Elementary Pump Theory

8/18/2019 Elementary Pump Theory

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Elementary

Pump Theory

Dr. P. I. Ayantha Gomes

1


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Water in

Waterout

Do always water inand out over a blade

is like this


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!

Water in

Waterout

May be water in and outcan be like this!!!


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"

Water in

Waterout

Water in

between inletand out let

Does always watermove alon# the blade

like this


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$

Water in

Waterout

Perhaps% the watermove like this &e.#.lo'alised (umps)***


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+

alon# the blade., evertheless%turbulen'es%eddies% lo'alised (umps that are not

visible to nakedeye are obvious, It is assumedthere are in/nitenumber o0 bladesand the #ap

between twoblades areetremely 'lose%when derivin#euations,Also% this doesnot mean velo'itywill be tan#entialto the blade% it willhave a resultantdire'tion that is in

many 'asesunknown% unless


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5ater parti'les &saystreamlines) will be

at di6erent dire'tions


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Water in

Waterout

w1

u1

V (water, earth) = V (water, blade) + V(blade, earth) v1 = w1 +u1

β1

v1w1α

1

u1 = r1


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Waterout

u1


β1

v1w1

ow we will introduce two"ore velocities#$

1) %he absolute (i$e$, relativeto earth) circu"&erential

velocity o& water

') radial velocityco"onent (radial "eans it

is erendicular to thecircu"&erential

co"onent)


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V (water, earth) = V (water, blade) +(blade, earth) v1 = w1u1

ow we will introduce two"ore velocities#$

1) %he absolute (i$e$, relative

to earth) circu"&erentialvelocity o& water') radial velocity

co"onent (radial "eans itis erendicular to the

circu"&erential

co"onent)

w1

u1

β1


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w1

u1

β1

α1

Vn1

•9n1 is the absolute normal velo'ity 'omponent o0the water. :ometimes re0er as radial velo'ity asthis 'omponent 'rosses the 'enter o0 the impeller

• 9t1 is the absolute 'ir'um0erential velo'ity o0 water

•

;oth these are velo'ities o0 water% and nothin# todo with the blade o0 the im eller

Vt1


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u1

β1

v1w1

Vn1

u1

β1

v1w1

Vn1

Does 9n1 is a'tuallya radial velo'ity


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1!

;y an#ular momentumtheory

9t1 and 9t2 are absolute 'ir'um0erential velo'ity

'omponents o0 the -ow< then Power delivered to -uid'an be 'al'ulated as

=e0erred as Euler euations 0or pumps. It shows torue%power and head are 0un'tions o0 rotor>tip velo'ities &u)and absolute -uid velo'ities &v) only< in other words

independent o0 any aial velo'ities throu#h thema'hine

;ernoulli euation inrotatin# 'oordinates


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1"

*a"le -iven are the &ollowin. data &or aco""ercial centri&u.al water u" r1= / in, r' = 0 in,

β1= 23, β'= '23, seed = 1//2 r4"in$ *sti"ate (a) the

desi.n5oint dischar.e, (b) the water horse ower, and(c) the head i& b1 = b' = 1$06 in$

• As radial velo'ity 9n 'an be

epressed as

• There0ore% by 'ontinuity euationpower o0 the pump 'an beepressed as @

• b1 and b2 are inlet and outlet

blade widths. This euationalso 'an be used to 'al'ulate

the desi#n -ow rate andusually estimated assumin#the -ow enters ea'tly normalto the impeller &i.e. 1 is 78B)

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Elementary Pump Theory