Forces Analysis on a Spherical Shaped Delivery Valve of Hydram Pump.

01213461278793873

12 39 9
7189
8473 1611 9134


!"#$$
%&!'#($()(
%%&#*()+
,%$(-"()((
.("&($(/.0
,%1#($2(
,3 3"((
,&4#)41(#5(
,%'((6#/($(

123245723898
4984
23 4


829
9584
2
722
245
 !"#$%&'()
* +,,$"',$-',&,',
.%$",$/0),''123!'(,
4+-0356789
:'/ *6;*75678?@A>BCDB



EFG 8HIFJFGFK4HIFIFJL848M8H
NFIFEO 4OHEFEF78 J872P8H
NFIFQK89HNFRFR8K 8KH
NFJFE4QO584KNFIF5OS

012345678


     !"#

$ % &' ( ) *   *  ) +,  ) 
+  , *+  , , + "  " )+ * 
)'

   
-
-./00 0 ***1
!"#
)233"""')'

4+ 556 *
7889:;;?@AB:?C=ABAD;E:A9C=
FGGH=8E:BD=IJJKLMNNJ=
FGGH=?U$'*%$dH%F&%"+,_!'!
'04J=?0Q.
d%
$H"%'*"$%'V$
%K$,

'"%'!&G
#%'+$
%V%
H"d
H%F&%"VK"$%H$'+,_!'
d$


H
J

W


!
!
7.P.0pm4=>60P.p.0O9Y60p.s.0a4;M60t.P.0@NN60r.7.0t4=>60s.O.0@9Y04=?0p.t.0O4=>
S&
&"%"'!'&%*V
*$%%Sv

'
%$"'G&'+
"Sv
$_V
!J#`K
H'%%"%
"#$"$V%_%'!$

"
'


&






!


"

e"
P2=4m4;Y4=60t.0tN3;960ZY;94?960L.0s4Y4;2=60ON=wrCA607.0L4M4904=?07.0L99=AY9
`$
%H*%!x!!V%
'%H"*'!!*$%S&&&&"'%T'+$
!%H*%_x'#%&hl+$%HG'$&'%V$"I
+$
%

+$
X.L.O.a.0LN>4;460-.X.7.O.072M260-.O.P.012>93460-.7.0Q:39M460-./.072:39M404=?0X.P.:979BA7a67B9p9B
$(%'#h('!&#rZ!".#2(Z'2#s+Z"!/#0!#S+Zii'#*2(/
D6k67b?>9;7t6G9BXF79BA7D`BA>?FBF
SZ/.#(#S("!#[!'#N!!Z&#)(#S("%'#L(i"#()#S2!/(1
86W67cd9Be;7k6k67a?G;786a675?G79BA7868675``
N
#"!"#SZ/.#(#2#R2+M&&#()#S!"&&#S"#!&#!#"+(/##N"M!"#QZ"

s
"
C67kEu?nX9;7_6C67kE9>A9G9B9;7_6a6l67kEe?X9;7C67kE9>A979BA7a67$ >">%
@6
A347B#1!,* ,*-C0+/&/-0*#!%"&0#*&%/!1/&/-32!"0"+%$(2$/&/

DEFGHIJGKLMNOPQRSTRSUQVWXXYZ[TYOR[PX\UQY\][^XY\TP_XVQ`[aQYOUQVWXXY]_OXbN
OXcXb[SXOQYO[SXPQ\XO\[\U_VOQNdM[]XcXPa^[YV\PQ_Y\V^[RSbQ_Y\VWN\UXSX[SbXQPXXQV_bN
OQRQ`XO[Y_\VPTWWXP[Z]QV\XcQbcXQYOOXb_cXPNcQbcX[Z\UXUNOPQRSTRSdeYQOO_\_[Ya\UX
PXb_QW_b_\N[Z\UXSbQ\XcQbcXR[OXbV_VQbV[Q]ZTbbN]UXPX_\VPTWWXP[Z\UXcQbcX_VfT_^gbN][PY[P
OQRQ`XOde\UQVWXXYPXOT^_Y`\UX_Y\XPXV\[Z\UX^[RRTY_\N_YT\_b_h_Y`UNOPQRSTRSVdi[PX[cXPa
\UXPX_VY[NX\Q^[RSPXUXYV_cXSP[^XOTPX_YSbQYY_Y`QYORQg_Y`O_RXYV_[YV[ZUNOPQRSTRSd
jUXYaOXV_`Y[ZQVSUXP_^QbVUQSXOOXb_cXPNcQbcXR[OXb[Y\UXUNOPQRSTRSUQVWXXYRQOXQYO
\XV\XOdk[YV_OXP_Y`\UQ\UNOPQRSTRS_VQbV[^QbbXO_RSTbVXSTRS]U_^U][PgOTX\[\UXXZZX^\V[Z
]Q\XPUQRRXPa\UXPXZ[PXa_\YXXO\[gY[]\UXZ[P^XV\UQ\\QgXSbQ^X_Y\UXUNOPQRSTRSdjUXYaZP[R
\UXVXZ[P^XV^QYWX^Qb^TbQ\XOO_RXYV_[YV[ZUNOPQRSTRSQYO_\VSXPZ[PRQY^X^QYWXSPXO_^\XOd
lP[R\UXPXVTb\V[Z\UXV\TONVU[]V\UQ\O_RXYV_[YVQYOSXPZ[PRQY^X[Z\UXUNOPQRSTRS_VcXPN
^b[VX\[\UXPXVTb\V[ZQVVXVVRXY\\UQ\UQVWXXYO[YXdl_YQbbNaQSP[^XOTPX_YSbQYY_Y`QUNOPQR
STRSUQVWXXYPX^[RRXYOXOdL
L

mnGHopqJGronL
sb\U[T`UV_Y^XtuuvUNOPQRSTRSUQVWXXYZ[TYOQYO]_OXbNTVXOZ[PSTRS_Y`]Q\XP_YPXR[\X
QPXQV]UXPX\UXPX_VQ]Q\XPV[TP^X]_\UQYQOXfTQ\XOUX_`U\QYOZb[]PQ\XdM[]XcXPa_\VTVX_V[Z\XY
^[YV\PQ_YXOWNOQRQ`X[Y_\VcQbcXdl[P_YV\QY^Xa_YwxtxaQUNOPQRSTRSUQVWXXYOXV_`YXOQYO
[SXPQ\XO\[STRSP_cXP]Q\XP\[RXX\\UXYXXOV[ZQ^[RRTY_\N_Yyz{|SP[c_Y^XdjU_VSTRSUQV
WXXYOXV_`YXOTV_Y`Q^[YcXY\_[YQbSbQ\XVUQSXOOXb_cXPNcQbcXd}TX\[_\UQVbQP`XO_RXYV_[YQYO
][PgV[YU_`UUXQOaQ^^[PO_Y`\[~QV^QbVbQ]\UXY_\VOXb_cXPNcQbcXPX^X_cXVQbQP`X]Q\XPUQRRXP
Z[P^X\UQ\SP[S[P\_[YQb\[\UXQPXQ[Z\UXSbQ\XcQbcXaV[_\_VcXPNXQV_bNOQRQ`XO[PbXVVPXb_QWbXd
jUXYa€TQPOQQYO€TgQOQYQt‚[Y\UX_PPXVXQP^UUQcXRQOXQYO\XV\XOUNOPQRSTRS]_\UcQP_[TV
cQbcXVUQSXOR[OXbVa\UXNQPXSbQ\XaRXRWPQYXaVSUXP_^QbQYOUQbZƒVSUXP_^QbVUQSXOdlP[R\UX\XV\
PXVTb\VVU[]XO\UQ\\UXVSUXP_^QbVUQSXOOXb_cXPNcQbcXR[OXbSP[OT^XV\UXWXV\c[bTRX\P_^
XZZ_^_XY^NaZ[bb[]XOWNRXRWPQYXaUQbZƒVSUXP_^QbVUQSXOaQYO\UXSbQ\XR[OXb`_cXV\UXb[]XV\
XZZ_^_XY^NdlTP\UXPR[PXa\UXVSUXP_^QbVUQSXOcQbcXR[OXbUQVWXXY_RSbXRXY\XO[YQUNOPQRSTRS
\[STRS]Q\XPZ[PSTWb_^VXPc_^XV_Y„…†|‡ˆz‰c_bbQ`XŠ‹zŒO_V\P_^\„z‰zŒz†…‡PX`XY^Nyz{|
SP[c_Y^XdjUQ\UNOPQRSTRSUQVWXXYQWbX\[[SXPQ\XSP[SXPbNaWT\]_\UV[RX\TY_Y`QYO
QOŽTV\RXY\V\UP[T`UQb[Y`XY[T`U\_RX\XV\XO][PgVdjU_V\[gXSbQ^XWX^QTVX\UXPX_VY[NX\Q
PXZXPXY^X\[OX\XPR_YX\UXO_RXYV_[Y[Z\UXOXb_cXPNcQbcXaVT^UQV\UXO_QRX\XPQYORQVV[Z\UX
VSUXPXdeY[POXP\[OX\XPR_YX\UXO_RXYV_[YV[Z\UXcQbcXVU[TbOWXgY[]Y\UXZ[P^XVQ^\_Y`[Y\UX
cQbcXQYOZb[]SUXY[RXYQ\UQ\[^^TPd
GIGLo‘LDHGL

MNOPQRSTRSUQVWXXYZ[TYOWN’PXXYQYOkQP\XP_YtuuvdMNOPQR“UNOPQTb_^PQR”[P_RSTbVX
STRS_VQ\[[b\[Zb[]]Q\XP^[Y\_YT[TVbNZP[RQb[]XP\[QU_`UXPV_\XWNTV_Y`QS[\XY\_QbXYXP`N
[Z]Q\XPV[TP^X\UQ\]_bbWXV\PXQRXOQVQOP_c_Y`Z[P^XdjU_VSTRS][PgV]_\U[T\QYNX•\XPYQb
XYXP`NV[TP^XVT^UQVXbX^\P_^_\N[PZTXbXYXP`Nw‚deY\U_V]QNZPQ^\_[Y]Q\XPZP[RQ]Q\XPV[TP^X




˜™š

›œœžŸ ¡œ¢£¢¤ž£ ¢ž ¥œ¦ž¤§¤¨¢œ£ ©¤ª «¬£Ÿ­¢ž­®§œ ¡œ¯œ§¤°±œžŸ

2345678963
6 8 3

69799 4 476886
648 93928939938 4
6 864836469 
3269834
6

8 386972 46986 48 4682646948
6 9
 38696 2834 8
64
2 49
6 58
66628 3869
3

69
6
342
 46487 
 93

396374

5

F 


'



C


 ‡ˆ‰Š‹ŒŽ‰ˆ
' ‹[‘’“Œ0”•[‘1‹•1‘
 [–“—‘Š
 ‰‘•“1‘Šˆ1‹•1‘
5 ‹“ŠH‡‹Œ‘Š
F ‰Š“1‘0“0‘
C ‰‘•“1‘Šˆ0“0‘

!342
 46487 
 93




"4268
6978
6 8
66#784 669368
3873335634 76 733867
36 $3869%
37
69237
36  66936
36 6746 34 
6
6486 5376  48
69967878
38
37
5664 46&8
3756647
48 9 2656886969 9
3426%'%34 75666 8 
363
 469 9468
65623768
377
369
3283963( 669%874 8684 4
8
6
 92673284 48
383643
 93


c\]^^_
c^]^^_
b\]^^_
b^]^^_
fghija\]^^_
a^]^^_
`\]^^_
`^]^^_
\\]^^_

d]\^

e]a\
\]^^
`]d\
klgmnopqrps
~€y|‚vuƒ„€vy… †vuƒ„€y|‚vuƒ„€vy…


')
397 4 8 8362642 39 7
67 
 93

 66936
*3869
3

697967796796 9362376 
643 4
8 47 926 8 78  92
346
9628 47 64+

648
2
346,-3869
3

692

4 2297
643362 767
7 64
64 3
64836.38 443869
3

698
6 99638679677962
3467%/0%8 
6 282
3467%/1%
2
72

44 4378
623  76.38 445%322 9 48 
6789:9;96