isentropic efficiencies that range from 75 to <\/font><font size=\"5\">85 percent.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">When the changes in potential and kinetic energies of a liquid are negligible, the isentropic efficiency of a pump is defined similarly as<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0245.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0245\" border=\"0\" alt=\"ENTROPY-0245\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0245_thumb.jpg\" width=\"262\" height=\"31\"><\/a><\/font> <\/p>\n<h6 align=\"justify\"><font size=\"5\">When no attempt is made to cool the gas as it is compressed, the actual compression process is nearly adiabatic and the reversible adiabatic (i.e., isentropic) process serves well as the ideal process. However, sometimes <i>comp<\/i><i>r<\/i><i>essor<\/i><i>s are cooled intentionally <\/i>by utilizing fins or a water jacket placed around the casing to reduce the work input requirements (Fig. 7\u201352). In this case, the isentropic process is not suitable as the model process since the device is no longer adiabatic and the isentropic compressor efficiency defined above is meaningless. A realistic model process for compressors that are intentionally cooled during the compression process is the <i>r<\/i><i>eversibl<\/i><i>e isothermal process. <\/i>Then we can conveniently define an <b>isothermal efficiency <\/b>for such cases by comparing the actual process to a reversible isothermal one:<\/font><\/h6>\n<p align=\"justify\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0246.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0246\" border=\"0\" alt=\"ENTROPY-0246\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0246_thumb.jpg\" width=\"214\" height=\"41\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0247.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0247\" border=\"0\" alt=\"ENTROPY-0247\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0247_thumb.jpg\" width=\"172\" height=\"484\"><\/a><\/p>\n<p align=\"justify\"><font size=\"5\">where <i>w<\/i><i>t <\/i>and <i>w<\/i><i>a <\/i>are the required work inputs to the compressor for the <\/font><font size=\"5\">reversible isothermal and actual cases, respectively.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0248.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0248\" border=\"0\" alt=\"ENTROPY-0248\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0248_thumb.jpg\" width=\"390\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0249.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0249\" border=\"0\" alt=\"ENTROPY-0249\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0249_thumb.jpg\" width=\"365\" height=\"169\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><strong>Isentropic Efficiency of Nozzles<\/strong><\/font> <\/p>\n<h6 align=\"justify\"><font size=\"5\">Nozzles are essentially adiabatic devices and are used to accelerate a fluid.<\/font><\/h6>\n<p align=\"justify\"><font size=\"5\">Therefore, the isentropic process serves as a suitable model for nozzles. The <b>isentropic efficiency of a nozzle <\/b>is defined as <i>the ratio of the actual kinetic energy of the fluid at the nozzle exit to the kinetic energy value at the exit of an isentropic nozzle for the same inlet state and exit pressure. <\/i>That is,<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0250.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0250\" border=\"0\" alt=\"ENTROPY-0250\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0250_thumb.jpg\" width=\"318\" height=\"32\"><\/a><\/font> <\/p>\n<h6 align=\"justify\"><font size=\"5\">Note that the exit pressure is the same for both the actual and isentropic processes, but the exit state is different.<\/font><\/h6>\n<p align=\"justify\"><font size=\"5\">Nozzles involve no work interactions, and the fluid experiences little or no change in its potential energy as it flows through the device. If, in addition, the <i>h <\/i>inlet velocity of the fluid is small relative to the exit velocity, the energy balance for this steady-flow device reduces to<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0251.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0251\" border=\"0\" alt=\"ENTROPY-0251\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0251_thumb.jpg\" width=\"368\" height=\"107\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0252.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0252\" border=\"0\" alt=\"ENTROPY-0252\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0252_thumb.jpg\" width=\"191\" height=\"229\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">where <i>h<\/i>2<i>a <\/i>and <i>h<\/i>2<i>s <\/i>are the enthalpy values at the nozzle exit for the actual and isentropic processes, respectively (Fig. 7\u201354). Isentropic efficiencies of noz<\/font><font size=\"5\">zles are typically above 90 percent, and nozzle efficiencies above 95 percent are not uncommon.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0253.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0253\" border=\"0\" alt=\"ENTROPY-0253\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0253_thumb.jpg\" width=\"350\" height=\"120\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0254.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0254\" border=\"0\" alt=\"ENTROPY-0254\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0254_thumb.jpg\" width=\"421\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0255.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0255\" border=\"0\" alt=\"ENTROPY-0255\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0255_thumb.jpg\" width=\"540\" height=\"343\"><\/a><\/font> <\/p>\n<p align=\"justify\">\n<p align=\"justify\"><font size=\"5\"><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0 ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICES We mentioned repeatedly that irreversibilities inherently accompany all actual processes and that their effect is always to downgrade the performance of devices. In engineering analysis, it would be very desirable to have some parameters that would enable us to quantify the degree of degradation of energy in these devices. [&hellip;]<br \/><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/entropyisentropic-efficiencies-of-steady-flow-devices\/\" class=\"more-link\" >Continue reading&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2275"}],"collection":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/comments?post=2275"}],"version-history":[{"count":1,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2275\/revisions"}],"predecessor-version":[{"id":2276,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2275\/revisions\/2276"}],"wp:attachment":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/media?parent=2275"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/categories?post=2275"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/tags?post=2275"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}