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left="36" top="8.25" width="416.25" height="13.5" align-x="53.25" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Insolation per day.xmcd<sp count="3"/>Charles Kim 2013</p> </text> </region> <region region-id="902" left="24" top="38.25" width="675" height="54" align-x="27.75" align-y="48" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Q.<sp count="2"/>Estimate the insolation on a south-facing collector at a tilt angle of 30 degress in Oakland, CA (latitude 37.73 degrres N).<sp count="2"/>Assume that (1) Avrage horizontal Insolation (IH) in July is 7.32 kWh.m^2-day, and (2) ground reflectivity os 0.2</p> </text> </region> <region region-id="946" left="30" top="96" width="265.5" height="223.5" align-x="30" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="2" display-width="264" display-height="222"/> </picture> <rendering item-idref="3"/> </region> <region region-id="948" left="342" top="96" width="300.75" height="225" align-x="342" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="4" display-width="299.25" display-height="223.5"/> </picture> <rendering item-idref="5"/> </region> <region region-id="979" left="498" top="332.25" width="180" height="27" align-x="505.5" align-y="342" show-border="true" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Try to change this angle</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">for your city.</p> </text> </region> <region region-id="968" left="330" top="342.75" width="46.5" height="15.75" align-x="345.75" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">L</ml:id> <ml:real>37.73</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="969" left="390" top="344.25" width="67.5" height="13.5" align-x="408" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Latitude </p> </text> </region> <region region-id="1008" left="150" top="348.75" width="37.5" height="15.75" align-x="165.75" align-y="360" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ρ</ml:id> <ml:real>0.2</ml:real> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="990" left="330" top="360.75" width="47.25" height="15.75" align-x="351" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IH</ml:id> <ml:real>7.32</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="1011" left="168" top="368.25" width="142.5" height="13.5" align-x="185.25" align-y="378" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Ground Reflectivity</p> </text> </region> <region region-id="1006" left="390" top="380.25" width="165" height="13.5" align-x="400.5" align-y="390" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">tilted angle in degree</p> </text> </region> <region region-id="921" left="18" top="386.25" width="67.5" height="13.5" align-x="47.25" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">SOLUTION </p> </text> </region> <region region-id="1004" left="330" top="384.75" width="35.25" height="15.75" align-x="345.75" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">S</ml:id> <ml:real>30</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="950" left="42" top="408" width="471.75" height="45" align-x="42" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="10" display-width="470.25" display-height="43.5"/> </picture> <rendering item-idref="11"/> </region> <region region-id="957" left="540" top="434.25" width="135" height="13.5" align-x="555.75" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Sunrise Hour Angle</p> </text> </region> <region region-id="952" left="30" top="470.25" width="180" height="13.5" align-x="33" align-y="480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">1. Sun declination angle</p> </text> </region> <region region-id="960" left="48" top="492.75" width="39.75" height="15.75" align-x="63.75" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">n</ml:id> <ml:real>197</ml:real> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="962" left="108" top="494.25" width="97.5" height="13.5" align-x="111" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">n for July 16</p> </text> </region> <region region-id="958" left="42" top="511.5" width="190.5" height="27.75" align-x="72" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:real>23.45</ml:real> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>360</ml:real> <ml:real>365</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">x</ml:id> <ml:real>81</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="970" left="324" top="540" width="195" height="44.25" align-x="324" align-y="540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="14" display-width="193.5" display-height="42.75"/> </picture> <rendering item-idref="15"/> </region> <region region-id="959" left="48" top="552.75" width="75.75" height="15.75" align-x="78" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>21.353678575709374</ml:real> </result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="964" left="30" top="584.25" width="195" height="13.5" align-x="33" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">2. Sunrise Hour Angle(HSR)</p> </text> </region> <region region-id="971" left="48" top="612.75" width="274.5" height="15.75" align-x="80.25" align-y="624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">HSR</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">acos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.8781086417198702</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="973" left="342" top="614.25" width="60" height="13.5" align-x="357.75" align-y="624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">radians </p> </text> </region> <region region-id="983" left="498" top="632.25" width="142.5" height="13.5" align-x="509.25" align-y="642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Solar Constant (SC)</p> </text> </region> <region region-id="975" left="30" top="656.25" width="420" height="13.5" align-x="33" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">3. Extraterrestrial Insolation (Io) with SC=1.37 kW/m^2 </p> </text> </region> <region region-id="981" left="504" top="654.75" width="50.25" height="15.75" align-x="528" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">SC</ml:id> <ml:real>1.37</ml:real> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="985" left="576" top="656.25" width="60" height="13.5" align-x="584.25" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kW / m^2</p> </text> </region> <region region-id="976" left="54" top="678" width="601.5" height="53.25" align-x="54" align-y="678" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="19" display-width="600" display-height="51.75"/> </picture> <rendering item-idref="20"/> </region> <region region-id="996" left="6" top="736.5" width="723.75" height="33.75" align-x="24.75" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Io</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:div/> <ml:real>24</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">SC</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:real>0.034</ml:real> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>360</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>365</ml:real> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">HSR</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">HSR</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>11.34165615536976</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="989" left="24" top="782.25" width="262.5" height="13.5" align-x="27" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">4. Clearness Index (KT): KT = IH/Io</p> </text> </region> <region region-id="991" left="78" top="796.5" width="98.25" height="33.75" align-x="102.75" align-y="816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">KT</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">IH</ml:id> <ml:id xml:space="preserve">Io</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.6454083865462904</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="993" left="30" top="848.25" width="285" height="13.5" align-x="33" align-y="858" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">5. Horizontal Diffuse Radiation (IDH):</p> </text> </region> <region region-id="995" left="72" top="870" width="450" height="79.5" align-x="72" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="23" display-width="448.5" display-height="78"/> </picture> <rendering item-idref="24"/> </region> <region region-id="997" left="42" top="944.25" width="336" height="20.25" align-x="71.25" align-y="960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IDH</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:real>1.390</ml:real> <ml:apply> <ml:mult/> <ml:real>4.027</ml:real> <ml:id xml:space="preserve">KT</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>5.531</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">KT</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3.108</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">KT</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">IH</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.8981904895041923</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="1000" left="372" top="990" width="225" height="61.5" align-x="372" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="26" display-width="223.5" display-height="60"/> </picture> <rendering item-idref="27"/> </region> <region region-id="999" left="24" top="986.25" width="307.5" height="13.5" align-x="27" align-y="996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">6. Diffuse Ration on the Collector (IDC):</p> </text> </region> <region region-id="1001" left="48" top="1036.5" width="210.75" height="30.75" align-x="77.25" align-y="1056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IDC</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">IDH</ml:id> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">S</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.771035837318421</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="1015" left="276" top="1046.25" width="82.5" height="13.5" align-x="287.25" align-y="1056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kWh/m^2-day</p> </text> </region> <region region-id="1007" left="414" top="1086" width="215.25" height="71.25" align-x="414" align-y="1086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="29" display-width="213.75" display-height="69.75"/> </picture> <rendering item-idref="30"/> </region> <region region-id="1003" left="30" top="1094.25" width="337.5" height="13.5" align-x="33" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">7. Reflected Radiation on the collector (IRC)</p> </text> </region> <region region-id="1012" left="48" top="1126.5" width="220.5" height="30.75" align-x="76.5" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IRC</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve">IH</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">S</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.098069404429790882</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="1017" left="288" top="1136.25" width="82.5" height="13.5" align-x="299.25" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kWh/m^2-day</p> </text> </region> <region region-id="1021" left="306" top="1176" width="400.5" height="49.5" align-x="306" align-y="1176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="32" display-width="399" display-height="48"/> </picture> <rendering item-idref="33"/> </region> <region region-id="1019" left="30" top="1184.25" width="262.5" height="13.5" align-x="33" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">8. Horizontal Beam Radiation (IBH):</p> </text> </region> <region region-id="1022" left="48" top="1236.75" width="132.75" height="15.75" align-x="76.5" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IBH</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">IH</ml:id> <ml:id xml:space="preserve">IDH</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>5.4218095104958079</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="1024" left="204" top="1238.25" width="82.5" height="13.5" align-x="204" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kWh/m^2-day</p> </text> </region> <region region-id="1026" left="30" top="1274.25" width="345" height="13.5" align-x="33" align-y="1284" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">9. Sunrise Hour Angle on the Collector (HSRC) </p> </text> </region> <region region-id="1035" left="234" top="1296" width="469.5" height="102.75" align-x="234" align-y="1296" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="35" display-width="468" display-height="101.25"/> </picture> <rendering item-idref="36"/> </region> <region region-id="1032" left="6" top="1302" width="210" height="69" align-x="6" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="37" display-width="208.5" display-height="67.5"/> </picture> <rendering item-idref="38"/> </region> <region region-id="1036" left="48" top="1404.75" width="288" height="15.75" align-x="93.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">HSRC1</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">acos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.8781086417198702</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="1038" left="54" top="1440.75" width="336.75" height="15.75" align-x="99.75" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">HSRC2</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">acos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">S</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.6238900561983376</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="1039" left="48" top="1470.75" width="204.75" height="15.75" align-x="87.75" align-y="1482" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">HSRC</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">min</ml:id> <ml:sequence> <ml:id xml:space="preserve">HSRC1</ml:id> <ml:id xml:space="preserve">HSRC2</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.6238900561983376</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="1041" left="276" top="1472.25" width="60" height="13.5" align-x="291.75" align-y="1482" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">radians </p> </text> </region> <region region-id="1043" left="24" top="1514.25" width="195" height="13.5" align-x="27.75" align-y="1524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">10. Beam Tilt Factor (RB):</p> </text> </region> <region region-id="1045" left="66" top="1530" width="468" height="81" align-x="66" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="42" display-width="466.5" display-height="79.5"/> </picture> <rendering item-idref="43"/> </region> <region region-id="1046" left="42" top="1624.5" width="597" height="33.75" align-x="66" align-y="1644" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">RB</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">S</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">HSRC</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">HSRC</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">S</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">HSR</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">HSR</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.89339153588562081</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="1048" left="24" top="1682.25" width="315" height="13.5" align-x="29.25" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">11. Beam Radiation on the Collector (IBC):</p> </text> </region> <region region-id="1049" left="48" top="1710" width="224.25" height="66.75" align-x="48" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="45" display-width="222.75" display-height="65.25"/> </picture> <rendering item-idref="46"/> </region> <region region-id="1050" left="306" top="1740.75" width="133.5" height="15.75" align-x="334.5" align-y="1752" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IBC</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">IBH</ml:id> <ml:id xml:space="preserve">RB</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>4.8437987258611157</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="1052" left="462" top="1742.25" width="97.5" height="13.5" align-x="474.75" align-y="1752" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kWh / m^2-day</p> </text> </region> <region region-id="1054" left="24" top="1808.25" width="450" height="13.5" align-x="29.25" align-y="1818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">12. Total Insolation on the Collector (IC):<sp count="2"/>IC=IBC+IDC+IRC </p> </text> </region> <region region-id="1055" left="60" top="1836.75" width="165.75" height="15.75" align-x="81" align-y="1848" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IC</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">IBC</ml:id> <ml:id xml:space="preserve">IDC</ml:id> </ml:apply> <ml:id xml:space="preserve">IRC</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>6.7129039676093276</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="1057" left="264" top="1838.25" width="82.5" height="13.5" align-x="275.25" align-y="1848" show-border="false" 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