On the Occurrence of Air Entrainment in a Suction Sump

On the Occurrence of Air Entrainment in a Suction Sump

Katsuya HIRATA^*, Jiro FUNAKI^*, Yoshihiro KUBOTA^*, Katsuhisa INAGAKI^* and Miki TAOKA^*

(Received October 19, 2010)

In the present study, we consider the air entrainment into a suction pipe which is vertically inserted down into a suction sump across a mean free-water surface. This configuration is often referred to as the “vertical wet-pit pump”, and has many practical advantages in construction, maintenance and operation. In particular, we focus our concern upon the critical submergence depth S_c, which is one of the prime and conventional indicators for the air-entrainment occurrence. By a systematic approach, we experimentally investigate the influences of kinetic and geometric parameters upon S_c. As the kinetic parameters, we consider the Reynolds number Re and the Weber number We, in addition to the Froude number Fr, on such a basis as Fr is not much larger than unity in many actual cases. As the geometric parameters, we consider back clearance X, sump breadth B and bottom clearance Z.

Here, all parameters are non-dimensionalized by the outside diameter D and the intake velocity Vi of the suction pipe. As a result, we reveal the effects of such six parameters upon S_c. The We effect, namely, the surface-tension effect can be ignored at We > 12. And, the Re effect, namely, the viscous effect becomes negligibly small at Re > 3×10⁴. Under such conditions for We and Re, we could consider only the Fr effect, namely, the gravitational effect. Concerning the X/D and B/D effects, S_c/D attains the maximum at a certain X/D or B/D. On the other hand, the Z/D effect is monotonous, and becomes small at Z/D > 2.5. Some aspects of these geometric effects can be evaluated by a local-Froude-number effect on the basis of the global relation between S_c/D and Fr. And, the other aspects is necessarily considered to be related with the flow structure in the suction sump.

-G[YQTFU pumps, air entrainment, vortices, open sump, water intake, two-phase flow

䉨䊷䊪䊷䊄㧦 ࡐࡦࡊ㧘ⓨ᳇ๆㄟ㧘᷵㧘ๆㄟ᳓ᮏ㧘ข᳓ญ㧘ੑ⋧ᵹ

ข᳓ᮏౝߩⓨ᳇ๆㄟߩ⊒↢ߦߟ޿ߡ

ᐔ↰ ൎ຦࡮⥱ᧁ ᴦ㇢࡮ਭ଻↰ ⟵໪࡮Ⓑ၂ ൎਭ࡮↰ጟ ᧂ᮸

㧚ߪߓ߼ߦ

⊒㔚ࡊ࡜ࡦ࠻߿ἠṴ⸳஻㧘ឃ᳓ᣉ⸳ߥߤߢߪ㧘ࠗ

࠾ࠪࡖ࡞ࠦࠬ࠻ߩ೥ᷫ߿ዊဳൻ㧘㜞ല₸ൻ㧘㜞ᕈ⢻

ൻߩታ⃻ߩߚ߼㧘ๆㄟ᳓ᮏߩᦨㆡ⸳⸘߇ᔅⷐߣߐࠇ ࠆ㧚ㄭᐕ㧘ߘࠇࠄߩⷐ᳞ࠍḩߚߔߚ߼ߩࠃࠅ㜞᳓Ḱ ߥ⸃᳿╷߇᳞߼ࠄࠇߡ޿ࠆ㧚ߘߩࠃ߁ߥ⁁ᴫਅߢߪ㧘 ๆㄟ▤౉ญ߳ߩⓨ᳇ๆㄟ߇⿠ࠅ߿ߔߊߥࠆ㧚ⓨ᳇ๆ

ㄟߪ㧘ᝄേ߿㛍㖸㧘឴᳓ല₸ૐਅ㧘ߘߒߡᦨᖡߩ႐ วߪࡐࡦࡊ፣უࠍᒁ߈⿠ߎߔ㧚ࠃߞߡ㧘ⓨ᳇ๆㄟࠍ 㒐ߋࠃ߁㧘౉ᔨߥๆㄟ᳓ᮏߣๆㄟ▤ߩ⸳⸘߇᳞߼ࠄ ࠇࠆ㧚

ๆㄟ᳓ᮏߢߪⓨ᳇ๆㄟ߇ታ↪⊛ዪ㕙ߢߩᦨ㊀ⷐ

੐㗄ߩ৻ߟߢ޽ࠆߩߢ㧘ߎࠇ߹ߢߦⓨ᳇ๆㄟߦ㑐ߔ ࠆᄙߊߩ⎇ⓥ߇ߥߐࠇߡ߈ߚ㧚

*Department of Mechanical Engineering, Doshisha University, Kyoto 610-0321, Japan Telephone:㧗81-774-65-6461, Fax:㧗81-774-65-6830, E-mail:[email protected]

Flow Flow X

BH SZ

d D

Iversen (1953)¹⁾ߪ㧘̌vertical wet-pit pump̍޽ࠆ޿

ߪ̌vertical suspended pump in a wet well̍ߣ๭߫ࠇ ࠆᒻ⁁ࠍᜬߟන⚐ߥࡕ࠺࡞ࠍ⠨߃ߚ㧚ߘߎߢߪ㧘ๆ ㄟ▤߇⥄↱⴫㕙ࠍ⽾޿ߡု⋥ߦๆㄟ᳓ᮏߦᝌ౉ߐ ࠇࠆ㧚ߎߩᒻ⁁ߪ㧘᭴ㅧ߿⛽ᜬ▤ℂ㧘ᠲ૞ߦ߅޿ߡ㧘 ᄙߊߩታ↪⊛ߥ೑ὐ߇޽ࠆ㧚ߎߎߢ㧘ๆ᳓▤ߪ౞ᒻ ᢿ㕙ࠍ᦭ߔࠆ⋥✢⁁ࡄࠗࡊߢ޽ࠅ㧘ๆㄟ᳓ᮏߪ㐿᳓

〝ߢ޽ࠆ㧚ߎߩ㐿᳓〝ߪ㧘ๆㄟ▤ߩਅᵹߢ㧘ု⋥ߥ

⢛㕙ࠍ᦭ߔࠆ㧔Fig. 1ෳᾖ㧕㧚ߘߩࠃ߁ߥ◲නߥᒻ

⁁ߦ߽㑐ࠊࠄߕ㧘ߎߩๆㄟ᳓ᮏౝߩᵹࠇߪ㧘㕖Ᏹߦ ⶄ㔀ߢ޽ࠆ㧚଀߃߫㧘ⓨ᳇ๆㄟߩၮ␆⎇ⓥߩὑߦࠃ ߊ⺞ߴࠄࠇߡ߈ߚ᳓ᐔࠝ࡝ࡈࠖࠬౝᵹࠇ㧔ᓟㅀ㧕ߣ Ყセߒߡ߽㧘ߕߞߣⶄ㔀ߢ޽ࠆ㧚 Iversenߪ㧘ᣢሽ ߩๆㄟ᳓ᮏౝߩᵹࠇࠍ㧘̌ዪᚲ᷵̍߿̌ᩇ⁁᷵̍ߥ ߤߩ޿ߊߟ߆ߩ࠲ࠗࡊߦಽ㘃ߒߚ㧚ᓐߩ⎇ⓥߪ㧘వ 㚟⊛ߥ߽ߩߢ޽ࠆ߇㧘㚂የ৻⽾ߒߚᰴర⸃ᨆࠍᰳ޿

ߡ߅ࠅ㧘߹ߚ㧘ቯᕈ⊛ߥ߽ߩߢ޽ߞߚ㧚৻ᣇߢ㧘ᓐ ߪ㧘ࡈ࡞࡯࠼ᢙFrࠍ໑৻ߩㆇേࡄ࡜ࡔ࡯࠲ߣߒߡ⠨

߃ࠆߛߌߢߪⓨ᳇ๆㄟࠍⷙቯߔࠆߩߦਇలಽߢ޽

ࠆߎߣ㧘ߟ߹ࠅ㧘೎ߩജቇࡄ࡜ࡔ࡯࠲߇ߎߩ⃻⽎ࠍ ⷙቯߔࠆߩߦᦝߦᔅⷐߢ޽ࠆߎߣࠍ㧘⚿⺰ߠߌߡ޿

ࠆ㧚Fraser & Harrison (1953)²⁾ߪ㧘ⶄ㔀ᒻ⁁ࠍ᦭ߔࠆ

޿ߊߟ߆ߩๆㄟ᳓ᮏߦ↢ߓࠆⓨ᳇ๆㄟࠍႎ๔ߒߚ㧚

Denny (1956)³⁾ߪ㧘◲නߥᐞ૗ᒻ⁁ߣⶄ㔀ߥᐞ૗ᒻ⁁

ߩๆㄟ᳓ᮏߩਔ⠪ߦߟ޿ߡ㧘᭽ޘߥᒻ⁁ലᨐࠍ⺞ᩏ ߒߚ㧚ᓐߪ㧘ታോ⊛ⷰὐ߆ࠄ㧘ⓨ᳇ๆㄟߩࠬࠤ࡯࡞

ലᨐߦᦨ߽㊀ⷐߥࡄ࡜ࡔ࡯࠲ߣߒߡ㧘Frߥߤߩήᰴ

ర㊂ߩઍࠊࠅߦ㧘ๆㄟ▤౉ญߩ᦭ᰴరᵹㅦࠍឭ᩺ߒ ߚ㧚ߎߎߢ㧘ࠬࠤ࡯࡞ലᨐߣߪ㧘ߔߴߡߩജቇࡄ࡜

ࡔ࡯࠲ലᨐࠍ൮᜝ߒߚ߽ߩࠍᜰߔ㧚

Stevens & Kolf (1957)⁴⁾ߪ㧘ᦨ߽◲නߥ໧㗴ߩ৻ߟ ߢ޽ࠆ̌᳓ᐔࠝ࡝ࡈࠖࠬ̍㧔޽ࠆ޿ߪ̌horizontal orifice̍㧘 ̌circular-drain basin̍㧕ࠍኻ⽎ߦߒߡ㧘

㊀ജ߅ࠃ߮☼ᕈ㧘ធㄭᵹߩᓴⅣ㧘ᐞ૗ᒻ⁁ߦ㑐ߔࠆ 4ߟߩήᰴరࡄ࡜ࡔ࡯࠲ߦߟ޿ߡ⠨߃ߚ㧚Hattersley (1965)⁵⁾ߪ㧘ୃᱜvertical-wet-pit-pumpᒻ⁁ࠍ฽߻޿ߊ ߟ߆ߩⶄ㔀ᒻ⁁ࠍᜬߞߚๆㄟ᳓ᮏߩታ㓙ߩㆇォ⁁

ᴫਅߢߩ⻉․ᕈࠍႎ๔ߒߚ㧚ᦝߦ㧘ᓐߪ㧘޿ߊߟ߆ ߩታ↪⊛ߥⓨ᳇ๆㄟߩ㒐ᱛᣇᴺࠍឭ᩺ߒߚ㧚߹ߚ㧘

Iversen ߣห᭽ߦ㧘ᓐߪ㧘ⓨ᳇ๆㄟ⃻⽎ࠍⷙቯߔࠆ

ὑߦ㧘Frߦട߃ߡ㧘ઁߩㆇേࡄ࡜ࡔ࡯࠲߇ᔅⷐߢ޽

ࠆߣᜰ៰ߒߚ㧚

Granger (1966)⁶⁾ߣAnwar (1966)⁷⁾㧘Maris (1967)⁸⁾㧘 Zielinski & Villemonte (1968)⁹⁾ߪ㧘Stevens & Kolfߣห

᭽ߦ㧘᳓ᐔࠝ࡝ࡈࠖࠬࠍ⎇ⓥኻ⽎ߣߒߚ㧚Granger ߪቯᏱ߆ߟゲኻ⒓ߩ઒ቯߩਅ㧘ᓸዊᡓੂࠍ⠨߃☼ᕈ

⸃ᨆ⸃ࠍዉ߈㧘ታ㛎ߣᲧセߒߚ㧚৻ᣇ㧘Marisߪ㕖

☼ᕈߩ઒ቯਅ㧘☼ᕈ৻ᰴㄭૃߩ߽ߣߢ⸃ᨆ⸃ࠍ᳞߼㧘

᷵ ᐲ ߩ ᤨ 㑆 ⊒ ዷ ࠍ ⺞ ߴ ߚ 㧚AnwarߣZielinski &

Villemonteߪ㧘ᵹ㊂ଥᢙ߳ߩ☼ᕈ߅ࠃ߮ធㄭᵹߩᓴ

Ⅳ㧘ᐞ૗ᒻ⁁ߩᓇ㗀ࠍ␜ߒߚ㧚Anwarߦࠃࠆߣඨᓘ

࡟ࠗࡁ࡞࠭ᢙReS (ŁǸQ/(QS)) • 10³ߩᤨ㧘Zelinski &

Villemonteߦࠃࠆߣ࡟ࠗࡁ࡞࠭ᢙReti (ŁǸDVti/Q) •

1.0×10⁴ߩᤨ㧘☼ᕈലᨐࠍήⷞߢ߈ࠆ㧚ߎߎߦ㧘Q߅

ࠃ߮Q㧘S㧘D㧘Vtiߪ㧘ߘࠇߙࠇ㧘ๆㄟญߢߩᵹ㊂߅ ࠃ߮േ☼ᐲ㧘᳓ᷓ㧘ๆㄟญ⋥ᓘ㧘ℂ⺰ᐔဋᵹㅦߢ޽

ࠆ㧚

Anwar (1968)¹⁰⁾ߣDomm et al. (1971)¹¹⁾߽ 㧘 Hattersleyߣห᭽㧘̌vertical-wet-pit-pump̍ᒻ⁁ࠍ฽

߻᭽ޘߥๆㄟ᳓ᮏࠍ⺞ᩏߒߡ㧘޿ߊߟ߆ߩⓨ᳇ๆㄟ ߩ㒐ᱛᣇᴺࠍឭ᩺ߒߚ㧚ᓐࠄߩ⎇ⓥߪ㧘ᰴర⸃ᨆ਄

ߩ৻⽾ᕈࠍᅤ޿ߡ޿ࠆߩߛ߇㧘ๆㄟญᴚ᳓ᷓߐSߣ ធㄭᵹߩᓴⅣߩਔᣇ߇ᣓ࿁ᵹࠇߦᄢ߈ߥᓇ㗀ࠍ෸

߷ ߔ ὐ ࠍ ᒝ ⺞ ߒ ߡ ޿ ࠆ 㧚 ৻ ᣇ 㧘Kondo & Maru (1972)¹²⁾ߪ㧘න⚐ߥ̌vertical-wet-pit-pump̍ᒻ⁁ࠍ ኻ⽎ߦߒߡ㧘❗ዤࡕ࠺࡞⹜㛎ߩߚ߼ߩ᛬ⴲⷙ▸ࠍឭ

Fig. 1. Suction sump and suction pipe, with the vertical-wet-pit-pump configuration. D, Outside diameter of a suction pipe; d, inside diameter of a suction pipe; B, sump breadth; X, back clearance;

H, water level; S, submergence depth; Z, bottom clearance.

᩺ߒߚ㧚ᓐࠄߩ᛬ⴲⷙ▸ߪ㧘Fr⋧ૃೣߣๆㄟ▤౉ญ ߩ᦭ᰴరㅦᐲ৻⥌ೣߩਛ㑆ೣߢ޽ࠆ㧚߽ߜࠈࠎ㧘ߎ ߩ᛬ⴲ⹏ଔߪ㧘࡟ࠗࡁ࡞࠭ᢙRe⋧ૃೣ߆ࠄ㧘ߪࠆ߆ ߦ ߌ㔌ࠇߡ޿ࠆ㧚

Reddy & Pickford (1972)¹³⁾ߪ㧘ๆㄟ᳓ᮏ⢛㕙ߦ᳓ᐔ ๆㄟญࠍᜬߟ̌ု⋥ࠝ࡝ࡈࠖࠬ̍㧔޽ࠆ޿ߪ̌vertical

orifice̍㧕ࠍ⺞ᩏߒߚ㧚̌ု⋥ࠝ࡝ࡈࠖࠬ̍ߣߪ᳓

ᐔߥๆㄟญࠍᜬߟๆㄟ᳓ᮏߢ޽ࠆ㧚ᓐࠄߪ㧘Fr⋧ૃ

ೣࠍ೨ឭߣߒߡ㧘Sc/ D = Frߥࠆ⚻㛎ೣࠍឭ᩺ߒߚ㧚

߹ߚ㧘ࠃࠅታ↪⊛ⷙ▸ߣߒߡSc / D = Fr + 1߽ឭ᩺ߒ ߚ㧚

Levi (1972)¹⁴⁾ߪ㧘ߐ߹ߑ߹ߥ᳓ᐔࠝ࡝ࡈࠖࠬࠍታ

㛎⊛ߦ⺞ߴ㧘ߘߩᵹࠇߩ㧘┥Ꮞߥߤ᳇⽎⃻⽎߳ߩᔕ

↪ࠍឭ᩺ߒߚ㧚Dagget & Keulegan (1974)¹⁵⁾ߪ㧘ࠣ࡝

࠮࡝ࡦ᳓ṁᶧ߿⒳ޘߩᷙวᴤߥߤᢙ⒳㘃ߩ૞േᵹ

૕ࠍ૶↪ߔࠆߎߣߢ㧘᳓ᐔࠝ࡝ࡈࠖࠬߢ൮᜝⊛ߥታ 㛎ࠍⴕߞߚ㧚ᓐࠄߩታ㛎ߢߪ㧘ቯᏱ⁁ᘒߦ޽ࠆⓨ᳇

♻߇⥄↱⴫㕙߆ࠄๆㄟญ߹ߢሽ࿷ߔࠆ㧚ߥ߅㧘એ೨ ⴕࠊࠇߚ᳓ᐔࠝ࡝ࡈࠖࠬߩၮ␆⎇ⓥߩᄙߊߪ㧘ⓨ᳇

ๆㄟࠍ઻ࠊߥ޿᧦ઙਅߢߩ⺞ᩏߢ޽ߞߚ㧚ᓐࠄߪ㧘

࠙ࠚ࡯ࡃ࡯ᢙWe㧔ቯ⟵ߪᓟㅀ㧕ߩലᨐ㧘ߐࠄߦ㧘 FrߣRe 㧘ធㄭᵹᓴⅣଥᢙN*㧘ੑߟߩᐞ૗ᒻ⁁ࡄ࡜

ࡔ࡯࠲ߩലᨐߦߟ޿ߡ㧘⺞ߴߚ㧚Weലᨐ㧔߹ߚߪ㧘

⴫㕙ᒛജലᨐ㧕ߦ㑐ߔࠆ⹦ㅀࠍᰳ޿ߡ޿ࠆ߇㧘ᓐࠄ ߪ㧘ᵹ㊂ଥᢙ߳ߩWeലᨐࠍήⷞߢ߈ࠆߣᜰ៰ߒߚ㧚

߹ߚ㧘ᓐࠄߪ㧘Reലᨐ㧔߹ߚߪ㧘☼ᕈലᨐ㧕߇㧘Re (Ł ViD/Q) • 3.2×10⁴ߩߣ߈㧘ήⷞߢ߈ࠆߣ⚿⺰ઃߌߚ㧚 ߎߎߢ㧘Viߩቯ⟵ߪᓟߢ␜ߔ㧚ᓐࠄߣห᭽㧘Weലᨐ ߅ࠃ߮Frലᨐ㧔߹ߚߪ㧘㊀ജലᨐ㧕㧘Reലᨐ㧘N_* ലᨐ㧘޿ߊߟ߆ߩᐞ૗ᒻ⁁ലᨐ߇㧘Baum (1974)¹⁶⁾

߿Baum & Cook (1974)¹⁷⁾㧘Anwar et al. (1978)¹⁸⁾㧘Jain et al. (1978)¹⁹⁾ߦࠃߞߡ⼏⺰ߐࠇߚ㧚BaumߣBaum &

Cookߪߐ߹ߑ߹ߥᵹ૕㧔sodium, ᳓, white spirit, Freon 113㧕ࠍ↪޿ߚታ㛎ࠍⴕߞߚ㧚Baum & Cookߪ㧘 ReലᨐࠍήⷞߒߡS_c/Dt = 700 (Fr^0.5 㧙 4.4Fr/We)ࠍ ឭ᩺ߒߚ㧚ߎߎߦ㧘Dtߪ౞ᩇ᳓ᮏ⋥ᓘߢ޽ࠆ㧚Anwar

et al.ߪ㧘̌᳓ᐔࠝ࡝ࡈࠖࠬ̍ߩઍࠊࠅߦ㧘ๆㄟ᳓ᮏ

஥㕙ߦๆㄟญࠍᜬߟ̌ု⋥ࠝ࡝ࡈࠖࠬ̍ࠍ⺞ᩏߒߚ㧚 ᓐࠄߩ⚿⺰ߢߪ㧘WeലᨐߣReലᨐߩਔᣇ߇㧘WeS (Ł UQ²S/(AV)) • 10⁴߆ߟReS (Ł Q/QS) • 3.0×10⁴ߩߣ߈ߦ

ήⷞߢ߈ࠆ㧚೨⠪ߣᓟ⠪ߩ᧦ઙߪ㧘ߘࠇߙࠇ㧘We • 41 㧙 71ߣRe • 2.3×10⁴ 㧙 3.8×10⁴ߦኻᔕߔࠆ㧚ߎ ߎߢ㧘WeߣReߩ឵▚୯ߪ৻ቯߢߪߥߊ㧘Frߩ୯ߦ

઻޿ᄌࠊࠆߎߣߦᵈᗧߔߴ߈ߢ޽ࠆ㧚ߥߗߥࠄ߫㧘 ᓐࠄߩታ㛎ⵝ⟎ߢߪ㧘޿ߊߟ߆ߩᒻ⁁ࡄ࡜ࡔ࡯࠲߇

৻ቯ୯ߦ࿕ቯߐࠇߡ߅ࠅ㧘߹ߚ㧘৻⒳㘃ߩ૞േᵹ૕㧘 ߟ߹ࠅ㧘᳓ߛߌ߇૶↪ߐࠇߡ޿ࠆ㧚৻ᣇ㧘Jain et al.

ߪ㧘ੑߟߩࠨࠗ࠭ߩๆㄟ᳓ᮏߣਃ⒳㘃ߩ૞േᵹ૕

㧔᳓㧘࠮࡞ࡠ࡯ࠬ᳓ṁᶧ㧘ࠕ࡞ࠦ࡯࡞᳓ṁᶧ㧕ࠍ૶

↪ߒߡ㧘ᢛวᕈߩ޽ࠆ᳓ᐔࠝ࡝ࡈࠖࠬታ㛎ࠍⴕߞߚ㧚 ᓐࠄߪ㧘ធㄭᵹߩᓴⅣ߇ᄢ߈ߊߥࠆߦߟࠇߡ㧘⥃⇇

ᴚ᳓ᷓߐS㧔ቯ⟵ߪᓟㅀ㧕߇ᄢ߈ߊߥࠆ㧘ߔߥࠊߜ㧘c

ⓨ᳇ๆㄟ߇ࠃࠅ⿠ߎࠅᤃߊߥࠆߣ⠨߃ߚ㧚ߎߩ᭎ᔨ ߩ߽ߣߦ⸃ᨆߐࠇߚታ㛎࠺࡯࠲ߪ㧘ߘߩ઒ቯߩᱜᒰ ᕈࠍ␜ߒߚ㧚ᓐࠄߩ⚿ᨐߦࠃࠆߣ㧘We • 11ߢWeല ᨐࠍ㧘Re/Fr² • 5.0×10⁴ߢReലᨐࠍ㧘ߘࠇߙࠇ㧘ήⷞ ߢ߈ࠆ㧚Hecker (1981)²⁰⁾ߪ㧘᭽ޘߥࡕ࠺࡞ߣේဳߣ ߩᲧセߦࠃࠅ㧘એ೨ߩ⎇ⓥߦ߅ߌࠆኸᴺലᨐࠍⷐ⚂

ߒߚ㧚Farell & Cuomo (1984)²¹⁾ߣPadmanabhan &

Hecker (1984)²²⁾ߪ㧘Reലᨐߪ㜞Reߢήⷞߢ߈ࠆߎߣ ࠍ⏕⹺ߒߚ㧚߽ߞߣ߽㧘ਔ⎇ⓥߢߪ㧘Weലᨐߪ⠨

ኤኻ⽎ᄖߢ޽ߞߚ㧚Odgaard (1986)²³⁾ߪ㧘ゲኻ⒓ߩ ጀᵹࠍᗐቯߒ㧘S_cߣFr߿N_*㧘Re㧘Weߣࠍ㑐ㅪઃߌ ࠆኸᴺലᨐⷙ▸ࠍឭ᩺ߒߚ㧚

Gulliver & Rindels (1987)²⁴⁾߿Takahashi et al.

(1988a, 1988b)^{25, 26)}ߪvertical-downward flowing intake ߦߟ޿ߡ㧘ⓨ᳇ๆㄟࠍታ㛎⊛ߦ⺞ߴ㧘ⓨ᳇ๆㄟߩ⊒

↢᧦ઙࠍFr߿Nnj㧔޽ࠆ޿ߪ㧘࿁ォࡈ࡞࡯࠼ᢙ㧕ߩ 㑐ᢙߣߔࠆ⚻㛎ೣࠍឭ᩺ߒߡ޿ࠆ㧚Hite Jr & Mih (1994)²⁷⁾߽ ๆㄟ ᳓ ᮏ ஥ ოߦ ๆ ㄟ ญ ࠍᜬ ߟ vertical orificeߦߟ޿ߡ㧘㜞Re߆ߟ㜞Weߦ߅޿ߡ㧘Reലᨐߣ Weലᨐࠍήⷞߒ㧘FrߣN*ߩᓇ㗀ࠍ᣿ࠄ߆ߦߒߚ㧚 Yildirim & Kocabas (1995, 1998)^{28, 29)} ߪ vertical-downward flowing intakeߦߟ޿ߡ⠨߃㧘We㧘 Fr㧘Re 㧘N_*ലᨐࠍήⷞߒ㧘ᵹㅦᲧߣᒻ⁁ࡄ࡜ࡔ࡯

࠲ߦߟ޿ߡߩߺ᣿ࠄ߆ߦߒߡ޿ࠆ㧚

ᦨ ㄭ 㧘 Werth & Frizell (2009)³⁰⁾ ߪ vertical-wet-pit-pump᳓ ᮏ ߦ ߟ ޿ ߡ 㧘Gulliver &

Rindels (1987)ߩ ⚻ 㛎 ೣ ࠍ ୃ ᱜ ߒSc / D = 2.1 + 4Fr^2/3/3ࠍឭ᩺ߒߚ㧚ߎࠇߪ㧘ANSIߩThe 1998 HI

Standard㧔Sc / D = 1 + 2.3Fr㧘ᓟㅀ㧕ࠃࠅ߽㧘ࠃ޿ㄭ

ૃࠍਈ߃ࠆ㧚

਄ㅀߩ⎇ⓥߩౝ㧘ᢛวᕈߩ޽ࠆᰴర⸃ᨆߪ㧘᳓ᐔ

ࠝ࡝ࡈࠖࠬߥߤߩᦨ߽◲නߥᒻ⁁ߢߩߺขࠅᛒࠊ ࠇߡ޿ࠆ㧚ߥߗߥࠄ߫㧘ᒻ⁁ࡄ࡜ࡔ࡯࠲ߩዋߥ޿ߘ ߩࠃ߁ߥන⚐ᵹࠇߦኻߒߡߩߺ㧘ᢛว⊛ߥขࠅ⚵ߺ ߇ㆡ↪น⢻ߥߚ߼ߢ޽ࠆ㧚ߒ߆ߒߥ߇ࠄ㧘ታ㓙ߩๆ ㄟ᳓ᮏ㧔଀߃߫㧘Iversen (1953)߿Fraser & Harrison

(1953)ߦ⷗ࠄࠇࠆ㧕ߪ㧘ߒ߫ߒ߫㧘ታ↪਄ߩᐢ▸࿐

ߩ೙㒢߿ⷐ᳞ߩߚ߼㧘ⶄ㔀ߥᒻ⁁ࠍ᦭ߔࠆ㧚ᱷᔨߥ ߇ࠄ㧘⃻⁁ߢߪන⚐ߥvertical-wet-pit-pumpᒻ⁁ߩࠃ ߁ߥ㧘ࠊߕ߆ߦⶄ㔀ߥᒻ⁁ߩๆㄟ᳓ᮏߦߟ޿ߡߐ߃ ᚒޘߩ⍮⼂ߪలಽߢߥ޿㧚ߘߩ᭽ߥࠊߕ߆ߦⶄ㔀ߥ ᒻ⁁ߩๆㄟ᳓ᮏߦ᳓ᐔࠝ࡝ࡈࠖࠬߩ⍮⼂ࠍㆡᔕߔ ࠆߎߣ߽⠨߃ࠄࠇࠆ߇㧘৻⥸⊛ߦන⚐ߢߪߥ޿㧚ߥ ߗߥࠄ㧘᳓ᐔࠝ࡝ࡈࠖࠬߢᗐቯߒߚN*ߩ୯ࠍ㧘ⶄ㔀 ᒻ⁁ߩๆㄟ᳓ᮏߢ⷗Ⓧ߽ࠆߎߣߪኈᤃߢߪߥ޿㧚ߟ

߹ࠅޔⶄ㔀ᒻ⁁ߩๆㄟ᳓ᮏౝߢᵹࠇߪ㧘ቢోߦਃᰴ

ర⊛ߢ޽ࠅ㧘߆ߟ㧘㕖Ᏹߦᒙ޿๟ᦼᕈࠍ઻߁ᒝ㕖ቯ Ᏹᕈࠍ␜ߔ㧚ߎߩ᭽ߥ⁁ᴫਅߢ㧘N*ߪㅢᏱ㧘ജቇࡄ

࡜ࡔ࡯࠲ߣᐞ૗ቇࡄ࡜ࡔ࡯࠲ߩਔᣇߩ㑐ᢙߣߒߡ ਈ߃ߨ߫ߥࠄߥ޿߆ࠄߢ޽ࠆ㧚

ᧄ⎇ⓥߢߪ㧘ๆㄟ▤߇⥄↱⴫㕙ࠍ⽾ㅢߒߡု⋥ਅ ᣇ ߦ ๆ ㄟ ᳓ ᮏ ߦ ᝌ ౉ ߐ ࠇ ࠆ 㧘 ޿ ࠊ ࠁ ࠆ 㧘 vertical-wet-pit-pumpᒻ⁁ߢߩⓨ᳇ๆㄟࠍ⠨߃ࠆ㧚․

ߦ㧘ᴚ᳓ᷓߐScߦᵈ⋡ߔࠆ㧚ߎߎߢ㧘Scߪ㧘ⓨ᳇ๆ ㄟ⊒↢ߩߚ߼ߩ㊀ⷐ߆ߟᘠ଀⊛ߦ૶↪ߐࠇࠆዤᐲ ߢ޽ࠆ㧚

vertical-wet-pit-pumpߩᒻ⁁ߪ㧘ታ↪⊛ߥ೑ὐ߇ᄙ

޿㧚ࠃߞߡ㧘ߎࠇ߹ߢߦℂ⺰ߣታോߩ෺ᣇߩⷞὐ߆ ࠄ㧘ᄙߊߩ⎇ⓥ߇ߥߐࠇߡ߈ߚ㧚ߘࠇࠄߦߪ㧘Iversen (1953)㧘Denny (1956)㧘Fujita & Oya (1962)³¹⁾㧘 Hattersley (1965)㧘Kyogoku (1965)³²⁾㧘Anwar (1968)㧘 Kitamura & Kida (1971)³³⁾㧘Kondo & Maru (1972)㧘 Isohata et al. (1975)³⁴⁾㧘Tagomori (1976)³⁵⁾㧘Kubota (1978)³⁶⁾㧘 Shinhama et al㧚 (1983)³⁷⁾㧘 Okamoto et al.

(1991)³⁸⁾㧘 Tagomori & Ueda (1991)³⁹⁾㧘Arboleda &

El-Fadel (1996)⁴⁰⁾ 㧘Constantinescue & Patel (1998)⁴¹⁾㧘 Werth &Frizell (2009)߿ᦨㄭߩ⪺⠪ࠄߩ⎇ⓥ(Funaki et al. (2008)⁴²⁾ߣHirata et al. (2009)⁴³⁾)ߥߤ߇޽ࠆ㧚ߥ

߅㧘Funaki et al.ߢߪ㧘ⓨ᳇ๆㄟࡔࠞ࠾࠭ࡓࠍ᣿ࠄ߆

ߦߔࠆߚ߼ߦ㧘⿥㖸ᵄ࠼࠶ࡊ࡜࡯ᴺࠍ૶↪ߒߡ㧘ๆ ㄟ᳓ᮏౝߩౖဳ⊛ߥਃᰴరᤨ㑆ᐔဋᵹࠇ႐㧘ߔߥࠊ ߜ㧘ᤨ㑆ᐔဋㅦᐲಽᏓ߿᷵ᐲಽᏓࠍ␜ߒߚ㧚ᦝߦ㧘 Hirata et al.ߢߪ㧘න⚐ߥࠦࡦ࠳ࠢ࠲ࡦࠬ࠲ࠗࡊߩ᳇

ᵃ࠮ࡦࠨ࡯ࠍ⵾૞ߒ㧘ⓨ᳇ๆㄟߩᱜ⏕ߥ⸘᷹ࠍⴕ޿㧘 ᓥ᧪ᴺߢߩ⚿ᨐߣᲧセߒߚ㧚ߎࠇ߹ߢߩᚑᨐߩ৻ㇱ ߪ㧘BHRA⁴⁴⁾߿JSME⁴⁵⁾㧘ANSI⁴⁶⁾ߥߤߩ᭽ޘߥၮḰߦ

෻ᤋߐࠇߡ޿ࠆ㧚

ߎࠇ߹ߢߩvertical-wet-pit-pumpᒻ⁁ߦ㑐ߔࠆ⎇ⓥߢ ߪ㧘޿ߊߟ߆ߩᒻ⁁ലᨐߦߟ޿ߡ⼏⺰ߒߡ޿ࠆ߇㧘 ߘࠇࠄߩ⚿ᨐߪ㧘᭽ޘߥജቇࡄ࡜ࡔ࡯࠲ലᨐ㧘ߔߥ ࠊߜ㧘ኸᴺലᨐࠍ൮฽ߒߡ߅ࠅ㧘ߘߩᔀᐩ⊛ߥ⼏⺰

ߩᰳᅤߩߚ߼㧘৻⥸ᕈߦਲߒ޿㧚੐㓙㧘ㆊ෰ߩ޿ߊ ߟ߆ߩ⎇ⓥߢߪ㧘ࠬࠤ࡯࡞ࡕ࠺࡞⹜㛎ߩ⚿ᨐࠍ⍦⋫

ߥߊ⺑᣿ߔࠆߚ߼ߦߪ㧘Frߦട߃ߡઁߩജቇࡄ࡜ࡔ

࡯࠲߇ᔅⷐߢ޽ࠆߣ⚿⺰ઃߌߡ޿ࠆ㧚ߘߎߢ㧘ᧄ⎇

ⓥߢߪ㧘ᢛวᕈࠍ଻⸽ߒߚ৻ㅪߩታ㛎ߦࠃࠅ㧘6୘ ߩήᰴరࡄ࡜ࡔ࡯࠲߇Sc߳෸߷ߔലᨐߩ⸃᣿ࠍ⹜

ߺࠆ㧚6୘ߩౝߩ3୘ߩࡄ࡜ࡔ࡯࠲ߪജቇലᨐ㧘ߔߥ ࠊߜ㧘㊀ജലᨐ߅ࠃ߮☼ᕈലᨐ㧘⴫㕙ᒛജലᨐߦ㑐 ߔࠆ߽ߩߢ޽ࠅ㧘ઁߩਃߟߩࡄ࡜ࡔ࡯࠲ߪᒻ⁁ലᨐ ߦ㑐ߔࠆ߽ߩߢ޽ࠆ㧚

㧚ታ㛎ᣇᴺ ๆㄟ᳓ᮏߣๆㄟ▤

Fig. 1ߪ㧘੹࿁ኻ⽎ߣߔࠆࡕ࠺࡞ࠍ␜ߔ㧚ߔߥࠊ

ߜ㧘න⚐ߥvertical-wet-pit-pumpᒻ⁁ࠍᜬߞߚๆㄟ᳓

ᮏ㧛ๆㄟ▤♽ߢ޽ࠆ㧚ߎߎߦ㧘Dߣdߣߪ㧘ߘࠇߙ ࠇ㧘ๆㄟญߩᄖᓘ߅ࠃ߮ౝᓘߢ޽ࠆ㧚೨⠪ߪ㧘ᧄ⺰

ߢߪઍ⴫㐳ߐࠬࠤ࡯࡞ߣߔࠆ㧚ᓟ⠪ߪ㧘0.9Dߦ࿕ቯ ߔࠆ㧚ๆㄟ▤ߩๆㄟญᒻ⁁ߪ㧘ࡌ࡞ࡑ࠙ࠬဳߢ޽

ࠆ㧚ๆㄟ▤ߪๆㄟ᳓ᮏߩਛᔃゲ਄ߦ㧘਄ᣇ߆ࠄု⋥

ߦᝌ౉ߔࠆ㧚ߎߎߦ㧘B߅ࠃ߮X㧘Zߪ㧘ߘࠇߙࠇ㧘 ๆㄟ᳓ᮏ᏷߅ࠃ߮ๆㄟ▤ਛᔃ߆ࠄๆㄟ᳓ᮏᓟო߹

ߢߩ㑆㓗㧘ๆㄟ▤౉ญߣๆㄟ᳓ᮏᐩოߣߩ㑆㓗ࠍ␜

ߔ㧚߹ߚ㧘Hߪ㧘᳓૏㧘ߔߥࠊߜ㧘ᐔဋ⥄↱᳓㕙ߩ 㜞ߐߢ޽ࠆ㧚ࠃߞߡ㧘ࡄࠗࡊߩᴚ᳓ᷓߐSߪ㧘HZ ߦ╬ߒ޿㧚ઍ⴫ㅦᐲࠬࠤ࡯࡞ࠍๆㄟ▤౉ญߩᐔဋᵹ ㅦViߣߔࠆ㧚Viߪ㧘એਅߩࠃ߁ߦቯ⟵ߔࠆ㧚

Table 1. Experimental parameters.

Vi = 4Q/(SD²). (1)

ߎߎߦ㧘Qߪᵹ಴ଥᢙ㧘ߔߥࠊߜ㧘ๆㄟ▤ౝߩᵹ㊂ ߢ޽ࠆ㧚߹ߚ㧘ࡈ࡞࡯࠼ᢙFr߅ࠃ߮࡟ࠗࡁ࡞࠭ᢙRe㧘

࠙ࠚ࡯ࡃ࡯ᢙWeࠍ㧘એਅߩࠃ߁ߦቯ⟵ߔࠆ㧚

Fr = Vi/(gD)^0.5. (2)

Re = ViD/Q. (3)

We = Vi(UD/V)^0.5. (4) ߎߎߦ㧘g߅ࠃ߮Q㧘U㧘Vߪ㧘ߘࠇߙࠇ㧘㊀ജടㅦ ᐲ㧘ᵹ૕ߩേ☼ᐲ㧘ᵹ૕ߩኒᐲ㧘᳓ߣⓨ᳇ߣߩ⴫㕙 ᒛജࠍ␜ߔ㧚߹ߚ㧘⵬ഥࡄ࡜ࡔ࡯࠲ߣߒߡ㧘Bond ᢙBoࠍ⠨߃ࠆ㧚Boߪએਅߩࠃ߁ߦቯ⟵ߔࠆ㧚

Bo = UgD²/V. (5)

Table 1ߪ㧘ᧄ⎇ⓥߦ߅ߌࠆታ㛎ࡄ࡜ࡔ࡯࠲ߣߘࠇ

ࠄߩ▸࿐ࠍ㧘ήᰴరᒻ⁁ࡄ࡜ࡔ࡯࠲߅ࠃ߮ήᰴరㆇ

േࡄ࡜ࡔ࡯࠲ߣ౒ߦ␜ߔ㧚

Fig. 2ߪ㧘ᧄታ㛎ⵝ⟎ߩ᭎⇛ࠍ␜ߔ㧚࠲࡯ࡏࡐࡦ

ࡊA(࿑ਛ㧘No.2)ߪ㧘૞േᵹ૕(᳓)ࠍ⾂᳓ᮏ(No.1)߆ ࠄๆㄟ᳓ᮏ(No.3)ߦㅍࠆ㧚೙ᓮᑯߦࠃࠅ㧘ࡐࡦࡊA ߩᵹ㊂ࠍ⺞▵ߒߡ㧘ๆㄟ᳓ᮏߩ᳓૏Hࠍቯ߼ࠆ㧚ๆ ㄟ᳓ᮏߩ਄ᵹ㧘ߔߥࠊߜ㧘ๆㄟ᳓ᮏᓟო߆ࠄ0.84m

਄ᵹߦ㧘ᢛᵹⵝ⟎(No.4)ࠍ⸳ߌࠆ㧚ᢛᵹⵝ⟎ߪ⋥ᓘ

0.001m߆ߟ㓗㑆0.001mߩࡢࠗࡗ࡯ࡔ࠶ࠪࡘ2ᨎߦࠃ

ߞߡ᜽߹ࠇߚ㧘ਇ❱Ꮣ߆ࠄᚑࠆ㧚ࡌࡦ࠼࡮࠲ࠗࡊ࡮

ࠫࠚ࠶࠻࡮ࡐࡦࡊ(No.6)ߦࠃࠅ㧘ๆㄟ᳓ᮏ߆ࠄๆㄟ

ญ(No.5)ߦ᳓ࠍๆ޿਄ߍࠆ㧚ߎߩࠫࠚ࠶࠻࡮ࡐࡦࡊ

ߪ㧘࠲࡯ࡏࡐࡦࡊB(No.7)ߦࠃࠅ㧘㚟േߔࠆ㧚ߎߎ ߢ㧘ࠫࠚ࠶࠻࡮ࡐࡦࡊߪ㧘ㅢᏱߩゲᵹࡐࡦࡊߥߤߣ Ყセߒߡ㧘ᣓ࿁ᵹᚑಽ߇ዊߐ޿․ᓽࠍ᦭ߔࠆ㧚㔚⏛

ᵹ㊂⸘(No.8)ߦࠃࠅ㧘ࠫࠚ࠶࠻࡮ࡐࡦࡊߩ৻ᰴᵹ㊂

ࠍ᷹ቯߔࠆ㧚߹ߚ㧘ਃႍⷺ(No.9)ߦࠃࠅ㧘ࠫࠚ࠶࠻࡮

ࡐࡦࡊߩ৻ᰴᵹ㊂ߣੑᰴᵹ㊂ߩ✚๺ࠍ᷹ቯߔࠆ㧚ߎ ߎߢ㧘ੑᰴᵹ㊂ߪ㧘ๆㄟ▤ౝߩᵹ㊂ߦ╬ߒ޿㧚ᦨᓟ ߦ㧘ਃႍⷺ߆ࠄߩ᳓ߪ㧘⾂᳓ᮏߦᚯߐࠇ㧘᳓ߩᓴⅣ

♽߇㐽ߓࠆ㧚

⥄↱⴫㕙ᒻ⁁ߩಽ㘃

Iversen (1953)߿Denny (1956)㧘 Prosser (1977)⁴⁴⁾㧘 Toyokura et al. (1984)⁴⁵⁾㧘 Padmanabham & Hecker

(1984)ࠍෳ⠨ߦߒߟߟ㧘੍஻᷹ⷰࠍታᣉߒ㧘ๆㄟ᳓

ᮏౝߦ․᦭ߩ⥄↱⴫㕙ࡄ࠲࡯ࡦࠍ㧘੖ߟߩ࠲ࠗࡊ(a) 㧙(e)ߦಽ㘃ߔࠆ (Fig. 3ࠍෳᾖ)㧚

ߎߩಽ㘃ᴺߪ㧘․ߦๆㄟ▤߳ߩⓨ᳇ๆㄟߦᵈ⋡ߒ ߚ߽ߩߢ޽ࠆ㧚⠨ኤߩኈᤃᕈߣ⏕ታᕈߣࠍ㊀ⷞߒߚ

⚿ᨐ㧘ᧄಽ㘃ߪ㧘BHRA⁴⁴⁾߿JSME⁴⁵⁾ߩಽ㘃ᴺߦㄭߊ㧘 ᨴᢱߥߤߦࠃࠆᵹࠇߩนⷞൻࠍ઻߁ANSI⁴⁶⁾ߩಽ㘃 ᴺߣߪ㧘⧯ᐓ⇣ߥࠆ㧚

એਅߦ㧘੖ߟߩ࠲ࠗࡊ(a)㧙(e)ࠍ⺑᣿ߔࠆ㧚

࠲ࠗࡊ(a): Fig. 3(a)ߦ␜ߔࠃ߁ߦ㧘ๆㄟ▤ઃㄭߩᐔဋ

⥄↱⴫㕙ߦᵻ޿߳ߎߺ㧘ߔߥࠊߜ㧘ߊ߷

ߺࠍ᷹ⷰߢ߈ࠆ㧚ߊ߷ߺߩᄙߊߪ㧘ๆㄟ ▤ߩਅᵹߦ⊒↢ߔࠆ㧚ߎߎߢ㧘ߊ߷ߺ߆ ࠄߩⓨ᳇ๆㄟߪߥ޿ߎߣߦᵈᗧߔߴ߈

Fig. 2. Experimental apparatus1. 1, Reservoir; 2, turbo pump A; 3, suction sump; 4, strainer; 5, suction pipe; 6, bend-type jet pump; 7, turbo pump B; 8, eletro-magnetic flow meter; 9, triangle weir.

2.3˜10³–4.9˜10⁴ Re/Fr²

8.6–27 We

8.3˜10³–4.6˜10⁴ Re

0.66–2.8 Fr

0.53–6.05 H/D

0.26–3.21 Z/D

0.79–5.0 X/D

1.43–5.30 B/D

0.45–1.20 V_i[m/s]

14–48 D[m]

7–23 Z[m]

20–215 X[m]

33–150 B[m]

20–500 Bo

2.3˜10³–4.9˜10⁴ Re/Fr²

8.6–27 We

8.3˜10³–4.6˜10⁴ Re

0.66–2.8 Fr

0.53–6.05 H/D

0.26–3.21 Z/D

0.79–5.0 X/D

1.43–5.30 B/D

0.45–1.20 V_i[m/s]

14–48 D[m]

7–23 Z[m]

20–215 X[m]

33–150 B[m]

20–500 Bo

6

5

9

3

4

2 8

7

1 6

5

9

3

4

2 8

7

1

ߢ޽ࠆ㧚

࠲ࠗࡊ(b): Fig. 3(b)ߣFig. 4(a)ߣߦ␜ߔࠃ߁ߦ㧘ⓨ㑆

⊛ߦᢿ⛯ߒߚⓨ᳇♻㧘ߔߥࠊߜ㧘޽ࠆ✢

਄ߦ৻೉ߦㅪߥߞߚ৻ㅪߩ᳇ᵃࠍ㧘᷹ⷰ

ߢ߈ࠆ㧚ⓨ᳇♻ߩ৻┵ߪ㧘ᐔဋ⥄↱⴫㕙 ߩⓨ᳇♻ߪๆㄟ▤ਅᵹߦ⊒↢ߒ㧘ⓨ᳇♻

ࠍਛᔃゲߣߒߡ㧘ߘߩ๟࿐ߩᵹ૕߇ᣓ࿁

ߔࠆ㧚ߎߩ࠲ࠗࡊߢߪ㧘ๆㄟ▤߳ߩⓨ᳇

ๆㄟߪ⿠ߎࠅ߃ࠆ߇㧘ๆㄟ߹ࠇࠆⓨ᳇ߪ㧘 ᓸ㊂ߢ޽ࠆ㧚

(a) A free-surface dimple near a suction pipe.

(b) A spatially-intermittent air string near a suction pipe

࠲ࠗࡊ(c): Fig. 3(c)ߣFig. 4(b)ߣߦ␜ߔࠃ߁ߦ㧘ⓨ㑆

⊛ߦㅪ⛯ߒߚⓨ᳇♻㧘ߔߥࠊߜ㧘ᐔဋ⥄

↱⴫㕙߆ࠄๆㄟ▤౉ญ߳⥋ࠆ⥄↱⴫㕙਄

ߩᷓ޿ߊ߷ߺࠍ㧘᷹ⷰߢ߈ࠆ㧚࠲ࠗࡊ(a)

߿࠲ࠗࡊ(b)ߣห᭽㧘ⓨ᳇♻ߪ㧘৻⥸ߦๆ ㄟ▤ਅᵹߦ⊒↢ߒ㧘ᵹ૕ᣓ࿁ߩਛᔃゲߣ ߥࠆ㧚ߎߩ࠲ࠗࡊߢߪ㧘ๆㄟ߹ࠇࠆⓨ᳇

ߩ㊂ߪᄢ߈ߊ㧘ㅢᏱ㧘ࡐࡦࡊᕈ⢻߳ߩᓇ 㗀ࠍήⷞߢ߈ߥ޿㧚

(d) A free-surface hollow exposed to the peripheral wallof a suction pipe

(e) Submerging air strings

(c) A spatially-continuous air string near a suction pipe

Fig. 3. Types of distinctive free-surface patterns in suction sumps.

࠲ࠗࡊ(d): Fig. 3(d)ߦ␜ߔࠃ߁ߦ㧘ๆㄟ▤ᄖ๟ოߦ ធߔࠆᐔဋ⥄↱⴫㕙ߦᄢ߈ߥߊ߷ߺࠍ

᷹ⷰߢ߈ࠆ㧚ߊ߷ߺߪ㧘ๆㄟ▤ߩ৻ㇱ޽

ࠆ޿ߪోㇱࠍขࠅ࿐߻㧚ᵹ૕ߪ㧘ᤨߦ㧘 ๆㄟ▤๟࿐ࠍᣓ࿁ߔࠆߎߣ߇޽ࠆ㧚ⓨ᳇

ߪ㧘ๆㄟ▤๟࿐ߩછᗧߩ႐ᚲ߆ࠄ㧘ਇⷙ

ೣߦๆㄟ߹ࠇ㧘ࡐࡦࡊᕈ⢻ߦ⥌๮⊛ߥᓇ 㗀ࠍਈ߃ࠆ㧚

࠲ࠗࡊ(e): Fig. 3(e)ߦ␜ߔࠃ߁ߦ㧘᳓ਛⓨ᳇♻߇᷹ⷰ

ߢ߈ࠆ㧚ߎߩ⥄↱⴫㕙Ⴚ⇇ߪᐔဋ⥄↱⴫

㕙ߦㅪ⚿ߒߡ޿ߥ޿㧚ߐࠄߦㅀߴࠆߣ㧘

ⓨ᳇♻ߩ৻┵ߪ㧘ๆㄟ▤౉ญߦ㆐ߒߡ߅ ࠅ㧘߽߁৻┵ߪ㧘ๆㄟ▤ߩᐩო޽ࠆ޿ߪ

஥ო㧘ᓟოߦ㆐ߔࠆ㧚ઁߩ࠲ࠗࡊߣห᭽

ߦ㧘ⓨ᳇♻ߪᵹ૕ᣓ࿁ߩਛᔃゲߣߥࠆ㧚 ๆㄟ᳓ᮏౝߢߪ㧘⥄↱⴫㕙ࡄ࠲࡯ࡦߪ㧘ࡐࡦࡊᴚ᳓

ᷓSߩᷫዋߣߣ߽ߦ㧘ㅢᏱ㧘࠲ࠗࡊ(a)߆ࠄ࠲ࠗࡊ(d)

߳ߣ⒖ⴕߔࠆ㧚৻ᣇ㧘࠲ࠗࡊ(e)ߪᐔဋ⥄↱⴫㕙ߩሽ

࿷ߣߪ㧘⋥ធ㧘㑐ଥ߇ߥ޿㧚឵⸒ߔࠇ߫㧘ߚߣ߃S ߇ᄢ߈޿ᤨߢ߽㧘࠲ࠗࡊ(e)ߪ಴⃻ߒᓧࠆ㧚એ਄ߩಽ 㘃ᴺߪ㧘ⓨ᳇ߣ᳓ߣߩ㑆ߩ⥄↱⴫㕙ߩ⋡ⷞ᷹ⷰߦၮ ߠ޿ߚᘠ଀⊛ߥ߽ߩߢ޽ࠆߎߣߦᵈᗧߔߴ߈ߢ޽

ࠆ㧚ࠃߞߡ㧘ߤߩ࠲ࠗࡊ߽㧘ⓨ᳇ๆㄟߩ⊒↢ߦ߽ๆ ㄟⓨ᳇㊂ߦ߽⋥ធ㑐ଥߠߌࠆߎߣߪߢ߈ߥ޿

⥃⇇ᴚ᳓ᷓ5_E

ᄙߊߩ⎇ⓥ⠪ߣห᭽㧘ᧄ⎇ⓥߢߪ㧘ⓨ᳇ๆㄟߩ╙

৻ߩᜰᮡࠍ㧘⥃⇇ᴚ᳓ᷓScߣߔࠆ㧚Scߩቯ⟵ߪ㧘એ ਅߩㅢࠅߢ޽ࠆ㧚ᴚ᳓ᷓS(Fig. 1ࠍෳᾖ)߇లಽᄢ߈

޿୯߆ࠄ㔖߹ߢᷫዋߔࠆߣ߈㧘߹ߕ㧘S = Scߦ߅޿

ߡⓨ㑆⊛ߦㅪ⛯ߒߚⓨ᳇♻(࠲ࠗࡊ(c))߇ᦨೋߦⷰ

ኤߢ߈ࠆ㧚ᧄታ㛎ߢߪ㧘Sࠍ0.005m㑆㓒ߢᲑ㓏⊛ߦ

ᷫዋߐߖࠆ㧚ฦᲑ㓏ߢߪ㧘ฦޘ5ಽ㑆㧘࠲ࠗࡊ(c)ࠍ ᝡ⚝ߔࠆ㧚ߥ߅㧘੍஻⹜㛎ߦࠃࠅ㧘࠲ࠗࡊ(c)⊒↢ߩ

๟ᦼᕈߪ㕖Ᏹߦᒙ޿߇㧘5ಽ㑆ߩ᷹ⷰߪ㧘࠲ࠗࡊ(c) ࠍ⏕⹺ߔࠆߩߦలಽߢ޽ࠆߎߣ߽⏕⹺ߢ߈ࠆ㧚࠲ࠗ

ࡊ(c)ߩ⊒↢ߪ㧘ๆㄟ▤߳ߩⓨ᳇ๆㄟߩ⊒↢ࠍ⋥ធᗧ

๧ߒߥ޿߇㧘ⓨ᳇ๆㄟ⊒↢ߩలಽߥᜰᮡߦߪߥࠅᓧ ࠆ(Hirata et al. (2009)ࠍෳᾖ)㧚

⚿ᨐߣ⠨ኤ ᡰ㈩ࡄ࡜ࡔ࡯࠲

⥃⇇ᴚ᳓ᷓߐScߦᓇ㗀ࠍ෸߷ߔ᦭ᰴర㊂9୘ࠍ⠨

߃ࠆ㧚ߔߥࠊߜ㧘ๆㄟ㑆౉ญㅦᐲVi߅ࠃ߮ๆㄟ▤ᄖ ᓘD㧘ๆㄟ᳓ᮏ᏷B㧘ᓟო㑆㓗X㧘ᐩო㑆㓗Z㧘㊀ജ ടㅦᐲg㧘⴫㕙ᒛജǻ㧘ᵹ૕ኒᐲǹ㧘ᵹ૕☼ᕈଥᢙ Ǵߢ޽ࠆ㧚ᰴర⸃ᨆࠃࠅ㧘ᰴᑼࠍᓧࠆ㧚

Sc/D = )₁ (Fr㧘Re㧘We㧘B/D㧘X/D㧘Z/D).

(6) ߎߎߦ㧘)iߪછᗧ㑐ᢙ(ᢛᢙi = 1㧘2㧘3, ̖)ߢ޽ࠆ㧚

(a) Spatially-intermittent air string from the atmosphere to a suction-pipe intake

(b) Spatially-continuous air string from the atmosphere to a suction-pipe intake Fig. 4. Photographs of air strings.

0 1 2 3

10 20 30 40

We

Sc㪆D

Jain et al. (1978),

We> 11 (Bo> 55) Dagget & Keulegan (1974),

We> 17 䋨on the assumption of D= 38mm) Anwar et al. (1978), We> 40 (Bo> 1100)

Odgaard (1986), We> 27

ᑼ(6)ߦ߅޿ߡ㧘ViߣDߣࠍ㧘ߘࠇߙࠇ㧘ઍ⴫ㅦᐲࠬ

ࠤ࡯࡞ߣઍ⴫㐳ߐࠬࠤ࡯࡞ߣߒߡ㧘ㆬ߱㧚߽ߒ㧘ᧄ

⃻⽎ߢᦨ߽㊀ⷐߥജࠍ㧘ᘠᕈജߩઍࠊࠅߦ㊀ജߣ⷗

ߥߔߥࠄ߫㧘ᑼ(6)ߦઍࠊࠅ㧘ᰴᑼࠍᓧࠆ㧚 Sc/D = ) (Fr㧘Re/Fr²㧘Bo㧘B/D㧘X/D㧘Z/D).

(7) એਅߩ▵ߢߪ㧘ᑼ(6)߹ߚߪᑼ(7)ࠍᗐቯߒߡ㧘Sc/D

߳ߩ6୘ߩήᰴరᡰ㈩ࡄ࡜ࡔ࡯࠲FrߣRe㧘We㧘B/D㧘 X/D㧘Z/D㧘߹ߚߪ㧘FrߣRe/Fr²㧘Bo㧘B/D㧘X/D㧘 Z/Dߩലᨐߩ⸃᣿ࠍ⹜ߺࠆ㧚

ᑼ(6)ߣᑼ(7)ߩߤߜࠄࠍ⠨߃ࠆ߆㧘ߔߥࠊߜ㧘╙

৻ߦᡰ㈩⊛ߥജ߇ᘠᕈജ߆㊀ജ߆ߪ㧘⥄↱⴫㕙ߩ⃻

⽎ࠍ⠨߃ࠆ਄ߢᦨ߽㊀ⷐߥജቇࡄ࡜ࡔ࡯࠲ߢ޽ࠆ Frߩ ୯ ߦ ଐ ሽ ߔ ࠆ 㧚(Iversen (1953)ߣHattersley

(1956)ࠍෳᾖ)㧚᣿⏕ߦㅀߴࠆߣ㧘Fr « 1ߦ߅޿ߡߪ

ᑼ(6)ࠍ㧘Fr »1ߦ߅޿ߡߪᑼ(7)ࠍ↪޿ࠆߴ߈ߢ޽ࠆ㧚 Fr²ߪ㧘ᘠᕈജߩ㊀ജߦኻߔࠆో૕⊛ߥࡃ࡜ࡦࠬࠍ

⴫ߒߡ޿ࠆ㧚ߘߒߡ㧘ߘࠇࠄੑߟߩജߪ㧘⥄↱⴫㕙

⃻⽎ࠍᡰ㈩ߔࠆਥⷐߥജߢ޽ࠆ㧚ߘࠇࠄੑߟߩਥⷐ ߥജߩࡃ࡜ࡦࠬࠍᄌᦝߔࠆ⵬ഥ⊛ߥജߣߒߡ㧘☼ᕈ ജߣ⴫㕙ᒛജߣࠍ⠨߃ࠆߎߣ߇ߢ߈ࠆ㧚ࠃߞߡ㧘ᘠ ᕈജ߇㊀ജࠃࠅ߽ዊߐߊߥࠅ߇ߜߥFr « 1ߩߣ߈㧘 ߘࠇࠄੑߟߩ⵬ഥ⊛ߥജߪ㧘㊀ജߢߪߥߊᘠᕈജߩ ᄢ߈ߐߦㄭߠߊ㧚ߘߒߡ㧘ߘࠇࠄੑ⵬ഥജߣᘠᕈജ

ߣߩ㑐ଥߪ㧘ੑ⵬ഥജߣ㊀ജߣߩ㑐ଥࠃࠅ߽㧘ࠃࠅ ᵹࠇߦᓇ㗀ࠍ෸߷ߒ߿ߔߊߥࠆ㧚ߘߒߡ㧘Fr » 1ߢ ߪ㧘ߘߩㅒߣߥࠆ㧚

ታ↪⊛ߥⷰὐ߆ࠄߔࠆߣ㧘Fr ߪᄙߊߩ႐ว1ࠃࠅ

߽ߕߞߣᄢ߈ߊߥࠆߎߣߪߥ޿ߩߢ㧘ᑼ(7)ࠃࠅ߽ᑼ (6)ߩᣇ߇᦭↪ߢ޽ࠈ߁㧚ߎߩ⠨߃ߦၮߠߊߣ㧘ജቇ ࡄ࡜ࡔ࡯࠲ߣߒߡ㧘Frߦട߃ߡ㧘Re/Fr²߿Boߢߪߥ ߊ㧘 Re߿Weࠍ⠨߃ࠆߴ߈ߢ޽ࠈ߁㧚

߹ߚ㧘ઍ⴫ㅦᐲࠬࠤ࡯࡞ߣߒߡ㧘Viߩઍࠊࠅߦ೎

ߩ㊂ࠍ૶↪ߢࠆ㧚଀߃߫㧘ઍ⴫ㅦᐲࠬࠤ࡯࡞ߣߒߡ㧘 ๆㄟ᳓ᮏߩᐔဋ᳓〝ㅦᐲV_sࠍㆬ߱ߎߣߪ㧘ઁߩ৻ㆬ

ᛯ⢇ߦߥࠅ߃ࠆ㧚ߒ߆ߒ㧘Viߪ㧘Vsࠃࠅ߽᦭ലߢ޽

ࠆߣᕁࠊࠇࠆ㧚ߥߗߥࠄ߫㧘ๆㄟ▤౉ญઃㄭߩዪᚲ ᵹࠇߪ㧘ࠃࠅⓨ᳇ๆㄟߦᓇ㗀ࠍਈ߃ᓧࠆ㧚ߐࠄߦ㧘 Vi ߩ૶↪ߪVsߣᲧߴߡ㧘ᐢ▸࿐ߥታ㛎࠺࡯࠲ࠍࠃࠅ ߁߹ߊ߹ߣ߼ᓧࠆ㧚⸒޿឵߃ࠆߣ㧘㕖Ᏹߦ᏷ߩᐢ޿

᳓ᮏ㧘ߟ߹ࠅB/D߇ᄢ߈޿ᤨ㧘V_sߪ㕖Ᏹߦዊߐ޿୯ ࠍߣࠆ㧚৻ᣇߢ㧘Vs ߩ૶↪ߪធㄭᵹ߇ࠃࠅലᨐ⊛

ߦߥࠆ᭽ߥ⁜޿ࡄ࡜ࡔ࡯࠲▸࿐ౝߢߪ᦭ലߣᕁࠊ ࠇࠆ㧚ઍ⴫ㅦᐲࠬࠤ࡯࡞ߣห᭽㧘ઍ⴫㐳ࠬࠤ࡯࡞ߣ ߒߡ㧘Dߩઍࠊࠅߦ೎ߩ㊂ࠍ૶↪ߢ߈ࠆ㧚଀߃߫㧘 ઍ⴫㐳ࠬࠤ࡯࡞ߣߒߡBࠍㆬ߱ߎߣߪ㧘ઁߩ৻ㆬᛯ

⢇ߢ޽ࠈ߁㧚ߒ߆ߒ㧘ઍ⴫ㅦᐲࠬࠤ࡯࡞ߢߩ⼏⺰ߣ ห᭽㧘DߪBࠃࠅ߽᦭ലߢ޽ࠆߣᕁࠊࠇࠆ㧚

Fig. 5. Critical submergence Sc/D versus Weber number We: Ɣ, B/D = 3.13, X/D = 5.0, Z/D = 0.48, Fr = 0.67 and Re

= 2.2˜10⁴ (Re/Fr² = 4.9˜10⁴, Bo = 380, 420, 440, 470); ٟ, B/D = 3.16, X/D = 1.71, Z/D = 0.71, Fr = 1.35 and Re = 3.8˜10⁴ (Re/Fr² = 2.1˜10⁴, Bo = 260, 300); ً, B/D = 3.16, X/D = 1.71, Z/D = 0.71, Fr = 2.8 and Re = 3.8˜10⁴ (Re/Fr² = 4.8×10³, Bo = 95, 130).

ജቇࡄ࡜ࡔ࡯࠲ߩᓇ㗀

੹㧘ᑼ(6)ਛߩਃߟߩജቇࡄ࡜ࡔ࡯࠲FrߣRe㧘We㧘 ߅ࠃ߮㧘ᑼ(7)ਛߩਃߟߩജቇࡄ࡜ࡔ࡯࠲FrߣRe/Fr²㧘 Boߩ㧘Sc/D߳ߩᓇ㗀ࠍ⠨߃ࠆ㧚߽ߒ㧘ⶄᢙߩജቇࡄ

࡜ࡔ࡯࠲ߩⶄวലᨐߩઍࠊࠅߦ㧘৻ߟߩജቇࡄ࡜ࡔ

࡯࠲ߛߌߩ⚐☴ߥലᨐࠍ⍮ࠅߚߌࠇ߫㧘৻ㅪߩ⹜㛎 ࠍㅢߒߡ㧘ઁߩജቇࡄ࡜ࡔ࡯࠲ߣߔߴߡߩᒻ⁁ࡄ࡜

ࡔ࡯࠲ߣࠍ৻ቯߩ୯ߦ଻ߟ᭽ߦታ㛎⁁ᴫࠍ೙ᓮߒ ߥߌࠇ߫ߥࠄߥ޿㧚

Fig. 5ߪ㧘WeߣSc/Dߣߩ㑐ଥࠍ␜ߔ㧚ߔߥࠊߜ㧘 Fig. 5ߢߪਃߟߩ႐วߦߟ޿ߡߩ⚿ᨐ߇㧘౞ᒻߣ⪉

ᒻ㧘ਃⷺᒻߢ⴫ࠊߐࠇߡ޿ࠆ㧚ߘࠇߙࠇߩ႐วߦ߅

޿ߡ㧘WeߣBoએᄖߩߔߴߡߩᡰ㈩ࡄ࡜ࡔ࡯࠲߇৻

ቯߦ଻ߚࠇߡ޿ࠆ㧚ߤߩ႐วߦ߅޿ߡ߽Sc/Dߩ୯߇

߶߷หߓߦߥࠆߎߣ߇ࠊ߆ࠆ㧚ߎߩ⚿ᨐߪ㧘Sc/D߳ ߩWeലᨐ߇⺞ᩏߐࠇߚWe▸࿐ౝߢήⷞߢ߈ࠆߎߣ㧘

߹ߚߪ㧘Sc/D߳ߩBoലᨐ߇⺞ᩏߐࠇߚBo▸࿐ౝߢή

ⷞߢ߈ࠆߎߣࠍ␜ߔ㧚ࠃߞߡ㧘We > 12ߦ߅޿ߡ㧘 ᑼ(6)ߪᰴᑼߣߥࠆ㧚

Sc/D = ) (Fr㧘Re㧘B/D㧘X/D㧘Z/D)㧚 (8)

߹ߚߪ㧘Bo > 95ߦ߅޿ߡ㧘ᑼ(7)ߪᰴᑼߣߥࠆ㧚 Sc/D = ) (Fr㧘Re/Fr²㧘B/D㧘X/D㧘Z/D)㧚 (9) ෩ኒߦㅀߴࠆߣ㧘એਅߦㅀߴࠆੑߟߩⷰὐ߆ࠄ㧘 એ਄ߩੑߟߩⷙ▸We > 12ߣBo > 95ߪㆊ೾ߢ޽ࠆ㧚

╙৻ߦ㧘ߔߴߡߩታ㛎߇We > 12߆ߟBo > 95ߢⴕࠊ ࠇߡ޿ࠆߚ߼㧘We߿Bo߇ࠃࠅዊߐ޿ᤨߩ⍮⼂ࠍᰳ

޿ߡ޿ࠆ㧚╙ੑߦ㧘ᧄታ㛎ߢߪ㧘Fr߇10⁰ߩࠝ࡯࠳

࡯ߢ޽ࠆ㧚߽ߒ㧘Fr « 1ߢߐࠄߦታ㛎ࠍⴕ߃߫㧘ࠃ ࠅᱜ⏕ߥWeⷙ▸ࠍ⷗಴ߒᓧࠆߛࠈ߁㧚߹ߚ㧘Fr » 1 ߢߐࠄߦታ㛎ࠍⴕ߃߫㧘ࠃࠅᱜ⏕ߥBoⷙ▸ࠍ⷗಴ߒ ᓧࠆߛࠈ߁㧚

ห᭽ߦ෩ኒߦㅀߴࠆߣ㧘ߚߣ߃㧘ࠃࠅᱜ⏕ߥⷙ▸

ࠍ⷗޿಴ߒߚߣߒߡ߽㧘ᑼ(8)ߦኻߔࠆWeⷙ▸ߩ㑣 ୯߇㧘ℂ⺰⊛ߦFr߿Re㧘B/D㧘X/D㧘Z/Dߩࠃ߁ߥઁ

ߩᡰ㈩ࡄ࡜ࡔ࡯࠲ߦଐሽߔࠆߎߣ߿㧘ᑼ(9)ߦኻߔࠆ Boⷙ▸ߩ㑣୯߇ℂ⺰⊛ߦFr߿Re/Fr²㧘B/D㧘 X/D㧘 Z/Dߩࠃ߁ߥઁߩᡰ㈩ࡄ࡜ࡔ࡯࠲ߦଐሽߔࠆߎߣߦ ᵈᗧߒߥߌࠇ߫ߥࠄߥ޿㧚એ਄ߪ㧘ᧄ⎇ⓥߢߪኻ⽎

▸࿐ᄖߢ޽ࠆ߇㧘ᑼ(10)ߢ㑐ㅪߒߚ⹤㗴ߦߟ޿ߡ⼏

⺰ߔࠆ㧚

ߜߥߺߦ㧘Fig. 5ߢ㧘Weലᨐࠍήⷞߢ߈ࠆ᭽ߥWe

▸࿐ߩਅ㒢⇇ߦ㑐ߒߡ㧘ઁߩ⎇ⓥ⠪ߩⷙ▸ߩ㑣୯߽

␜ߒߡ޿ࠆ㧚ߎࠇࠄߩⷙ▸ߪ㧘“vertical orifice”߿

“horizontal orifice”ߩࠃ߁ߥ◲නߥᵹࠇ႐ߦ㑐ߔࠆ

߽ߩߢ޽ࠆ߇㧘ߘࠇࠄߪWe > 12ߣ޿߁ⷙ▸ߣߐ߶

ߤ⇣ߥࠄߥ޿㧚Boߦ㑐ߒߡߪ㧘ઁߩ⎇ⓥ⠪ߩⷙ▸ߩ

޿ߊߟ߆߇㧘⺰ᢥਛߦ᣿⸥ߐࠇߡ޿ߥ޿ὑ㧘⸥ㅀߐ ࠇߡ޿ߥ޿㧚Anwar et al. (1978) ߢߪBo > 1100ߢ޽

Fig. 6. Critical submergence Sc/D versus Reynolds number Re, for several value of suction-sump breadth B: ٟ, B/D

= 1.43, X/D = 2.11, Z/D = 0.71, Fr = 1.9 and We = 15–27 (Bo = 62–198); Ŷ, B/D = 2.11, X/D = 2.11, Z/D = 0.71, Fr = 1.9 and We = 8.7–27 (Bo = 20–198); ً, B/D = 3.57, X/D = 2.11, Z/D = 0.71, Fr = 1.9 and We = 8.7–24 (Bo = 20–155); ٨, B/D = 4.21, X/D = 2.11, Z/D = 0.71, Fr = 1.9 and We = 8.7–24 (Bo = 20–155).

Sc/D

Re 0

0.5 1 1.5

2 2.5

0 1 2 3 4 5

˜10⁴

Anwar (1978), Re> 3.0˜10⁴

Dagget & Keulegan (1976), Re> 3.2˜10⁴

We> 12

(Odgaard (1986), Re > 1.4˜10⁵)

10

2 12

0

Re/Fr² ˜10³

4 6 8

Bo> 95

ࠅ㧘Bo > 95ߥࠆᧄ⹏ଔၮḰߣߪ߆ߥࠅ⇣ߥࠆ߇㧘 Jain et al. (1978) ߦࠃࠆBo > 55 ߥࠆⷙ▸ߪᧄⷙ▸

ߦలಽㄭ޿㧚

Fig. 6㨪Fig. 8ߪ㧘Re߹ߚߪRe/Fr²ߦኻߔࠆSc/Dߦ␜

ߔ㧚᣿⏕ߦㅀߴࠆߣ㧘Fig. 6߅ࠃ߮Fig. 7㧘Fig. 8ߪ㧘 ߘࠇߙࠇ㧘୯ߩ⇣ߥࠆ྾ߟߩB/D㧘߅ࠃ߮㧘ੑߟߩ X/D㧘ਃߟߩZ/Dߦ㑐ߔࠆ߽ߩߢ޽ࠆ㧚߽ߜࠈࠎ㧘ฦޘ ߩ႐วߢ㧘WeߣBoࠍ㒰߈㧘Fr ߣߔߴߡߩᒻ⁁ࡄ࡜

ࡔ࡯࠲ࠍ৻ቯߩ୯ߦ࿕ቯߒߡ޿ࠆ㧚ࠃߞߡ㧘ฦ࿑ߢ

ߪ㧘WeߣBoߪ㧘৻ቯߦ଻ߚࠇߡ߅ࠄߕ㧘Re޽ࠆ޿

ߪRe/Fr²ߩ୯ߦᔕߓߡ㧘ߘࠇࠄߩ୯ࠍᄌ߃ࠆ㧚ߒ߆ ߒߥ߇ࠄ㧘⚿ᨐߩᄢㇱಽ߇We > 12ߢ޽ࠅ㧘⚿ᨐߩ ᄢඨ߇Bo > 95ߢ޽ࠆ㧚ߥ߅㧘࿑ਛߩ⎕✢߇㧘ߎࠇ ࠄߩ㑣୯ࠍ␜ߔ㧚ᓥߞߡ㧘એਅߩ⼏⺰ߢߪ㧘Weല ᨐ߹ߚߪBoലᨐࠍήⷞߔࠆ㧚ߥߗߥࠄ߫㧘એਅߩ⼏

⺰ߢߪ㧘We > 12 ߹ߚߪ Bo > 95ߩ⚿ᨐߛߌࠍ⠨ኤ ኻ⽎ߦߒߡ㧘ߘࠇߙࠇ㧘Reലᨐ߹ߚߪRe/Fr²ലᨐߩ ߺࠍኾࠄ⠨߃ࠆὑߢ޽ࠆ㧚

Fig. 7. Critical submergence Sc/D versus Reynolds number Re, for several value of back clearance X: ٨, B/D = 3.57, X/D = 2.11, Z/D = 0.71, Fr = 1.9 and We = 8.7–27 (Bo = 20–198); ً, B/D = 3.57, X/D = 2.52, Z/D = 0.71, Fr = 1.9 and We = 8.7–27 (Bo = 20–198).

Fig. 8. Critical submergence Sc/D versus Reynolds number Re, for several value of bottom clearance Z: ٟ, B/D = 3.57, X/D = 2.11, Z/D = 0.26, Fr = 1.9 and We = 8.7–21 (Bo = 20–124); Ŷ, B/D = 3.57, X/D = 2.11, Z/D = 0.71, Fr

= 1.9 and We = 8.7–21 (Bo = 20–124); ً, B/D = 3.57, X/D = 2.11, Z/D = 1.43, Fr = 1.9 and We = 8.7–24 (Bo = 20–155).

Sc/D

Re 0

0.5 1 1.5 2

0 1 2 3 4 5

˜10⁴

We> 12

0

Re/Fr²

2 10 12

˜10³

4 6 8

0

Re/Fr²

2 10 12

˜10³

4 6 8

Bo> 95

Sc/D

Re 0

0.5 1 1.5 2 2.5 3

0 1 2 3 4 5

˜10⁴

We> 12

Bo>95

2 10 12

0

Re/Fr² ˜10³

4 6 8

Fr

8

30 20 6

’

Re/Fr² 10 12

˜10³

0 0.5 1 1.5 2 2.5 3 3.5 4

0 0.5 1 1.5 2 2.5 3

Sc/D

߹ߕ㧘Fig. 6ࠍ⷗ࠆ㧚Re߇㔖߆ࠄ⚂3˜10⁴߹ߢჇ ടߔࠆᤨ㧘Sc/Dߪන⺞Ⴧടߒ㧘Re > 3˜10⁴ߩ▸࿐ߢ ߪ㧘Sc/Dߪ৻ቯ୯ࠍ଻ߟ㧚߹ߚ㧘Re/Fr²߇࠯ࡠ߆ࠄ

⚂8˜10³߹ߢჇടߔࠆᤨ㧘Sc/D߇න⺞Ⴧടߒ㧘Re/Fr²

> 8˜10³ߩ▸࿐ߢߪ㧘Sc/Dߪ৻ቯ୯ࠍ଻ߟ㧚ࠃߞߡ㧘 Sc/D߳ߩReലᨐ߇㧘Re > 3˜10⁴ߩ▸࿐ߢήⷞߢ߈ࠆ ߎߣ߇ࠊ߆ࠆ㧚߹ߚߪ㧘Sc/D߳ߩRe/Fr^㧞ലᨐ߇㧘 Re/Fr² > 8˜10³ߩ▸࿐ߢήⷞߢ߈ࠆߎߣ߇ಽ߆ࠆ㧚

Reߦ㑐ߔࠆⷙ▸ߪ㧘ታ㛎▸࿐߇Re > 1.4˜10⁵ߦኻ ߔࠆOdgaard (1986)ߦࠃࠆRe > 1.4˜10⁵ߥࠆⷙ▸ࠍ 㒰ߊߣ㧘Anwar et al (1978)ߦࠃࠆRe > 3.0˜10⁴ߥࠆ ⷙ▸߿Dagget & Keulegan (1974) ߦࠃࠆRe > 3.2˜ 10⁴ߥࠆⷙ▸ߦ㧘ࠃߊ৻⥌ߔࠆ㧚Fig. 7ߣFig. 8ߣߪ㧘

Fig. 6ߣ⇣ߥࠆᒻ⁁ࡄ࡜ࡔ࡯࠲ߦᵈ⋡ߒߚ⚿ᨐߢ޽

ࠆ㧚Fig. 7ߣFig. 8ߣߢߪ㧘Fig. 6ߣห᭽ߥ௑ะ߅ࠃ߮

หߓⷙ▸ࠍ⏕⹺ߢ߈ࠆ㧚ᓥߞߡ㧘ᑼ(8)ߣᑼ(9)ߣߪ㧘 Re > 3×10⁴ ޽ࠆ޿ߪRe/Fr² > 8×10³ߩ᧦ઙਅߢ㧘ᰴᑼ ߣ⷗ߥߖࠆ㧚

Sc/D = ) (Fr㧘 B/D㧘 X/D㧘 Z/D)㧚 (10) ෩ኒߦㅀߴࠆߣ㧘WeߣBoߦ㑐ߔࠆⷙ▸ߣห᭽ߦ㧘 Re > 3×10⁴ߣRe/Fr² > 8˜10³ߩࠃ߁ߥ2ߟߩⷙ▸ߪㆊ

೾ߢ޽ࠆ㧚ߥߗߥࠄ߫㧘Fig. 6㨪Fig. 8ߩߔߴߡߩታ 㛎ߪFr = 1.9ߢ޽ࠅ㧘10⁰ߩࠝ࡯࠳࡯ߢ޽ࠆ㧚߽ߒ㧘

Fr « 1ߢㅊടታ㛎ࠍⴕ߃߫㧘Reߦ㑐ߒߡ㧘ࠃࠅᱜ⏕

ߥⷙ▸ࠍ⷗಴ߒᓧࠆߛࠈ߁㧚߽ߒ㧘Fr » 1㧘ߢㅊട ታ㛎ࠍⴕ߃߫㧘Re/Fr²ߦ㑐ߒߡ㧘ࠃࠅᱜ⏕ߥⷙ▸ࠍ

⷗಴ߒᓧࠆߛࠈ߁㧚

ห᭽ߦ㧘෩ኒߦㅀߴࠆߣ㧘ߚߣ߃ᑼ(10)ߦ߅ߌࠆ Re߿Re/Fr²ߩⷙ▸ߩᱜ⏕ߥ㑣୯߇ಽ߆ߞߚߣߒߡ

߽㧘ߘࠇࠄߩ㑣୯ߪℂ⺰⊛ߦઁߩᡰ㈩ࡄ࡜ࡔ࡯࠲ߦ ଐሽߔࠆߎߣߦᵈᗧߔߴ߈ߢ޽ࠆ㧚੐ታ㧘Fig. 8ߢ ߪZ/DߩჇടߦᓥ޿㧘ReߣRe/Fr²ߣߩਔ㑣୯߇ࠊߕ ߆ߦჇടߔࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚ߚߛߒ㧘Fig. 6ߣ Fig. 7ߣߦ߅ߌࠆ㑣୯߇ߘࠇߙࠇB/DߣX/Dߣߩ᣿⏕

ߥᓇ㗀ࠍฃߌߡ޿ࠆߣߪ㧘⹺߼㔍޿㧚ߘߒߡ㧘ᑼ(8) ߣᑼ(9)ߣߦߟ޿ߡߩએ೨ߩ⼏⺰ߣห᭽㧘Fr߇ਔ㑣୯ ߦ෸߷ߔᓇ㗀ߪ㧘B/D߿X/D㧘Z/D߇ਔ㑣୯ߦ෸߷ߔ ᓇ㗀ߣ౒ߦ㧘ᧄ⺰ߩ⠨ኤ▸࿐ᄖߢ޽ࠆ㧚৻⥸ߦ㧘Fr ߩჇടߦ઻޿㧘Reߩ㑣୯ߪჇടߔࠆߣ⠨߃ࠄࠇࠆ㧚 ߥߗߥࠄ߫㧘FrߩჇടߪ㧘৻ቯߩReߢߩ☼ᕈജߦኻ ߔࠆ㊀ജߩ⋧ኻ⊛ᷫዋࠍᒁ߈⿠ߎߔ߆ࠄߢ޽ࠆ㧚ኻ ᾖ⊛ߦ㧘FrߩჇടߦ઻޿㧘Re/Fr²ߩ㑣୯ߪᷫዋߔࠆ ߣ⠨߃ࠄࠇࠆ㧚ߥߗߥࠄ߫㧘FrߩჇടߪ㧘৻ቯߩ Re/Fr²ߢߩ☼ᕈജߦኻߔࠆᘠᕈജߩ⋧ኻ⊛Ⴧᄢࠍᒁ ߈⿠ߎߔ߆ࠄߢ޽ࠆ㧚

Fig. 9. Critical submergence Sc/D versus Froude number Fr, for several value of suction-sump breadth B: ٟ, B/D = 2.11, X/D = 2.11, Z/D = 0.71, Re = 3.8˜10⁴ and We = 20–26 (Bo = 105–309); Ŷ, B/D = 3.57, X/D = 2.11, Z/D = 0.71, Re = 3.8˜10⁴ and We = 20–26 (Bo = 105–309); ً, B/D = 4.21, X/D = 2.11, Z/D = 0.71, Re = 3.8˜10⁴ and We = 20–26 (Bo = 105–309). ̆ ̆ ̆ and ̆·̆·̆, Reddy & Pickford (1972); ̆··̆··̆, the 1998 HI Standard; ̖, Werth & Frizell (2009).

ࠃߞߡ㧘એ㒠ߦ␜ߔోߡߩ⚿ᨐߪRe > 3˜10⁴ߩ߽ߩ ߢ޽ࠆ㧚ߟ߹ࠅ㧘Reലᨐߩ⼏⺰ࠍㆱߌࠆὑ㧘3˜10⁴ ࠃࠅలಽᄢ߈ߥReࠍ⠨߃ࠆ㧚ห᭽ߦ㧘એ㒠ߦ␜ߔో

ߡߩ⚿ᨐߪRe/Fr²ലᨐߩ⼏⺰ࠍㆱߌࠆὑ㧘Fig. 9ࠍ㒰 ߈㧘Re/Fr² » 8×10³ߩ߽ߩߢ޽ࠆ㧚

⵬⿷ߔࠆߣ㧘Fig. 6߅ࠃ߮Fig. 7㧘Fig. 8ߢߪ㧘ߘࠇ ߙࠇ㧘B/D߅ࠃ߮X/D㧘Z/DߩSc/D߳ߩലᨐࠍ⏕⹺ߢ ߈ࠆ㧚ᰴߩ▵ߢߪ㧘ߘߩࠃ߁ߥᒻ⁁ലᨐࠍ⹦⚦ߦ⼏

⺰ߔࠆ㧚Fig. 6㨪Fig. 8ਛߩRe > 3×10⁴ ޽ࠆ޿ߪ Re/Fr² > 8×10³ߢ㧘Sc/D߇ขࠅᓧࠆ୯ߩ▸࿐ࠍᲧセߔ ࠆߣ㧘B/DലᨐߣZ/Dലᨐߪ㧘X/Dലᨐࠃࠅ৻⷗ߒߡ ᒝߘ߁ߢ޽ࠆ㧚ߘߒߡ㧘ਃߟߩലᨐߣ߽㧘৻⷗ߒߡ ⶄ㔀ߢߪߥߐߘ߁ߢ޽ࠆ㧚ߥߗߥࠄ߫㧘B/DߩჇട ߦߟࠇߡ߽(Fig. 6ࠍෳᾖ)㧘޽ࠆ޿ߪ㧘X/Dߩᷫዋߦ ߟࠇߡ߽(Fig. 7ࠍෳᾖ)㧘Z/Dߩᷫዋߦߟࠇߡ߽(Fig.

8ࠍෳᾖ)㧘Sc/Dߪන⺞Ⴧടߔࠆ㧚ߒ߆ߒߥ߇ࠄ㧘એ

਄ߩ⚿⺰ߪ㧘B/D߿X/D㧘Z/Dߥߤߩࡄ࡜ࡔ࡯࠲ߩ⹜

㛎▸࿐ߦଐሽߔࠆ(ห᭽ߦᰴߩ▵ࠍෳᾖ)㧚

Re < 3×10⁴ ޽ࠆ޿ߪRe/Fr² < 8×10³ߢߩ⚿ᨐࠍ⠨

ᘦߔࠆߣ߈ߪ㧘☼ᕈലᨐߩὑߦ㧘ઁߦ೎ߩᵈᗧ߇ᔅ ⷐߦߥࠆ㧚ߔߥࠊߜ㧘Re߿Re/Fr²ߩ୯ߦଐሽߔࠆ᭽

ߥ⚿ᨐߪ㧘৻⥸ᕈ߇ਲߒ޿㧚଀߃߫㧘Fig. 6ߦ߅޿

ߡ㧘3×10⁴એਅߩ޽ࠆ৻ቯߩReߢ㧘߹ߚߪ㧘8×10³ એਅߩ޽ࠆ৻ቯߩRe/Fr²ߢ㧘Sc/DߪB/D = 2.11ߢᭂዊ ୯ࠍ␜ߔ㧚ኻᾖ⊛ߦ㧘㧔ᓟߦ␜ߐࠇࠆ߇㧕☼ᕈലᨐ ࠍήⷞߢ߈ࠆߊࠄ޿ᄢ߈޿Re/Fr²޽ࠆ޿ߪReߦ߅

޿ߡߪ㧘޽ࠆB/Dߩ୯ߢSc/Dߪᭂᄢ୯ࠍ␜ߔ㧚

਄ߩᲑ⪭ࠍ⵬⿷ߔࠆߣ㧘ᭂዊߐ޿୯ߩRe߹ߚߪ Re/Fr²ߢߪ㧘ߘࠇࠄߩ୯߇ᷫዋߔࠆߦߟࠇߡ㧘S_c/D ߪ㧘න⺞ᷫዋ௑ะࠍ␜ߔߩߢߪߥߊ㧘߻ߒࠈ㧘⚂0.5 ߩ৻ቯ୯ࠍ଻ߟ௑ะࠍ␜ߔ㧔Fig. 6ߣFig. 8ߣࠍෳᾖ㧕㧚 ߎߩSc/D߇৻ቯ୯ࠍߣࠆ௑ะߪ㧘࠲ࠗࡊ(d)ߩⓨ᳇ๆ ㄟߩ⊒↢ߦ㑐ଥߠߌࠄࠇࠆߎߣࠍ⏕⹺ߒߚ㧚

Fig. 9ߪ㧘⇣ߥࠆB/Dߩਃߟߩࠤ࡯ࠬߦ߅ߌࠆ㧘Fr

ߣS_c/Dߣߩ㑐ଥࠍ␜ߔ㧚߽ߜࠈࠎ㧘ฦࠤ࡯ࠬᲤߦ㧘

Re/Fr²߅ࠃ߮We㧘Boࠍ㒰߈㧘ઁߩᡰ㈩ࡄ࡜ࡔ࡯࠲㧔Re

߿B/D㧘X/D㧘Z/D㧕ߪ৻ቯ୯ߦ଻ߟ㧚ోߡߩ⚿ᨐߪ㧘 We > 12߆ߟBo > 95ߢ޽ࠆߩߢ㧘WeലᨐߣBoലᨐߪ

౒ߦήⷞߢ߈ࠆ㧚ߒ߆ߒߥ߇ࠄ㧘޿ߊߟ߆ߩ⚿ᨐߪ Re/Fr² < 8×10³ߢ޽ࠅ㧘Re/Fr²ലᨐߪᏱߦήⷞ಴᧪ࠆ

⸶ߢߪߥ޿㧚ᓥߞߡ㧘Re/Fr² 㧨 8×10³ߦኻᔕߔࠆFr

> 2ߢߪ㧘⚐☴ߥFrലᨐ߇⃻ࠇߡ߅ࠄߕ㧘☼ᕈലᨐ

ߦᓇ㗀ࠍฃߌߚFrലᨐ߇⃻ࠇߡ޿ࠆน⢻ᕈ߇޽ࠆ㧚 ታ㓙㧘Fig. 9ߢߪ㧘Fr > 2ߢ㧘FrߩჇടߦ઻߁Sc/Dߩ Ⴧട₸߇ᷫዋߒߡ޿ࠆ߇㧘ߎߩ௑ะߪ㧘Re/Fr²ലᨐ ߦ㑐ଥߠߌࠄࠇࠆ߆߽ߒࠇߥ޿㧚

৻⥸ߦ㧘Frߪ㧘⥄↱⴫㕙ࠍ᦭ߔࠆ᭽ޘߥᵹ૕ㆇേ

⃻⽎ߦ߅޿ߡ㧘ᦨ߽㊀ⷐߥജቇࡄ࡜ࡔ࡯࠲ߩ1ߟߢ

޽ࠆ㧔Iversen (1953) ߣFarell & Cuomo (1984)ࠍෳ

ᾖ㧕㧚Fr < 2ߢߪ㧘Fr߇Sc/Dߦ෸߷ߔ⚐☴ߥലᨐࠍ⏕

⹺ߢ߈ࠆ㧚ߟ߹ࠅ㧘Fr߇Ⴧടߔࠆߦߟࠇߡ㧘S_c/Dߪ න⺞Ⴧടߔࠆ㧚ߒ߆ߒߥ߇ࠄ㧘Fr > 2ߢߪ㧘⚐☴ߥ Frലᨐ߇᷹ⷰߢ߈ߡ޿ࠆߣߪ㒢ࠄߕ㧘Frലᨐߣ Re/Fr²ലᨐߩⶄวലᨐࠍ᷹ⷰߒߡ޿ࠆ߆߽ߒࠇߥ޿㧚 ߘߒߡ㧘ߎߩⶄวലᨐߪ㧘ᄙߊߩታ㓙ߩࡕ࠺࡞⹜㛎 ߢ㧘ኈᤃߦ⿠ߎࠅᓧࠆ㧚

ߥ߅㧘Fig. 9ߦߪ㧘ઁߩ⎇ⓥ⠪ߦࠃࠆ㧘FrߣS_c/D ߣߩ㑐 ଥᑼ߽␜ߒ ߡ޿ࠆ㧚ߘ ߩౝߢ㧘Reddy &

Pickford (1972) ߦࠃࠆSc/D = Frߥࠆ⚻㛎ᑼߪ㧘ᧄታ 㛎ߣߩࠃ޿ㄭૃࠍ␜ߔ㧚ઁߩਃߟߩ⚻㛎ᑼ㧘․ߦ HI Standard (1998) ߣ㧘Werth & Frizell (2009) ߪ㧘ㆊ

೾ߥSc/Dࠍ␜ߔ㧚ߥ߅㧘Werth & Frizellߩ⚻㛎ᑼߦ߽㧘 ᧄ⎇ⓥߣห᭽ߦ㧘FrߩჇടߦ઻߁S_c/DჇട₸ߩᷫዋ

௑ะ߇⷗ࠄࠇࠆ߇㧘ᓐࠄߩᷫዋ௑ะߪ㧘Re/Fr²ലᨐ ߢߪߥߊ㧘↪޿ߚGulliver & Rindels (1987) ߦࠃࠆታ 㛎⚿ᨐߩ߫ࠄߟ߈ࠍ෻ᤋߒߡ޿ࠆߣᕁࠊࠇࠆ㧚

ߣߎࠈߢ㧘Fig. 9ߢߪ㧘B/D߇Sc/D߳෸߷ߔലᨐࠍ

⏕⹺ߔࠆߎߣ߇ߢ߈ࠆ㧚ᰴߩ▵ߢߪ㧘ߘߩࠃ߁ߥᒻ

⁁ലᨐߦߟ޿ߡ⹦ߒߊ⼏⺰ߔࠆ㧚৻⷗ߒߡ㧘B/Dല ᨐߪⶄ㔀ߢߪߥߐߘ߁ߢ޽ࠆ㧚ታ㓙㧘Fig. 9ߢߪ㧘 Re/Fr² >8˜10³ߦᵈ⋡ߔࠆߣ㧘B/DߩჇടߦߟࠇߡ Sc/D߇න⺞Ⴧടߔࠆ㧚ߒ߆ߒߥ߇ࠄ㧘ߎߩන⺞ߐߪ㧘

࠹ࠬ࠻ߐࠇߚ▸࿐ߩB/Dߦଐሽߔࠆߎߣࠍᓟߦ␜ߔ㧚 㧔ᰴߩ▵ࠍෳᾖ㧕㧚

ᒻ⁁ࡄ࡜ࡔ࡯࠲ߩᓇ㗀

ᰴߦ㧘ਃߟߩᒻ⁁ࡄ࡜ࡔ࡯࠲B/D߅ࠃ߮X/D㧘Z/D ߩSc/D߳ߩലᨐࠍ⠨߃ࠆ㧚

Fig. 10ߪ㧘B/DߣSc/Dߣߩ㑐ଥࠍ␜ߔ㧚ߎߎߢߪ㧘

⇣ߥࠆX/Dߩੑߟߩࠤ࡯ࠬࠍ⺞ߴ㧘ߘࠇࠄࠍ࿑ਛߩ

ਛታ⪉ᒻߣਛታᱜᣇᒻߣߢ␜ߔ㧚߽ߜࠈࠎ㧘ߘࠇߙ ࠇߩࠤ࡯ࠬߢ㧘B/Dએᄖߩోߡߩᡰ㈩ࡄ࡜ࡔ࡯࠲ߪ

৻ቯߦ଻ߟ㧚ਔࠤ࡯ࠬߢ㧘྾ߟߩⷙ▸㧘ߔߥࠊߜ㧘 We > 12ߣBo > 95㧘Re > 3×10⁴㧘Re/Fr² > 8×10³ࠍోߡ ḩ⿷ߒߡ޿ࠆߎߣߦᵈᗧߔߴ߈ߢ޽ࠆ㧚ࠃߞߡ㧘ᧄ

⚿ᨐߪ㧘৻⥸ᕈ߇଻㓚ߐࠇߡ޿ࠆ㧚ߔߥࠊߜ㧘We >

12߆ߟBo > 95㧘Re > 3×10⁴㧘Re/Fr² > 8×10³ߢߩ㧘ᓧ ࠄࠇࠆ⚿ᨐߪోߡหߓߦߥࠆߣ⠨߃ࠄࠇࠆ㧚ߜߥߺ ߦ㧘࿑10ਛߩਛⓨ⪉ᒻߣਛⓨᱜᣇᒻߪ㧘ߘࠇߙࠇ㧘 Kitamura & Kida㧔1971㧕ߣTagomori㧔1976㧕ߥߤઁ

ߩ⎇ⓥ⠪ߩታ㛎⚿ᨐࠍ␜ߔ㧚

Fig. 10. Critical submergence Sc/D versus suction-sump breadth B, for several value of back clearance X: ٟ, X/D

= 0.79, Z/D = 0.71, Fr = 1.6, Re = 3.8˜10⁴ and We = 22.4 (Re/Fr² = 1.5˜10⁴, Bo = 197); Ŷ, X/D = 1.32, Z/D = 0.71, Fr = 1.6, Re = 3.8˜10⁴ and We = 22.4 (Re/Fr² = 1.5˜10⁴, Bo = 197); ٠, Kitamura & Kida (1971), X/D = 0.95, Z/D = 0.48, Fr = 0.68–0.75 and Re = 1.3˜10⁵; Ƒ, Tagomori (1976), X/D = 0.92, Z/D = 0.58, Fr = 0.68 and Re = 1.0˜10⁵ .

Fig. 11. Critical submergence Sc/D versus back clearance X, for several value of sump breath B: ٟ, B/D = 3.16, Z/D = 0.71, Fr = 1.6, Re = 3.8˜10⁴ and We = 22.4 (Re/Fr² = 1.5˜10⁴, Bo=197); Ŷ, B/D = 4.21, Z/D = 0.71, Fr = 1.6, Re = 3.8˜10⁴ and We = 22.4 (Re/Fr² = 1.5˜10⁴, Bo = 197); ٠, Isohata et al. (1975), B/D = 2.5, Z/D = 0.60, Fr = 0.68 and Re = unknown; غ, Tagomori (1976), B/D = 2.3, Z/D = 0.58, Fr = 0.68 and Re = 1.0˜10⁵.

Sc/D

B/D 0

0.5 1 1.5

2 2.5

0 1 2 3 4 5 6 7

S

/ D

X/D 0

0.5 1 1.5

2 2.5

0 0.5 1 1.5 2 2.5 3 3.5

ᧄታ㛎ߩਔࠤ࡯ࠬߣ߽㧘B/D߇㔖߆ࠄჇ߃ࠆߦߟ ࠇߡ㧘Sc/DߪჇടߔࠆ㧚ߘߩᓟ㧘޽ࠆB/Dߢ㧘Sc/D ߪᦨᄢ୯ߦ㆐ߔࠆ㧚ߐࠄߦ㧘B/D߇Ⴧߔߣ㧘ㅒߦ㧘 B/DߩჇടߦߟࠇߡSc/Dߪᷫዋߔࠆ㧚ߎߩ᭽ߥB/Dല ᨐߪ㧘ⶄ㔀ߢ޽ࠆ㧚଀߃߫㧘Tagomoriߦࠃࠆߣ㧘B/D ߩჇട ߦߟࠇߡ㧘Sc/Dߪන⺞ ᷫዋߔࠆ㧚 ৻ᣇ㧘 Kitamura & Kidaߦࠃࠆߣ㧘ㅒߦ㧘B/DߩჇടߦߟࠇ ߡSc/Dߪන⺞Ⴧടߔࠆ㧚੹࿁ߩ⚿ᨐߣᓐࠄߩ⚿ᨐߣ ߩਇ৻⥌ߪ㧘ᡰ㈩ࡄ࡜ࡔ࡯࠲ߩਇ৻⥌ߦട߃㧘ᓐࠄ ߩB/D▸࿐߇㒢ࠄࠇߚ⁜ߐߢ޽ࠆߎߣߦࠃࠅ↢ߓߚ ߣ⠨߃ࠄࠇࠆ㧚

B/DߩჇടߦ઻߁Sc/DߩჇട௑ะࠍ㧘⋥ធ⺑᣿ߔ ࠆߎߣߪ㔍ߒߘ߁ߢ޽ࠆ㧚ߎߩ௑ะߪ㧘ๆㄟ▤ਅᵹ ㄭறߢߩ᷵ᒻᚑ߳ߩๆㄟ᳓ᮏ஥ოߩᐓᷤ߇㑐ଥߒ ߡ޿ࠆߎߣ߽⠨߃ࠄࠇ (Funaki et al. (2008) ࠍෳ

ᾖ㧕㧘੹ᓟߩࠃࠅ⹦⚦ߥ⎇ⓥ߇ᔅⷐߢ޽ࠈ߁㧚৻ᣇ㧘 B/DߩᦝߥࠆჇടߦ઻߁㧘S_c/Dߩᷫዋ௑ะߦߟ޿ߡ

ߪ㧘߽ߒFig. 9ߢ⷗ࠄࠇࠆSc/Dߦኻߔࠆ㧔ో૕⊛㧕

Frലᨐࠍᗐቯߔࠆߥࠄ߫㧘ߘߩℂ⸃ߪኈᤃߘ߁ߢ޽

ࠆ㧚ߔߥࠊߜ㧘B/DߩჇടߦ઻޿㧘ๆㄟ▤౉ญㄭߊ ߩዪᚲᵹㅦ߇ᷫዋߔࠆߎߣߪ޽ࠅ߇ߜߢ޽ࠈ߁㧚ዪ ᚲᵹㅦߩᷫዋߪኻᔕߔࠆዪᚲࡈ࡞࡯࠼ᢙߩᷫዋࠍ ᒁ߈⿠ߎߔ㧚߽ߒㆡᒰߥ૏⟎ߢߩዪᚲࡈ࡞࡯࠼ᢙ߇ Sc/Dߦ෸߷ߔലᨐ߽㧔ో૕㧕ࡈ࡞࡯࠼ᢙ߇Sc/Dߦ෸

߷ߔലᨐߣห௑ะߢ޽ࠆߣ઒ቯߔࠆߥࠄ㧘B/DჇട ߦ઻߁Sc/Dߩᷫዋ௑ะߪኈ⹺ߐࠇࠃ߁㧚ߥߗߥࠄ㧘

ⓨ᳇ๆㄟߦߪ㧘ో૕⊛ࡈ࡞࡯࠼ᢙࠃࠅ߽ๆㄟ▤౉ญ ㄭߊߩዪᚲ⊛ࡈ࡞࡯࠼ᢙߩ߶߁߇㧘ࠃࠅ᳿ቯ⊛߆ߟ ലᨐ⊛ߢ޽ࠆߣ⠨߃ࠄࠇࠆ߆ࠄߢ޽ࠆ㧚

Fig. 11ߪ㧘X/DߣSc/Dߣߩ㑐ଥࠍ␜ߔ㧚ߎߎߢߪ㧘

⇣ߥࠆB/Dߩੑߟߩࠤ࡯ࠬࠍ⺞ߴ㧘ߘࠇࠄࠍ࿑ਛߩ ਛታ⪉ᒻߣਛታᱜᣇᒻߣߢ␜ߔ㧚߽ߜࠈࠎ㧘ߘࠇߙ ࠇߩࠤ࡯ࠬߢ㧘X/Dએᄖߩోߡߩᡰ㈩ࡄ࡜ࡔ࡯࠲ߪ

৻ቯߦ଻ߟ㧚ࠃࠅᐢ޿ㆡ↪น⢻ᕈࠍ଻㓚ߔࠆߚ߼㧘 ਔࠤ࡯ࠬߢ㧘྾ߟߩⷙ▸㧘ߔߥࠊߜWe > 12ߣBo > 95㧘 Re > 3×10⁴㧘Re/Fr² > 8×10³ࠍోߡḩ⿷ߒߡ޿ࠆߎߣ ߦᵈᗧߔߴ߈ߢ޽ࠆ㧚ߜߥߺߦ㧘Fig. 11ਛߩਛⓨ⪉

ᒻߣਛⓨᱜᣇᒻߣߪ㧘ߘࠇߙࠇ㧘Isohata et al. (1975)

ߣTagomori (1976) ߥߤઁߩ⎇ⓥ⠪ߩታ㛎⚿ᨐࠍ␜

ߔ㧚

ߘࠇߙࠇߩࠤ࡯ࠬߢ㧘X/D߇㔖߆ࠄჇߔߦߟࠇߡ㧘 Sc/DߪჇടߔࠆ㧚 ߘߒߡ㧘޽ࠆX/Dߢ㧘Sc/Dߪᦨᄢ ୯ߦ㆐ߔࠆ㧚X/D߇ߐࠄߦჇടߔࠆߣ߈㧘 X/DߩჇ ടߦߟࠇߡSc/Dߪ৻ቯ୯ߦㄭߠ߈ߥ߇ࠄᷫዋߔࠆ㧚 ߎߩ᭽ߥX/Dലᨐߪ㧘Tagomori (1976) ߣቯᕈ⊛ߦห

᭽ߢ޽ࠅ㧘Isohata et al. (1975) ࠃࠅ߽ⶄ㔀ߢ޽ࠆ㧚 ߟ߹ࠅ㧘Isohata et al.ߢߪ㧘X/DߩჇടߦߟࠇߡSc/D ߇න⺞Ⴧടߔࠆ㧚੹࿁ߩ⚿ᨐߣᓐࠄߩ⚿ᨐߣߩਇ৻

⥌ߪ㧘ᡰ㈩ࡄ࡜ࡔ࡯࠲ߩਇ৻⥌ߦട߃㧘ᓐࠄߩX/D

▸࿐߇㒢ࠄࠇߚ⁜ߐߢ޽ࠆߎߣߦࠃࠅ↢ߓߚߣ⠨

߃ࠄࠇࠆ㧚

Fig. 12. Critical submergence Sc/D versus bottom clearance Z: ٠, B/D = 3.16, X/D = 2.11, Fr = 1.6, Re = 3.8×10⁴ and We = 22.4 (Re/Fr² = 1.5˜10⁴, Bo = 197); غ, B/D = 3.16, X/D = 2.52, Fr = 1.6, Re = 3.8˜10⁴ and We = 22.4 (Re/Fr² = 1.5˜10⁴, Bo = 197); ---, Kondo & Maru (1972), B/D = 2.50, X/D = 1.40, Fr = 1.3 and Re = 2.4˜10⁵.

Sc/D

Z/D 0

0.5 1 1.5

2 2.5

3

0 0.5 1 1.5 2 2.5 3 3.5

B/D߇㔖߆ࠄ޽ࠆ୯߹ߢჇടߔࠆߦߟࠇߡ㧘Sc/D ߇Ⴧടߔࠆ௑ะ㧔Fig. 10ࠍ㧘ෳᾖ㧕ߣห᭽ߦ㧘਄ㅀ ߩⶄ㔀ߥX/Dലᨐࠍ⋥ធ⺑᣿ߔࠆߎߣߪ㔍ߒߘ߁ߢ

޽ࠆ㧚ߎߩⶄ㔀ߥലᨐࠍℂ⸃ߔࠆߚ߼ߦߪ㧘ๆㄟ▤

ਅᵹㄭறߢߩ᷵ᒻᚑ߳ߩๆㄟ᳓ᮏ⢛ოߣߩᐓᷤ㧘޽

ࠆ޿ߪ㧘᷵ᒻᚑߩ⢛ოߦࠃࠆჇ᏷ߦ㑐ߔࠆᦝߥࠆ⹦

⚦ߥ⺞ᩏ߇ᔅⷐߢ޽ࠈ߁㧚(Funaki et al. (2008) ࠍ㧘

ෳᾖ) 㧚

Fig. 12ߪ㧘Z/DߣSc/Dߣߩ㑐ଥࠍ␜ߔ㧚ߎߎߢߪ㧘

⇣ߥࠆX/Dߩੑߟࠤ࡯ࠬࠍ⺞ߴ㧘ߘࠇࠄࠍ࿑ਛߩਛ

ⓨ⪉ᒻߣਛⓨᱜᣇᒻߣߢ␜ߔ㧚߽ߜࠈࠎ㧘ߘࠇߙࠇ ߩࠤ࡯ࠬߢ㧘Z/Dએᄖߩోߡߩᡰ㈩ࡄ࡜ࡔ࡯࠲ߪ৻

ቯߦ଻ߟ㧚ࠃࠅᐢ޿ㆡ↪น⢻ᕈࠍ଻㓚ߔࠆߚ߼㧘ਔ ࠤ࡯ࠬߢ㧘྾ߟߩⷙ▸㧘ߔߥࠊߜWe > 12ߣBo > 95㧘 Re > 3×10⁴㧘Re/Fr² > 8×10³ࠍోߡḩ⿷ߒߡ޿ࠆߎߣ ߦᵈᗧߔߴ߈ߢ޽ࠆ㧚ߜߥߺߦ㧘Fig. 12ਛߩ⎕✢ߪ㧘

ઁߩ⎇ⓥ⠪㧘ߔߥࠊߜ㧘Kondo & Maru (1972)ߩታ㛎

⚿ᨐࠍ␜ߔ㧚

B/D߇޽ࠆ୯ࠍ⿥߃ߡߐࠄߦჇടߔࠆߦߟࠇߡ Sc/D߇ᷫዋߔࠆ௑ะߣห᭽㧔Fig. 10ࠍ㧘ෳᾖ㧕㧘Z/D ߩჇടߦߟࠇߡSc/D߇ᷫዋߔࠆ௑ะࠍℂ⸃ߔࠆߎ ߣߪ㧘߽ߒFig. 9ߢ⷗ࠄࠇࠆSc/Dߦኻߔࠆ㧔ో૕⊛㧕 Frലᨐࠍᗐቯߔࠆߥࠄ߫㧘ߘߩℂ⸃ߪኈᤃߘ߁ߢ޽

ࠆ㧚ߥߗߥࠄ߫㧘ๆㄟ▤౉ญߣๆㄟ᳓ᮏᐩოߣߩ㑆 㓗߇ᐢ߇ࠆ߶ߤ㧘ዪᚲᵹㅦߪૐਅߒ߇ߜߦߥࠆ߆ࠄ ߢ޽ࠆ㧚ዪᚲᵹㅦߩૐਅߪ㧘ኻᔕߔࠆዪᚲࡈ࡞࡯࠼

ᢙߩᷫዋࠍᒁ߈⿠ߎߔ㧚ࠃߞߡห᭽ߦ㧘߽ߒㆡᒰߥ

૏⟎ߢߩዪᚲࡈ࡞࡯࠼ᢙ߇Sc/Dߦ෸߷ߔലᨐ߽㧘 㧔ో૕㧕ࡈ࡞࡯࠼ᢙ߇S_c/Dߦ෸߷ߔലᨐߣห௑ะߢ

޽ࠆߣ઒ቯߔࠆߥࠄ㧘Z/DჇടߦ઻߁Sc/Dߩᷫዋ௑

ะߪኈ⹺ߐࠇࠃ߁㧚

ᦝߦㅀߴࠆߣ㧘Z/D > 2.5ߢ㧘Sc/Dߪ㧘ዊߐߥ୯ࠍ

␜ߔ௑ะ߇޽ࠆ㧚ߘߒߡ㧘ߘߩ୯ߪ㧘Z/Dߦࠃࠄߕ

߶߷৻ቯߢ޽ࠆ㧚ߎߩߎߣߪ㧘޽ࠆ⒟ᐲᄢ߈ߥZ/D ߢߪ㧘ๆㄟ᳓ᮏᐩოߩሽ࿷ߩᓇ㗀ࠍήⷞߢ߈ࠆߎߣ ࠍ␜ໂߒߡ޿ࠆ㧚

߅ࠊࠅߦ

vertical wet-pit pumpᒻ⁁ࠍᜬߟๆㄟ᳓ᮏ/ๆㄟ▤

♽ߢߩๆㄟ▤߳ߩⓨ᳇ๆㄟࠍ⠨߃ߚ㧚ⓨ᳇ๆㄟ⊒↢

ߦߟ޿ߡߩᦨ㊀ⷐ߆ߟᘠ଀⊛ᜰᮡߢ޽ࠆ⥃⇇ᴚ᳓

ᷓߐScߦ㑐ߒߡ㧘ᄙߊߩታ㛎ࠍታᣉߒߡ㧘ਥⷐߥജ ቇ߅ࠃ߮ᐞ૗ቇࡄ࡜ࡔ࡯࠲߇Sc߳෸߷ߔᓇ㗀ࠍ᣿

ࠄ߆ߦߒߚ㧚⚿ᨐߪએਅߩߣ߅ࠅߢ޽ࠆ㧚

(1) Sc/D߳ߩFr㧘Re㧘Weߩਃߟߩജቇࡄ࡜ࡔ࡯࠲

ലᨐࠍ⠨߃ࠆߣ߈㧘ReലᨐߪRe > 3˜10⁴ߢήⷞߢ߈㧘 WeലᨐߪWe > 12ߢήⷞߢ߈ࠆ㧚৻ᣇ㧘Re/Fr²ലᨐ ߪRe/Fr² > 8˜10³ߢήⷞߢ߈㧘BoലᨐߪBo > 95ߢή ⷞߢ߈ࠆ㧚೨⠪ߪ㧘Fr « 1ߢ㧘ㆡᒰߣ⠨߃ࠄࠇࠆ㧚 ᓟ⠪ߪ㧘Fr » 1ߢ㧘ㆡᒰߣ⠨߃ࠄࠇࠆ㧚ታ↪⊛ߥⷰ

ὐ߆ࠄߔࠆߣ㧘Fr ߪᄙߊߩ႐ว1ࠃࠅ߽ߕߞߣᄢ߈ ߊߥࠆߎߣߪߥ޿ߩߢ㧘೨⠪ߩߺࠍ⠨߃ࠇ߫ࠃ޿ߢ

޽ࠈ߁㧚ࠃߞߡ㧘ㅢᏱ㧘Re > 3˜10⁴߆ߟWe > 12ߥ ࠆੑߟߩⷙ▸ߩਅߢ㧘ߚߛ৻ߟߩജቇࡄ࡜ࡔ࡯࠲Fr ߩߺࠍ⠨߃ࠇ߫ࠃ޿㧚

(2) ᐞ૗ቇࡄ࡜ࡔ࡯࠲X/D㧘B/D㧘Z/DߩSc/D߳ߩ ലᨐࠍ⠨߃ࠆߣ߈㧘X/DലᨐߣB/Dലᨐߦ㑐ߒߡߪ㧘

޽ࠆX/D߹ߚߪ޽ࠆB/Dߢ㧘Sc/Dߪᦨᄢ୯ࠍ␜ߔ㧚৻

ᣇ㧘Z/Dലᨐߪන⺞ߢ޽ࠆ߇㧘Z/D > 2.5ߩߣ߈Sc/D ߪZ/Dߦଐሽߒߥ޿৻ቯߩዊߐߥ୯ࠍߣࠆ㧚

ߎࠇࠄߩᒻ⁁ലᨐߩ޿ߊߟ߆ߩዪ㕙ߪ㧘Sc/Dߦኻ ߔࠆ㧔ో૕⊛㧕Frലᨐࠍᗐቯߔࠆߣ㧘ኈᤃߦ⺑᣿ߢ ߈ࠆ㧚৻ᣇ㧘ઁߩ޿ߊߟ߆ߩዪ㕙ߪ㧘⋥ធ⺑᣿ߔࠆ ߎߣ߇⃻Ბ㓏ߢߪ㔍ߒߘ߁ߢ޽ࠆ㧚ߎࠇࠄߩዪ㕙ࠍ ℂ⸃ߔࠆߚ߼ߦߪ㧘ๆㄟ᳓ᮏౝߩⶄ㔀ߥᵹࠇ᭴ㅧߦ ߟ޿ߡߩ⸃᣿ߣߘߩὑߩᦝߥࠆ⹦⚦ߥ⺞ᩏ߇ᔅⷐ ߢ޽ࠆ㧚

ᧄ⺰ᢥߩ✬㓸ߦߪ㧘หᔒ␠ᄢቇ㧘ጊญ㆐㇢᳁ߣട ᴦᄢિ᳁ߩេഥࠍฃߌߚ㧚ߎߎߦ⸥ߒߡ㧘ᗵ⻢ߩᗧ ࠍ⴫ߔ㧚

ෳ⠨ᢥ₂㩷

1) Iversen, H. W., “Studies of Submergence Requirement of High Specific Speed Pumps,” Trans. of ASME, Vol. 75, pp.

635-641 (1953).

2) Fraser, W. H. and Harrison, N. J., “Hydraulic Problems Encountered in Intake Structures of Vertical Wet-Pit Pumps and Methods Leading to Their Solution,” Trans. of ASME, Vol. 75, No. 4, pp. 643-652 (1953).

3) Denny, D. F., “An Experimental Study of Airentraining Vortices at Pump Sumps,” Proc. of IMechE, Vol. 170, No.

2, pp. 106-116 (1956).

4) Stevens, J. C. and Kolf, R. C., “Vortex Flow through

“horizontal Orifices,” Journal of the Sanitary Engineering Division, Proc. of ASCE, Vol. 83, No. SA6, pp. 1-22 (1957).

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Journals of the Hydraulics Division, Proc. of ASCE, Vol.

91, No. HY2, pp. 223-248 (1965).

6) Granger, R., “Steady Three-Dimensional Vortex Flow,”

Journal of Fruid Mechanics, Vol. 25, No. 3, pp. 557-576 (1966).

7) Anwar, H. O., “Formation of a Weak Vortex,” Journal of Hydraulics Research, Vol. 4, No. 1, pp. 1-16 (1966).

8) Marris, A. W., “Theory of the Bathtub Vortex,” Journal of Applied Mechanics, March, pp. 11-15 (1967)

9) Zielinski, P. B., and Villemonte, J. R., “Effect of Viscosity on Vortex-Orifice Flow,” Journal of the Hydraulics Division, Proc. of ASCE, Vol. 94, No. HY3, pp. 745-752 (1968).

10) Anwar, H. O., “Prevention of Vortices at Intakes,” Water Power, October, pp. 393-401 (1968).

11) Domm, U., Rosemann, P. and Siekmann, H.,

“Modelluntersuchung der Einlaufstromung einer groben Kuhlwasserpumpe,” Z. Flugwiss., 19, Heft 8/9, pp.

374-379 (1971).

12) Kondo, M. and Maru, S., “Submergence Requirements of Pumps in Rectangular Open Sumps,” Hitachi Hyoron, Vol.

54, No. 6, pp. 511-515 (1972). (in Japanese)

13) Reddy, Y. R. and Pickford, J.A., “Vortics at Intakes in Conventional Sumps,” Water Power, March, pp. 108-109 (1972).

14) Levi, E., “Experiments on Unstable Vortices,” Journal of the Engineering Mechanics Division, Proc. of ASCE, Vol.

98, No. EM3, pp. 539-559 (1972).

15) Dagget, L. L., and Keulegan, G. H, “Similitude in Free-Surface Vortex Formation,” Journal of the Hydraulics Division, Proc. of ASCE, Vol. 100, No. HY11, pp.

1565-1581 (1974).

16) Baum, M.R., “Gas Entrainment at the Free Surface of a Liquid: Entrainment Inception at a Laminar Vortex,”

Journal of British Nuclear Engineering System, Vol. 13, pp.

203-209 (1974).

17) Baum, M. R. and Cook, M. E., “Gas Entrainment at the Free Surface of a Liquid: Entrainment Inception at a Vortex with an Unstable Gas Core,” Nuclear Engineering and Design, Vol. 32, pp 239-245 (1975).

18) Anwar, H. O., Weller, J. A. and Amphlett, M. B.,

“Similarity of Free-Vortex at Horizontal Intakes,” Journal of Hydraulic Research, Vol. 16, No. 2, pp. 95-105 (1978).

19) Jain, A. K., Ranga Raju, K. G. and Garde, R. J., “Vortex Formation at Pipe Intakes,” Journal of the Hydraulic Division, Proc. of ASCE, Vol. 104, No. HY10, pp.

1429-1445 (1978).

20) Hecker, G. E., “Model/Prototype Comparison of Free Surface Vortices,” Journal of the Hydraulic Division, Proc.

of ASCE, Vol. 107, No. HY10, pp. 1243-1259 (1981).

21) Farell, C. and Cuomo, A. R., “Characteristics and Modeling of Intake Vortices,” Journal of Engineering Mechanics, ASCE, Vol. 110, No. 5, pp. 723-742 (1984).

22) Padmanabhan, M. and Hecker, G. E., “Scale Effect in Pump Sump Models,” Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 11, pp. 1540-1556 (1984).

23) Odgaard, A. J., “Free Surface Air Core Vortex,” Journal of Hydraulic Engineering, ASCE, Vol.112, No.7, pp.

610-620 (1986).

24) Gulliver, J. S. and Rindels, A. J., “Weak Vortices at Vertical Intakes,” Journal of Hydraulic Engineering, ASCE, Vol. 113, No. 9, pp. 1101-1116 (1987).

25) Takahashi, M., Inoue, A, and Aritomi, M,“Gas Entrainment at Free Surface of Liquid (Σ),” Journal of Nuclear Science and Technology, Vol. 25, No. 2, pp.

131-142 (1988).

26) Takahashi, M., Inoue, A. and Aritomi, M., “Gas Entrainment at Free Surface of Liquid (Τ)” Journal of Nuclear Science and Technology, Vol. 25, No. 3, pp.

245-253 (1988).

27) Hite Jr., J. E. and Mih, W. C., “Verocity of Air-Core Vortics at Hydraulic Intakes,” Journal of Hydraulic Engineering, ASCE, Vol. 120, No. 3, pp. 284-297 (1994).

28) Yildirim, N. and Kocabas, F., “Critical Submergence for Intakes in Open Channel Flow,” Journal of Hydraulic Engineering, ASCE, Vol. 121, No. 12, pp. 900-905 (1995).

29) Yildirim, N. and Kocabas, F., “Critical Submergence for Intakes in Still-Water Reservoir,” Journal of Hydraulic Engineering, ASCE, Vol. 124, No. 1, pp.103-104 (1998).

30) Werth, D. and Frizzell, C., “Minimum Pump Submergence to Prevent Surface Vortex Formation,”

Journal of Hydraulic Research, Vol. 47, No. 1, pp. 142-144 (2009).

31) Fujita, K. and Oya, K., “Suction Water Tank of the Pump,” Hitachi Hyoron, Vol. 45, Suppl., pp. 41-46 (1962).

(in Japanese)

32) Kyogoku, T., “Suction Sump of Diagonal Pump with Vertical Axis – Part 2,” Pump Kougaku, Vol. 1, No. 3, pp.

160-165 (1965). (in Japanese)

33) Kitamura, N. and Kida, K, “Problems in Planning of Pump Suction Sump,” Journal of JSME, Vol. 74, No. 630, pp.