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Water cooling tower
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EXERIMENTAL CALCULATIONS :

 

Diameter of Orifice, mm (d1) =34

Diameter of pipe, mm (d2) =68

Coefficient of discharge Cd= 0.6
Density of manometer fluid (water), «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨»§#929;«/mi»«/math»w (kg/m3)  =1000

Density of air, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold-italic¨»§#929;«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«/msub»«/math» (kg/m3)  =1.126

g = 9.81 m/s2

Flow rate = 70 ltr/hr

 

 

S. No. T1 T2 T3 T4 T5 T6 R1(cm) R2(cm) QW (LPH)
1  19  17.5  38.6  36  44.5  30.5  5.6  9.5  3.9
2  19.5  18.1  35.4  34.4  43.7  28.3  3  12.1  9.1
3  20 18.7 35.1  34  44.1  28  0.2  14.1  13.9

 

CALCULATIONS :

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#9651;«/mo»«mi mathvariant=¨bold¨»H«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mrow»«msub»«mi mathvariant=¨bold¨»R«/mi»«mn»1«/mn»«/msub»«mo»§nbsp;«/mo»«mo»-«/mo»«msub»«mi mathvariant=¨bold¨»R«/mi»«mn»2«/mn»«/msub»«/mrow»«mn»100«/mn»«/mfrac»«mfenced»«mrow»«mfrac»«msub»«mi mathvariant=¨bold-italic¨»§#929;«/mi»«mi mathvariant=¨bold¨»W«/mi»«/msub»«msub»«mi mathvariant=¨bold-italic¨»§#929;«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/math» =34.54 m

a1 =Cross Section area of Orifice, m2= 907.46 *10-6  m   

a2 = Cross Section area of pipe, m2 =3629.84*10-6 m

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»Q«/mi»«mi mathvariant=¨bold¨»a«/mi»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«msub»«mi mathvariant=¨bold¨»a«/mi»«mn»1«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»a«/mi»«mn»2«/mn»«/msub»«/mrow»«msqrt»«mrow»«msup»«msub»«mi mathvariant=¨bold¨»a«/mi»«mn»2«/mn»«/msub»«mn»2«/mn»«/msup»«mo»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»a«/mi»«mn»1«/mn»«/msub»«mn»2«/mn»«/msup»«/mrow»«/msqrt»«/mfrac»«msub»«mi mathvariant=¨bold¨»C«/mi»«mrow»«mi mathvariant=¨bold¨»d«/mi»«msqrt»«mrow»«mn»2«/mn»«mi mathvariant=¨bold¨»g«/mi»«mo»§#9651;«/mo»«mi mathvariant=¨bold¨»H«/mi»«/mrow»«/msqrt»«/mrow»«/msub»«/math»  = 0.01463 m3/s

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»G«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«msub»«mi mathvariant=¨bold¨»Q«/mi»«mi mathvariant=¨bold¨»a«/mi»«/msub»«msub»«mi mathvariant=¨bold-italic¨»§#929;«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«/msub»«/math» = 0.0165 kg/s

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»L«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mrow»«msub»«mi mathvariant=¨bold¨»Q«/mi»«mi mathvariant=¨bold¨»W«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»§#929;«/mi»«mi mathvariant=¨bold¨»W«/mi»«/msub»«/mrow»«mrow»«mn»1000«/mn»«mo»§#215;«/mo»«mn»3600«/mn»«/mrow»«/mfrac»«/math» =0.01944 kg/s

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi mathvariant=¨bold¨»L«/mi»«mi mathvariant=¨bold¨»G«/mi»«/mfrac»«/math» =1.178

From Enthalpy table, the enthalpy of entering air at a wet bulb temp i.e.17.5 0C is h1= 15.274 Btu/lb of air

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»h«/mi»«mrow»«mi mathvariant=¨bold¨»a«/mi»«mo»§nbsp;«/mo»«/mrow»«/msub»«mo»=«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mrow»«mn»2«/mn»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mrow»«/msub»«mo»=«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mrow»«mn»1«/mn»«mo»§nbsp;«/mo»«/mrow»«/msub»«mo»+«/mo»«mfenced»«mfrac»«mi mathvariant=¨bold¨»L«/mi»«mi mathvariant=¨bold¨»G«/mi»«/mfrac»«/mfenced»«mfenced»«mrow»«msub»«mi mathvariant=¨bold¨»T«/mi»«mrow»«mn»5«/mn»«mo»-«/mo»«/mrow»«/msub»«msub»«mi mathvariant=¨bold¨»T«/mi»«mn»6«/mn»«/msub»«/mrow»«/mfenced»«/math»

                    =15.274 + 1.178(44.5-30.5)

                    =31.766 Btu/lb of air

         T,0F                             hwi                        hai               «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#9651;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mrow»«mi mathvariant=¨bold¨»w«/mi»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/msub»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mrow»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/msub»«/math»
T=T2 =63.5 hw =   -------- ha  = h=15.274   --------
T=T2 +0.1(T1-T2)=63.77 hw =32.12 ha  = h1+0.1(L/G)(T5-T6) =18.25
 13.87
T=T2 +0.4(T1-T2)=64.56 hw =33.12  ha  = h1+0.4(L/G)(T5-T6) =27.19  5.93
T=T2 -0.4(T1-T2)=65.12 hw =33.62  ha  = h2-0.4(L/G)(T5-T6)= 19.84  13.78
T=T2 -0.1(T1-T2)=65.93 hw =34.11  ha  = h2-0.1(L/G)(T5-T6) = 28.78  5.33
T=T =66.2 hw =34.32  ha  = h2 = 31.76  2.56

 

Cooling range = T5-T6  = 140C

Temperature approach =T2-T6 = -130C

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8721;«/mo»«mfrac»«mn»1«/mn»«mrow»«mo»§#9651;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mrow»«mo»§#9651;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mn»1«/mn»«/msub»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mo»§#9651;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mn»2«/mn»«/msub»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mo»§#9651;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mn»3«/mn»«/msub»«/mrow»«/mfrac»«mfrac»«mn»1«/mn»«mrow»«mo»§#9651;«/mo»«msub»«mi mathvariant=¨bold¨»h«/mi»«mn»4«/mn»«/msub»«/mrow»«/mfrac»«/math»

                    = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mn»13«/mn»«mo».«/mo»«mn»67«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»5«/mn»«mo».«/mo»«mn»93«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»13«/mn»«mo».«/mo»«mn»67«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»5«/mn»«mo».«/mo»«mn»33«/mn»«/mrow»«/mfrac»«/math»

                     = 0.501

Now tower characteristics

 

             =1.7535

 On doing the similar calculations for different values of (L/G),we get the complete calculation table.From there we draw a graph between tower characteristics and (L/G).

 

 

 

 

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