­®­´¤¡´œ›rÁ·Šž¦³‹´„¬rĜ„µ¦šÎµœµ¥„ε¨´ŠÅ¢¢jµ °ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Empirical Correlations for Predicting Electric Power of Centrifugal Pump

­®­´¤¡´œ›rÁ·Šž¦³‹´„¬rĜ„µ¦šÎµœµ¥„ε¨´ŠÅ¢¢jµ…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Empirical Correlations for Predicting Electric Power of Centrifugal Pump

¤µœ¡ ¡·¡´•®´˜™„»¨^* š¦Š›¦¦¤ Á®¨nµ­»ª¦¦– ¨³ Œ´˜¦´¥ Áž¨nŠ­³°µ—

­µ…µª·µª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ‡–³ª·«ª„¦¦¤«µ­˜¦r ­™µ´œÁš‡ÃœÃ¨¥¸žš»¤ª´œ

833 ™œœ¡¦³¦µ¤ 1 …ªŠª´ŠÄ®¤n Á…˜žš»¤ª´œ „¦»ŠÁš¡² 10330 Ú¦«´¡šr: 0-2104-9099 Manop Pipathattakul^*, Songtam Laosuwan and Chatchai Plengsaard

Department of Mechanical Engineering, Faculty of Engineering, Pathumwan Institute of Technology 833 Rama I Road, Wangmai, Pathumwan, Bangkok 10330, THAILAND. Tel: 66(0)-2104-9099,

E-mail: Nop_mt@hotmail.com

š‡´—¥n°

Šµœª·‹´¥œ¸Êŗo„¨nµª™¹Š­®­´¤¡´œ›rÁ·Šž¦³‹´„¬r­Îµ®¦´„µ¦šÎµœµ¥„ε¨´ŠÅ¢¢jµ…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š

®œ¸«¼œ¥r ¦³š—¨°Šž¦³„°—oª¥Á‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r ¦»nœ A65-130 …´—oª¥¤°Á˜°¦rÅ¢¢jµ 3 Á¢­

…œµ— 5.5 ¦Š¤oµ ×¥¤¸ÁŠºÉ°œÅ…Äœ„µ¦š—¨°ŠÄœnªŠ‡ªµ¤Á¦Èª¦° 1100 – 1750 ¦°˜n°œµš¸Â¨³°´˜¦µ„µ¦Å®¨ 1 – 6 ¨·˜¦˜n°ª·œµš¸ ‹µ„Ÿ¨„µ¦š—¨°ŠÂ­—ŠÄ®oÁ®Èœªnµ ‡nµ„ε¨´ŠÅ¢¢jµ š¸Éŗo‹µ„„µ¦‡Îµœª– ×¥­®­´¤¡´œ›rÁ·Š

ž¦³‹´„¬r ¤¸‡nµ‡ªµ¤Ÿ·—¡¨µ—ž¦³¤µ– r10 Áž°¦rÁŽÈœ˜rÁ¤ºÉ°Áš¸¥„´‡nµ„ε¨´ŠÅ¢¢jµ‹¦·Š š¸Éŗo‹µ„„µ¦š—¨°Š

‡Îµ­Îµ‡´: ­®­´¤¡´œ›rÁ·Šž¦³‹´„¬r, „ε¨´ŠÅ¢¢jµ, Á‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Abstract

This research describes the empirical correlations for predicting electric power of centrifugal pump. The experimental system consists of the centrifugal pump A65-130 Model which is driven by 3 phases, 5.5 HP of electric motor. The experimental conditions of rotational speed and flow rate are in the range of 1100 – 1750 rpm and 1 – 6 L/s, respectively. From the experimental results, it can be found that the electric power is obtained by the empirical correlations which have error about r10% that compares with the electric power obtained from the experiment.

Keywords: Empirical correlations, Electric Power, Centrifugal Pump

1. šœÎµ

„ε¨´ŠÅ¢¢jµš¸É˜o°Š„µ¦Äœ„µ¦…´Á‡¨ºÉ°œ…°ŠÅ®¨Ÿnµœ¦³Á­oœšn° Ş¥´Š˜ÎµÂ®œnŠš¸É˜o°Š„µ¦ …°ŠÁ‡¦ºÉ°Š­¼

Â¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r š¸Éčo¤°Á˜°¦rÅ¢¢jµÁž}œ˜oœ„ε¨´Š…¹Êœ°¥¼n„´°´˜¦µ„µ¦Å®¨ ¨³ Á±—×¥ž„˜·¤°Á˜°¦rÅ¢¢jµ

šÎµŠµœš¸É‡ªµ¤Á¦Èª¦°‡Šš¸É —´Šœ´Êœ Á¤ºÉ°¤¸„µ¦žd—ªµ¨rªž¦³˜¼œÊ嚵Š—oµœšµŠ‹nµ¥…°ŠÁ‡¦ºÉ°Š­¼Á¡ºÉ°¨—°´˜¦µ„µ¦Å®¨

šÎµÄ®oÁ±—š¸ÉÁ‡¦ºÉ°Š­¼šÎµÅ—o¤¸‡nµ­¼Š…¹Êœ Ĝ…–³Á—¸¥ª„´œšÎµÄ®oÁ‡¦ºÉ°Š­¼¤¸£µ¦³„µ¦šÎµŠµœ¨—¨Š Áž}œŸ¨šÎµÄ®o

„ε¨´ŠÅ¢¢jµš¸É¤°Á˜°¦r˜o°Š„µ¦¤¸‡nµ¨—¨Š˜µ¤ ×¥­µ¤µ¦™šÎµœµ¥„ε¨´ŠÅ¢¢jµš¸Éčo Ž¹ÉŠ­´¤¡´œ›r„´°´˜¦µ„µ¦Å®¨ ¨³ Á±— š¸ÉÁ‡¦ºÉ°Š­¼šÎµŠµœš¸É‡ªµ¤Á¦Èª¦°‡Šš¸Éŗo ˜nÁ¤ºÉ°¤¸„µ¦žd—ªµ¨rªž¦³˜¼œÊ嚵Š—oµœšµŠ‹nµ¥ Ž¹ÉŠšÎµÄ®o

ž¦³­·š›·£µ¡„µ¦šÎµŠµœ…°ŠÁ‡¦ºÉ°Š­¼ ¨—˜É娊 ÁœºÉ°Š‹µ„‡ªµ¤˜oµœšµœ„µ¦Å®¨…°Š¦³¤¸‡nµ­¼Š…¹Êœ ­nŠŸ¨šÎµÄ®o

‹»—šÎµŠµœ…°ŠÁ‡¦ºÉ°Š­¼š¸É™¼„°°„Åªo ¤¸„µ¦Á¸É¥ŠÁœ°°„‹µ„‹»—š¸É¤¸ž¦³­·š›·£µ¡­¼Š­»— Ž¹ÉŠÄœž{‹‹»´œÅ—oœÎµ

¦³ VSD (Variable Speed Drive) Á¡ºÉ°ž¦´‡ªµ¤Á¦Èª¦°…°Š¤°Á˜°¦r Ä®oÁ®¤µ³­¤„´£µ¦³ŠµœÁ¡ºÉ°Ä®oÁ‡¦ºÉ°Š­¼

šÎµŠµœÄœ‹»—š¸É¤¸ž¦³­·š›·£µ¡­¼Š°¥¼nÁ­¤°Ã—¥´¥¡¦Ã„¡¨¦´˜œr¨³‡–³ [1] ¨³‹Îµ¨°Šž¦µÂ„oªÂ¨³‡–³ [2]

ŗošÎµ„µ¦š—¨°Š®µ­¤¦¦™œ³ …°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r š¸É¤¸„µ¦‡ª‡»¤°´˜¦µ„µ¦Å®¨˜µ¤­£µª³„µ¦

čoŠµœÃ—¥ž¦´‡ªµ¤Á¦Èª¦° „µ¦šÎµŠµœ…°ŠÁ‡¦ºÉ°Š­¼ Ž¹ÉŠ‹µ„Ÿ¨„µ¦š—¨°ŠÂ­—ŠÄ®oÁ®Èœªnµ ¦³š¸É¤¸„µ¦‡ª‡»¤

‡ªµ¤Á¦Èª¦° ¤¸­¤¦¦™œ³„µ¦šÎµŠµœš¸É­¼Š„ªnµ¦³š¸ÉšÎµŠµœš¸É‡ªµ¤Á¦Èª¦°‡Šš¸É ĜnªŠ…°Š„µ¦š—¨°Š°¥¼nÁ­¤°

‹µ„œ´Êœ ¤µœ¡ ¡·¡´•®´˜™„»¨ ¨³ª¸œ´­ š´—Áœ¸¥¤ [3] ŗošÎµ„µ¦š—¨°Š¦³ VSD Á¡ºÉ°®µŸ¨„¦³š…°Š‡ªµ¤Á¦Èª

¦° š¸É¤¸˜n°­¤¦¦™œ³…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r ץčo°·œÁª°¦rÁ˜°¦r Ĝ„µ¦ž¦´‡ªµ¤Á¦Èª¦°…°Š

¤°Á˜°¦rÅ¢¢jµŽ¹ÉŠ‹µ„Ÿ¨„µ¦š—¨°ŠÂ­—ŠÄ®oÁ®Èœªnµ ‡ªµ¤Á¦Èª¦° ­nŠŸ¨„¦³šÃ—¥˜¦Š„´ °´˜¦µ„µ¦Å®¨ Á±—

¨³„ε¨´ŠÅ¢¢jµš¸ÉÁ‡¦ºÉ°Š­¼˜o°Š„µ¦Ž¹ÉŠ„ε¨´ŠÅ¢¢jµš¸ÉÁ‡¦ºÉ°Š­¼˜o°Š„µ¦Á¤ºÉ°‡ªµ¤Á¦Èª¦°Áž¨¸É¥œÅž­µ¤µ¦™šÎµœµ¥

ŗo‹µ„ „‘…°Šž{€¤ (Affinity laws) ×¥¦³ VSD ‹³Ä®oŸ¨—¸ Á¤ºÉ°¦³šn°¨ÎµÁ¨¸¥Š…°ŠÅ®¨ ¤¸Á±—‡ªµ¤Á­¸¥—šµœ

š¸É­¼Š¤µ„¡° ˜n°¤µ ¤µœ¡ ¡·¡´•®´˜™„»¨ ¨³ ¤„¦ ¨´„…–µ [4] ŗoœÎµÁ­œ°ª·›¸„µ¦ª·Á‡¦µ³®r¤·˜· ×¥ª·›¸…°ŠÁ¦¥rÁ¨šr›

(Rayleigh's method) Á¡ºÉ°®µ„¨»n¤˜´ªÂž¦Å¦o¤·˜· š¸ÉčoĜ„µ¦šÎµœµ¥­¤¦¦™œ³…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Ĝ¦¼ž…°Š­´¤ž¦³­·š›·Í„ε¨´Š (The power coefficient), ­´¤ž¦³­·š›·ÍÁ±— (The head coefficient) ¨³­´¤ž¦³­·š›·Í

„µ¦Å®¨ (The flow coefficient) ץ­—Šª·›¸„µ¦š—¨°ŠÁ„ȝ‡nµ˜´ªÂž¦˜nµŠÇ „´Á‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Á¡ºÉ°ÄoĜ„µ¦‡Îµœª– ‹µ„œ´ÊœÂ­—Šª·›¸„µ¦®µ­®­´¤¡´œ›r ‹µ„…o°¤¼¨„µ¦š—¨°Š ץčoª·›¸„µ¦™—™°¥ÂÁ·ŠÁ­oœ

(Linear regression) Á¡ºÉ°®µ­®­´¤¡´œ›rĜ¦¼ž…°Š ­´¤ž¦³­·š›·Í„ε¨´Š š¸ÉčoĜ„µ¦šÎµœµ¥„ε¨´ŠÅ¢¢jµ­Îµ®¦´Á‡¦ºÉ°Š

­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r š¸É…¹Êœ°¥¼n„´ ‡ªµ¤Á¦Èª¦° °´˜¦µ„µ¦Å®¨ ¨³Á±—

‹µ„„µ¦«¹„¬µŸ¨Šµœª·‹´¥˜nµŠÇ š¸ÉŸnµœ¤µ Á®ÈœÅ—oªnµÄœ„µ¦šÎµœµ¥ ‡ªµ¤˜o°Š„µ¦„ε¨´ŠÅ¢¢jµ…°Š¤°Á˜°¦rš¸É čoĜ„µ¦…´Á‡¨ºÉ°œÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r š¸É¤¸‡ªµ¤Á¦Èª¦°Áž¨¸É¥œÅž ‹ÎµÁž}œ˜o°Šš¦µ™¹Š‡»–¨´„¬–³ Á±— – °´˜¦µ„µ¦Å®¨ ®¦º° „¦µ¢ H – Q š¸É‡ªµ¤Á¦Èª¦°‡Šš¸Éž„˜· š¸ÉÁ‡¦ºÉ°Š­¼šÎµŠµœÁ­¸¥„n°œ‹µ„œ´Êœ ‹¹ŠÄo„‘…°Š

ž{€¤ Ĝ„µ¦šÎµœµ¥„ε¨´ŠÅ¢¢jµ Á¤ºÉ°‡ªµ¤Á¦Èª¦°Áž¨¸É¥œÅž ‹¹ŠÁž}œš¸É¤µ…°ŠŠµœª·‹´¥œ¸Ê Á¡ºÉ°š¸É‹³­¦oµŠ­®­´¤¡´œ›r š¸Éčo

Ĝ„µ¦šÎµœµ¥ „ε¨´ŠÅ¢¢jµ …°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Ä®o°¥¼nĜ¦¼ž…°Š˜´ªÂž¦Å¦o¤·˜· Ž¹ÉŠ…¹Êœ°¥¼n„´

‡ªµ¤Á¦Èª¦°°´˜¦µ„µ¦Å®¨Â¨³Á±—š¸ÉÁ‡¦ºÉ°Š­¼šÎµÅ—o 2. š§¬‘¸Äœ„µ¦ª·Á‡¦µ³®r

ž¦·¤µ˜¦‡ª‡»¤š¸Éčo­Îµ®¦´„µ¦ª·Á‡¦µ³®r¤·˜· Á¡ºÉ°®µ„¨»n¤˜´ªÂž¦Å¦o¤·˜· …°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸

«¼œ¥r ­—Š—´Š¦¼žš¸É 1 ×¥¤¸­¤¤˜·“µœ Áž}œ„µ¦Å®¨Â­¤ÉεÁ­¤° …°Š…°ŠÅ®¨š¸É°´—˜´ªÅ¤nŗo

¦¼žš¸É 1 ž¦·¤µ˜¦‡ª‡»¤…°ŠÂ‹Îµ¨°ŠÁ‡¦ºÉ°Š‹´„¦„¨…°ŠÅ®¨

×¥ª·›¸…°ŠÁ¦¥rÁ¨šr› (Rayleigh's method) ‹³Å—o„¨»n¤˜´ªÂž¦Å¦o¤·˜· š¸Éčo­Îµ®¦´„µ¦š—¨°Š®µ­¤¦¦™œ³ …°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Ž¹ÉŠ¤¸ºÉ°Á¦¸¥„„¨»n¤˜´ªÂž¦Å¦o¤·˜·—´Š­¤„µ¦š¸É (1), (2), (3) ¨³ (4) ˜µ¤¨Îµ—´

[4]

_{3 5}

D N P P

U ­´¤ž¦³­·š›·Í„ε¨´Š (1)

(The power coefficient)

₃

ND

I Q ­´¤ž¦³­·š›·Í„µ¦Å®¨ (2)

(The flow coefficient)

_{2 2}

D N

\ gH ­´¤ž¦³­·š›·ÍÁ±— (3)

Q

Q gH

D N P

2

1

Control surface

Flow rate, Q (m³/s) Rotational speed, N (rev/s) Input power, P (Watt) Energy difference across fluid machinery, gH (N.m/kg) Fluid density, U (kg/m³) Fluid viscosity, P (Pa.s) Diameter, D (m) Acceleration due to gravity, g (m/s²) Throttle

valve

Q

Q gH

D N P

2

1

Control surface

Flow rate, Q (m³/s) Rotational speed, N (rev/s) Input power, P (Watt) Energy difference across fluid machinery, gH (N.m/kg) Fluid density, (kg/m³) Fluid viscosity, (Pa.s) Diameter, D (m) Acceleration due to gravity, g (m/s²) Throttle

valve

P UVD

Re Á¨…Á¦¥rܨ—­r (4)

(The Reynolds number)

ÁœºÉ°Š‹µ„ ×¥ž„˜· ĜnªŠ„µ¦šÎµŠµœ…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Á¨…Á¦¥rܨ—­r¤¸‡nµ­¼Š¤µ„ —´Šœ´Êœ

­µ¤µ¦™Á…¸¥œ‡ªµ¤­´¤¡´œ›rĜÁ·Š¢{Š„r´œ…°Š­´¤ž¦³­·š›·Í„ε¨´Š Ä®o°¥¼nĜÁš°¤¢{Š„r´œ…°Š­´¤ž¦³­·š›·Í„µ¦

Å®¨ ¨³­´¤ž¦³­·š›·ÍÁ±— ŗo—´Š­¤„µ¦š¸É (5)

) , (I \ f

P (5)

Á¤ºÉ°

P = „ε¨´ŠÅ¢¢jµš¸É‹nµ¥Ä®o„´Á‡¦ºÉ°Š˜oœ„ε¨´Š ¤¸®œnª¥Áž}œ Watt

U= ‡ªµ¤®œµÂœnœ…°Š…°ŠÅ®¨ ¤¸®œnª¥Áž}œ kg/m³ N = ‡ªµ¤Á¦Èª¦°…°ŠÁ‡¦ºÉ°Š‹´„¦¤¸®œnª¥Áž}œ rev/s D = …œµ—Á­oœŸnµœ«¼œ¥r„¨µŠ…°ŠÄ¡´— ¤¸®œnª¥Áž}œ m Q = °´˜¦µ„µ¦Å®¨ ¤¸®œnª¥Áž}œ m³/s

g = ‡ªµ¤Á¦nŠÁœºÉ°Š‹µ„¦ŠÃœo¤™nªŠ…°ŠÃ¨„Ášnµ„´ 9.81 m/s² H = Á±—š¸ÉÁ‡¦ºÉ°Š‹´„¦šÎµÅ—o ¤¸®œnª¥Áž}œ m

V = ‡ªµ¤Á¦Èª…°Š…°ŠÅ®¨ ¤¸®œnª¥Áž}œ m/s

P= ‡ªµ¤®œº—­™·˜¥r…°Š…°ŠÅ®¨ ¤¸®œnª¥Áž}œ Pa.s

„µ¦®µ­®­´¤¡´œ›r…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r Ž¹ÉŠ°¥¼nĜ¦¼ž…°ŠÁ¨…¥„„ε¨´Š‡¼–„´‡nµ‡Šš¸ÉÄ—Ç Äoª·›¸„µ¦™—™°¥ÂÁ·ŠÁ­oœ (Linear regression) ‹µ„­¤„µ¦š¸É (5) ­µ¤µ¦™Á…¸¥œ­®­´¤¡´œ›r¦³®ªnµŠ ­´¤ž¦³­·š›·Í

„ε¨´Š„´­´¤ž¦³­·š›·Í„µ¦Å®¨ ¨³­´¤ž¦³­·š›·ÍÁ±— ŗo—´Š­¤„µ¦š¸É (6) ¨³ (7) Ž¹ÉŠ‡nµ‡Šš¸É C, M ¨³ N ­µ¤µ¦™®µ ŗo‹µ„…o°¤¼¨„µ¦š—¨°Š‹Îµœªœ n …o°¤¼¨ Ž¹ÉŠÁ…¸¥œÅ—o—´Š­¤„µ¦š¸É (8) [4]

N

C M

P I \ (6)

\ I ^Log Log

Log

LogP CM N (7)

Á¤ºÉ°„ε®œ—Ä®o

\ I , Log Log

,

LogP x y

z

N a M a C

a₀ Log , ₁ , ₂

»»

»»

»»

»

¼ º

««

««

««

«

¬ ª

»»

»

¼ º

««

«

¬ ª

»»

»»

»»

»

¼ º

««

««

««

«

¬ ª

¦

¦

¦

¦

¦

¦

¦

¦

¦

¦

¦

n

i i i n

i i i n

i i

n

i i n

i i i n

i i

n

i i i n

i i n

i i

n

i i n

i i

z y

z x

z

a a a

y y

x y

y x x

x

y x

n

1 1 1

2 1 0

1 2 1

1

1 1

2 1

1

1 (8)

„ε¨´Š…°ŠÅ®¨®¦º° Fluid power ‡º° „ε¨´ŠŠµœš¸ÉÁ‡¦ºÉ°Š­¼˜o°ŠÁ¡·É¤Ä®o„´…°ŠÁ®¨ª Á¡ºÉ°Ä®o…°ŠÁ®¨ªÅ®¨Ÿnµœ¦³

—oª¥°´˜¦µ„µ¦Å®¨š¸É„ε®œ— ¤¸®œnª¥Áž}œ „·Ã¨ª´˜˜r (kW) ‡Îµœª–Å—o‹µ„­¤„µ¦š¸É (9) [5]

Fluid power = UgQ(TDH) (9)

Á¤ºÉ° TDH = Total discharge head ¤¸®œnª¥Áž}œ m

ž¦³­·š›·£µ¡…°Š¦³­¼ (K) ‡º° „ε¨´Š…°Š…°ŠÅ®¨š¸Éŗo¦´Åž‹µ„Á‡¦ºÉ°Š­¼˜n°„ε¨´ŠÅ¢¢jµš¸É‹nµ¥Ä®o„´

Á‡¦ºÉ°Š˜oœ„ε¨´Š (P_E) ‡Îµœª–Å—o‹µ„­¤„µ¦š¸É (10) [5]

_u100

PE

TDH UgQ

K (10)

Á¤ºÉ°

K= ž¦³­·š›·£µ¡…°Š¦³­¼ ¤¸®œnª¥Áž}œÁž°¦rÁŽœ˜r (%) P_E = „ε¨´ŠÅ¢¢jµš¸É‹nµ¥Ä®o„´Á‡¦ºÉ°Š˜oœ„ε¨´Š¤¸®œnª¥Áž}œ kW

3. »—š—¨°ŠÂ¨³ª·›¸„µ¦š—¨°Š

Ĝ„µ¦š—¨°Š®µ„ε¨´ŠÅ¢¢jµ…°Š¤°Á˜°¦rš¸ÉčoĜ„µ¦…´Á‡¨ºÉ°œÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r¤¸

°»ž„¦–r„µ¦š—¨°Š—´Š¦¼žš¸É 2 ×¥Á¦·É¤˜oœ‹µ„˜¦ª‹­°°»ž„¦–rš»„˜´ªÄ®o°¥¼nĜ­£µ¡¡¦o°¤ÄoŠµœ ‹µ„œ´Êœ®¦¸É

ž¦³˜¼œÊ室µ¥Á¨… 6 Ä®ožd—°¥nµŠœo°¥‡¦¹ÉŠ®œ¹ÉŠ…°Š¦³¥³Ážd—­»— Á¡ºÉ°žj°Š„´œ„µ¦Á„·—‡¨ºÉœ­´Éœ­³Ášº°œÁœºÉ°Š‹µ„„µ¦

Áž¨¸É¥œÂž¨Š‡ªµ¤—´œ°¥nµŠ¦ª—Á¦Èª£µ¥Äœšn°šµŠ—oµœšµŠ‹nµ¥ ‹µ„œ´ÊœšÎµ„µ¦„—­ª·šŽr ON š¸É˜¼o‡ª‡»¤®¤µ¥Á¨… 3 Á¡ºÉ°‹nµ¥„¦³Â­Å¢¢jµÁ…oµ­¼n¤°Á˜°¦rÅ¢¢jµ®¤µ¥Á¨… 2 Á¡ºÉ°…´Á‡¨ºÉ°œÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r®¤µ¥Á¨… 1 š¸É

¤¸ …œµ—Á­oœŸnµœ«¼œ¥r„¨µŠÄ¡´— 139 mm ×¥„ε¨´ŠÅ¢¢jµš¸Éčo ­µ¤µ¦™°nµœ‡nµÅ—o‹µ„ª´˜˜r¤·Á˜°¦r®¤µ¥Á¨… 9 ¨³

­µ¤µ¦™‡ª‡»¤‡ªµ¤Á¦Èª¦°…°Š¤°Á˜°¦rÅ¢¢jµÅ—o‹µ„°·œÁª°¦rÁ˜°¦r®¤µ¥Á¨… 8 ×¥‡ªµ¤Á¦Èª¦°…°Š¤°Á˜°¦r

Å¢¢jµ°nµœ‡nµÅ—o‹µ„ Tachometer ®¤µ¥Á¨… 10 ‹µ„œ´Êœ‡n°¥Ç Ážd—ž¦³˜¼œÊ室µ¥Á¨… 6 °°„‹œ­»— ¨³ž¦´

‡ªµ¤Á¦Èª¦°…°Š¤°Á˜°¦rÅ¢¢jµÄ®oŗo‡ªµ¤Á¦Èª¦° 1100 rpm Á¤ºÉ°Å—o‡ªµ¤Á¦Èª˜µ¤š¸É˜o°Š„µ¦Ä®ošÎµ„µ¦®¦¸Éž¦³˜¼œÊε

®¤µ¥Á¨… 6 Á¡ºÉ°ž¦´°´˜¦µ„µ¦Å®¨…°ŠœÊεĮoŗo 6 L/s ×¥°nµœ‡nµ°´˜¦µ„µ¦Å®¨…°ŠœÊε‹µ„ Flow meter ®¤µ¥Á¨…

7 ‹µ„œ´ÊœšÎµ„µ¦´œš¹„‡nµ ‡ªµ¤—´œšµŠ—oµœšµŠ—¼— ‹µ„ Vacuum gauge ®¤µ¥Á¨… 5, ‡ªµ¤—´œšµŠ—oµœšµŠ‹nµ¥‹µ„

Pressure gauge ®¤µ¥Á¨… 4 ¨³ „ε¨´ŠÅ¢¢jµš¸Éčo‹µ„ª´˜˜r¤·Á˜°¦r®¤µ¥Á¨… 9 Á¤ºÉ°´œš¹„‡nµ˜µ¤˜o°Š„µ¦Â¨oª Ä®ož¦´

°´˜¦µ„µ¦Å®¨…°ŠœÊε Áž}œ 5, 4, 3, 2 ¨³ 1 L/s ×¥šÎµ„µ¦´œš¹„‡nµ˜nµŠÇ …oµŠ˜oœŽÊε‹œ‡¦ ‹µ„œ´ÊœÁž¨¸É¥œ

‡ªµ¤Á¦Èª¦°…°Š¤°Á˜°¦rÅ¢¢jµ Áž}œ 1250, 1485, 1650 ¨³ 1750 rpm ‹œ‡¦˜µ¤š¸É˜o°Š„µ¦ ‹µ„œ´ÊœœÎµŸ¨š¸Éŗo

‹µ„„µ¦š—¨°ŠÅž‡Îµœª–®µ‡nµ˜nµŠÇ ¨³®µ‡ªµ¤­´¤¡´œ›r…°Š„ε¨´ŠÅ¢¢jµš¸Éčo „´°´˜¦µ„µ¦Å®¨, Á±— ¨³

‡ªµ¤Á¦Èª¦° ×¥­¦oµŠÁž}œ­®­´¤¡´œ›r­Îµ®¦´šÎµœµ¥„ε¨´ŠÅ¢¢jµš¸Éčo …°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r ĜnªŠ…°Š„µ¦š—¨°Š

1. Centrifugal pump 6. Gate valve 2. Electric motor 7. Flow meter 3. Control unit 8. Inverter 4. Pressure gauge 9. Watt meter

5. Vacuum gauge 10. Tachometer

¦¼žš¸É 2 Schematic diagram …°Š°»ž„¦–rš—¨°Š

4. Ÿ¨š—¨°Š

„ε¨´ŠÅ¢¢jµš¸É‹nµ¥Ä®o„´¤°Á˜°¦rÁ¡ºÉ°…´Á‡¨ºÉ°œÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r …¹Êœ°¥¼n„´ °´˜¦µ„µ¦Å®¨, Á±— ¨³‡ªµ¤Á¦Èª¦°…°ŠÁ‡¦ºÉ°Š­¼ Á¤ºÉ°œÎµ…o°¤¼¨š¸Éŗo‹µ„„µ¦š—¨°Š ¤µ¡¨°˜„¦µ¢‡ªµ¤­´¤¡´œ›r ¦³®ªnµŠ Á±—

¨³°´˜¦µ„µ¦Å®¨ ‹³Å—oÁ­oœÃ‡oŠ‡»–¨´„¬–³ Á±— – °´˜¦µ„µ¦Å®¨ (H – Q Curve) …°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸

«¼œ¥r —´Š¦¼žš¸É 3 ×¥‹³Á®ÈœÅ—oªnµ Á¤ºÉ°¤¸„µ¦®¦¸Éž¦³˜¼œÊ嚵Š—oµœšµŠ‹nµ¥ ‹³šÎµÄ®o°´˜¦µ„µ¦Å®¨¤¸‡nµ¨—¨Š ¨³­nŠŸ¨

šÎµÄ®o Á±—š¸ÉšÎµÅ—o…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r ¤¸‡nµ­¼Š…¹Êœ ÁœºÉ°Š‹µ„¡¨´ŠŠµœ‹¨œr…°Š…°ŠÅ®¨µŠ­nªœ

™¼„Áž¨¸É¥œ¦¼žÄ®o„¨µ¥Áž}œÁ±—‡ªµ¤—´œÂšœ Ž¹ÉŠÁž}œ‡»–¨´„¬–³…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥rš¸Éčoĝ¡´—

Å®¨˜µ¤Âœª¦´«¤¸ (Radial flow) ×¥‹³Á®ÈœÅ—oªnµ Á¤ºÉ°Á‡¦ºÉ°Š­¼šÎµŠµœš¸É‡ªµ¤Á¦Èª¦°­¼Š…¹Êœ ‹³šÎµÄ®o Áª„Á˜°¦r…°Š‡ªµ¤Á¦ÈªÄœÂœªÁ­oœ­´¤Ÿ´­­nªœÃ‡oŠ š¸É¦´«¤¸šµŠ°°„…°ŠÄ¡´—¤¸‡nµ­¼Š…¹Êœ˜µ¤ —´Šœ´ÊœšÎµÄ®o„µ¦

™nµ¥š°—¡¨´ŠŠµœ¦³®ªnµŠ‡¦¸Ä¡´—„´…°ŠÅ®¨¤¸‡nµ­¼Š…¹ÊœŽ¹ÉŠ­nŠŸ¨šÎµÄ®oÁ±—¨³°´˜¦µ„µ¦Å®¨š¸ÉÁ‡¦ºÉ°Š­¼

Â¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥ršÎµÅ—o¤¸‡nµ­¼Š…¹Êœ˜µ¤ [3]

Flow rate, Q (L/s)

0 1 2 3 4 5 6 7

Head, H (m)

0 2 4 6 8 10 12

Power, P (kW)

0 1000 2000 3000 4000 5000 6000

H (m) P (kW)

1 2

0

1100 rpm 1250 rpm

1485 rpm 1650 rpm

1750 rpm

¦¼žš¸É 3 H – Q Curve ¨³ „ε¨´ŠÅ¢¢jµš¸É‹nµ¥Ä®o„´Á‡¦ºÉ°Š­¼ÂÂ¦ŠÁ®ª¸É¥Š®œ¸«¼œ¥r

Á¤ºÉ°¡·‹µ¦–µ™¹Š„ε¨´ŠÅ¢¢jµš¸É‹nµ¥Ä®o„´Á‡¦ºÉ°Š­¼ ‹³Á®ÈœÅ—oªnµÁ¤ºÉ°°´˜¦µ„µ¦Å®¨¤¸‡nµ¨—¨Š ‹³šÎµÄ®o

„ε¨´ŠÅ¢¢jµš¸ÉÁ‡¦ºÉ°Š­¼˜o°Š„µ¦¤¸‡nµ¨—¨Š˜µ¤ÁœºÉ°Š‹µ„ „ε¨´Š­nªœÄ®nš¸Éžj°œÄ®o„´Á‡¦ºÉ°Š­¼ ‹³­¼Á­¸¥Åž„´

‡ªµ¤Á­¸¥—šµœÁœºÉ°Š¤µ‹µ„„µ¦Å®¨…°Š¦³šn°—´Šœ´ÊœÁ¤ºÉ°°´˜¦µ„µ¦Å®¨¤¸‡nµ¨—¨Š¡¨´ŠŠµœš¸ÉÁ‡¦ºÉ°Š­¼˜o°Š„µ¦

Á¡ºÉ°Á°µœ³‡ªµ¤Á­¸¥—šµœ „È‹³¤¸‡nµ¨—¨Š˜µ¤Åž—oª¥œ´ÉœÁ°Š šÎµÄ®o¤°Á˜°¦rčo„ε¨´ŠÅ¢¢jµ¨—¨Š Ĝ…–³š¸ÉÁ¤ºÉ°

‡ªµ¤Á¦Èª¦°­¼Š…¹Êœ „È‹³šÎµÄ®o‡ªµ¤˜o°Š„µ¦„ε¨´ŠÅ¢¢jµ¤¸‡nµÁ¡·É¤…¹Êœ˜µ¤ ÁœºÉ°Š‹µ„Á‡¦ºÉ°Š­¼¤¸£µ¦³„µ¦­¼œÊε ¨³ Á±—š¸ÉÁ¡·É¤…¹Êœœ´ÉœÁ°Š

‹µ„„µ¦š—¨°ŠÁ¤ºÉ°¡·‹µ¦–µ™¹Šž¦³­·š›·£µ¡…°Š¦³­¼—´ŠÂ­—ŠÄœ¦¼žš¸É 4 ‹³Á®ÈœÅ—oªnµš¸É‡ªµ¤Á¦Èª¦°

‡Šš¸É Á¤ºÉ°°´˜¦µ„µ¦Å®¨¤¸‡nµ¨—¨Š ­nŠŸ¨šÎµÄ®ož¦³­·š›·£µ¡…°Š¦³­¼¨—˜É娊 ÁœºÉ°Š‹µ„Á¤ºÉ°®¦¸Éž¦³˜¼œÊε

šµŠ—oµœšµŠ‹nµ¥ ‹³šÎµÄ®o„ε¨´Š…°Š…°ŠÅ®¨ š¸ÉÁ‡¦ºÉ°Š­¼šÎµÅ—o¤¸‡nµ¨—¨Š Ĝ…–³š¸É ™¹ŠÂ¤oªnµ£µ¦³„µ¦šÎµŠµœ…°Š

‹¹ŠšÎµÄ®ož¦³­·š›·£µ¡„µ¦šÎµŠµœ…°Š¦³­¼š¸É¤¸„µ¦®¦¸Éž¦³˜¼œÊ嚵Š—oµœšµŠ‹nµ¥ ¨³¤°Á˜°¦ršÎµŠµœš¸É‡ªµ¤Á¦Èª

¦°‡Šš¸É ¨—˜É娊 ץĜnªŠ…°Š„µ¦š—¨°Š š¸É°´˜¦µ„µ¦Å®¨ 1 – 6 L/s ‹³Á®ÈœÅ—oªnµ ž¦³­·š›·£µ¡„µ¦šÎµŠµœ…°Š

¦³­¼ š¸É‡ªµ¤Á¦Èª¦° 1100 ¨³ 1250 rpm ‹³Ä®o‡nµž¦³­·š›·£µ¡ š¸É­¼Š„ªnµ š¸É‡ªµ¤Á¦Èª¦°°ºÉœÇ ÁœºÉ°Š‹µ„

ĜnªŠ…°Š„µ¦š—¨°Š¤¸‡nµ°´˜¦µ„µ¦Å®¨‡n°œ…oµŠ˜Éε Ĝ…–³š¸ÉÁ¤ºÉ°‡ªµ¤Á¦Èª¦°­¼Š…¹Êœ‹³šÎµÄ®o°´˜¦µ„µ¦Å®¨¤¸‡nµ Á¡·É¤…¹Êœ —´Šœ´ÊœÄœnªŠ…°Š‡ªµ¤Á¦Èª¦° 1485, 1650 ¨³ 1750 rpm ‹³¤¸°´˜¦µ„µ¦Å®¨­¼Š­»—š¸ÉÁ‡¦ºÉ°Š­¼­µ¤µ¦™šÎµ ŗo¤µ„„ªnµ 6 L/s ‹¹Š˜o°Š®¦¸Éž¦³˜¼œÊ嚵Š—oµœšµŠ‹nµ¥¨Š ­nŠŸ¨šÎµÄ®ož¦³­·š›·£µ¡„µ¦šÎµŠµœ…°Š¦³­¼¨—

˜É娊 œ´ÉœÁ°Š ×¥‹³¤¸ž¦³­·š›·£µ¡­¼Š­»—°¥¼nš¸É 44.8% š¸É °´˜¦µ„µ¦Å®¨ 6 L/s ¨³‡ªµ¤Á¦Èª¦° 1250 rpm

Flow rate, Q (L/s)

0 1 2 3 4 5 6 7

Efficiency,K (%)

0 10 20 30 40 50

1100 rpm 1250 rpm 1485 rpm 1650 rpm 1750 rpm

¦¼žš¸É 4 „¦µ¢‡ªµ¤­´¤¡´œ›r¦³®ªnµŠž¦³­·š›·£µ¡Â¨³°´˜¦µ„µ¦Å®¨ š¸É‡ªµ¤Á¦Èª¦°˜nµŠÇ

Power coefficient (Predicted)

0.0 .5 1.0 1.5 2.0

Power coefficient (Experimental)

0.0 .5 1.0 1.5 2.0

1100 rpm 1250 rpm 1485 rpm 1650 rpm 1750 rpm

-10%

+10%

¦¼žš¸É 5 ­®­´¤¡´œ›rĜ„µ¦šÎµœµ¥­´¤ž¦³­·š›·Í„ε¨´ŠÁž¦¸¥Áš¸¥„´­´¤ž¦³­·š›·Í„ε¨´Šš¸Éŗo‹µ„„µ¦š—¨°Š

5 . 1 2 . 15 0 . 0 , t coefficien

Power ^P I \

‹µ„…o°¤¼¨„µ¦š—¨°ŠÁ¤ºÉ°œÎµ¤µ­¦oµŠÁž}œ­®­´¤¡´œ›r­Îµ®¦´ÄošÎµœµ¥„ε¨´ŠÅ¢¢jµ š¸É°¥¼nĜ¦¼ž…°Š

­´¤ž¦³­·š›·Í„ε¨´Š (Power coefficient, ^P) ˜µ¤­¤„µ¦š¸É (6) ŗo—´Š­¤„µ¦š¸É (11)

5 . 1 2 .

15 0

.

0 I \

P (11)

×¥­®­´¤¡´œ›rš¸É­¦oµŠ…¹Êœ­Îµ®¦´šÎµœµ¥„ε¨´ŠÅ¢¢jµÄœ¦¼ž…°Š­´¤ž¦³­·š›·Í„ε¨´ŠÁ¤ºÉ°‡Îµœª–Áž¦¸¥Áš¸¥„´

­´¤ž¦³­·š›·Í„ε¨´Šš¸Éŗo‹µ„„µ¦š—¨°Š ¤¸‡nµ‡ªµ¤Ÿ·—¡¨µ—°¥¼nĜnªŠž¦³¤µ– ^r 10 Áž°¦rÁŽÈœ˜r —´Š¦¼žš¸É 5

5. ­¦»ž

Šµœª·‹´¥œ¸ÊŗošÎµ„µ¦«¹„¬µ ‡ªµ¤˜o°Š„µ¦„ε¨´ŠÅ¢¢jµ…°Š¤°Á˜°¦r š¸ÉčoĜ„µ¦…´Á‡¨ºÉ°œÁ‡¦ºÉ°Š­¼ÂÂ¦Š

Á®ª¸É¥Š®œ¸«¼œ¥r Ž¹ÉŠ…¹Êœ°¥¼n„´ °´˜¦µ„µ¦Å®¨, Á±— ¨³‡ªµ¤Á¦Èª¦° ×¥šÎµ„µ¦š—¨°Š ĜnªŠ‡ªµ¤Á¦Èª¦° 1100, 1250, 1485, 1650 ¨³ 1750 rpm ¨³ °´˜¦µ„µ¦Å®¨ 1 – 6 L/s ˜µ¤¨Îµ—´‹µ„Ÿ¨„µ¦š—¨°Š °´˜¦µ„µ¦Å®¨š¸ÉÁ‡¦ºÉ°Š

­¼šÎµÅ—o ž¦Ÿ„Ÿ´œ„´Á±— š¸É‡ªµ¤Á¦Èª¦°‡Šš¸É ‹µ„œ´ÊœÁ¤ºÉ°‡ªµ¤Á¦Èª¦°­¼Š…¹Êœ šÎµÄ®o°´˜¦µ„µ¦Å®¨Â¨³Á±— š¸É Á‡¦ºÉ°Š­¼šÎµÅ—o¤¸‡nµ­¼Š…¹Êœ˜µ¤ Ĝ…–³š¸É„ε¨´ŠÅ¢¢jµ ž¦Ÿ´œÃ—¥˜¦Š„´ °´˜¦µ„µ¦Å®¨Â¨³‡ªµ¤Á¦Èª¦° ×¥

¦³­¼œÊεš¸ÉšÎµ„µ¦š—¨°Š¤¸ž¦³­·š›·£µ¡­¼Š­»—°¥¼nš¸É 44.8% š¸É °´˜¦µ„µ¦Å®¨ 6 L/s ¨³‡ªµ¤Á¦Èª¦° 1250 rpm Á¤ºÉ°œÎµ…o°¤¼¨š¸Éŗo‹µ„„µ¦š—¨°Š¤µ­¦oµŠÁž}œ­®­´¤¡´œ›rš¸Éčo­Îµ®¦´šÎµœµ¥„ε¨´ŠÅ¢¢jµ…°ŠÁ‡¦ºÉ°Š­¼ÂÂ¦Š

Á®ª¸É¥Š®œ¸«¼œ¥r ĜnªŠ…°Š„µ¦š—¨°Š Ĝ¦¼ž…°Š­´¤ž¦³­·š›·Í„ε¨´Š (^P) ŗoÁž}œ P ^0.15I^0.2\^1.5 ×¥­®­´¤¡´œ›r

š¸É­¦oµŠ…¹ÊœÁ¤ºÉ°‡Îµœª–Áž¦¸¥Áš¸¥„´ ­´¤ž¦³­·š›·Í„ε¨´Šš¸Éŗo‹µ„„µ¦š—¨°Š ¤¸‡nµ‡ªµ¤Ÿ·—¡¨µ—°¥¼nĜnªŠ

ž¦³¤µ– ^r 10 Áž°¦rÁŽÈœ˜r

Á°„­µ¦°oµŠ°·Š

[1] ´¥¡¦ Ä¡¨¦´˜œr¨³‡–³. (2542). »—š—­°­¤¦¦™œ³…°Šž{€¤ÂÅ®¨˜µ¤Âœª¦´«¤¸. ž¦·µœ·¡œ›r ª·«ª„¦¦¤«µ­˜¦r ‡–³ª·«ª„¦¦¤«µ­˜¦r ­™µ´œÁš‡ÃœÃ¨¥¸¡¦³‹°¤Á„¨oµ¡¦³œ‡¦Á®œº°, „¦»ŠÁš¡¤®µœ‡¦.

[2] ‹Îµ¨°Š ž¦µÂ„oªÂ¨³‡–³. (2546). „µ¦‡ª‡»¤°´˜¦µ„µ¦Å®¨…°Šž{€¤®°¥Ã…nŠ˜µ¤­£µª³ÄoŠµœ. ž¦·µ

œ·¡œ›rª·«ª„¦¦¤«µ­˜¦r ‡–³ª·«ª„¦¦¤«µ­˜¦r ­™µ´œÁš‡ÃœÃ¨¥¸¡¦³‹°¤Á„¨oµÁ‹oµ‡»–š®µ¦¨µ—„¦³´Š,

„¦»ŠÁš¡¤®µœ‡¦.

[3] ¤µœ¡ ¡·¡´•®´˜™„»¨ ¨³ ª¸œ´­ š´—Áœ¸¥¤. Ÿ¨„¦³š…°Š‡ªµ¤Á¦Èª¦°š¸É¤¸˜n°­¤¦¦™œ³ž{€¤. ªµ¦­µ¦ª·µ„µ¦

žš»¤ª´œ žeš¸É 1 Œ´š¸É 1 ¡§¬£µ‡¤ – ­·Š®µ‡¤ 2554, ®œoµ 59 – 64.

[4] ¤µœ¡ ¡·¡´•®´˜™„»¨ ¨³ ¤„¦ ¨´„…–µ. „µ¦ª·Á‡¦µ³®r¤·˜·Â¨³„µ¦®µ­®­´¤¡´œ›r­Îµ®¦´Á‡¦ºÉ°Š­¼ÂÂ¦Š

Á®ª¸É¥Š®œ¸«¼œ¥r„¨µŠ. ªµ¦­µ¦ª·µ„µ¦žš»¤ª´œ žeš¸É 2 Œ´š¸É 3 ¤„¦µ‡¤ – Á¤¬µ¥œ 2555, ®œoµ 27-31.

[5] A.T. Sayers. (1992). Hydraulic and Compressible Flow Turbo machines. Singapore: McGraw-Hill, pp. 4-7.

ž¦³ª´˜·Ÿ¼oÁ…¸¥œš‡ªµ¤

œµ¥¤µœ¡ ¡·¡´•®´˜™„»¨ ­ÎµÁ¦È‹„µ¦«¹„¬µ¦³—´ž¦·µ˜¦¸ ­µ…µª·µª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ¤.Á°Á¸¥°µ‡Áœ¥r ¨³¦³—´ž¦·µÃš ­µ…µª·µª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ¤‹›. ž{‹‹»´œ—ε¦Š˜ÎµÂ®œnŠ °µ‹µ¦¥rž¦³‹Îµ­µ…µª·µ ª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ­™µ´œÁš‡ÃœÃ¨¥¸žš»¤ª´œ

Šµœª·‹´¥š¸É­œÄ‹: Thermal and Fluid Sciences.

œµ¥š¦Š›¦¦¤ Á®¨nµ­»ª¦¦– ­ÎµÁ¦È‹„µ¦«¹„¬µ¦³—´ž¦·µ˜¦¸ ­µ…µª·µª·«ª„¦¦¤Á‡¦ºÉ°Š„¨

¤®µª·š¥µ¨´¥Á„¬˜¦«µ­˜¦r ª·š¥µÁ…˜ÁŒ¨·¤¡¦³Á„¸¥¦˜·‹´Š®ª´—­„¨œ‡¦ ¨³¦³—´ž¦·µÃš ­µ…µª·µ ª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ­‹¨. ž{‹‹»´œ—ε¦Š˜ÎµÂ®œnŠ °µ‹µ¦¥rž¦³‹Îµ­µ…µª·µª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ­™µ´œÁš‡ÃœÃ¨¥¸

žš»¤ª´œ

Šµœª·‹´¥š¸É­œÄ‹: Flow Measurement and Combustion.

œµ¥Œ´˜¦´¥ Áž¨nŠ­³°µ— ­ÎµÁ¦È‹„µ¦«¹„¬µ¦³—´ž¦·µ˜¦¸ ­µ…µª·µª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ¤‹›. ¨³¦³—´

ž¦·µÃš ­µ…µª·µª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ‹»¯µ¨Š„¦–r¤®µª·š¥µ¨´¥ž{‹‹»´œ—ε¦Š˜ÎµÂ®œnŠ °µ‹µ¦¥rž¦³‹Îµ­µ…µª·µ ª·«ª„¦¦¤Á‡¦ºÉ°Š„¨ ­™µ´œÁš‡ÃœÃ¨¥¸žš»¤ª´œ

Šµœª·‹´¥š¸É­œÄ‹: Refrigeration and Air Condition.