Impact of Jet

AIM: To calculate calculat e the force generated by a jet of water as it strikes a at and hemispherical cup and to compare compare it with the t he momentum ow rate in the jet. THEORY: Mechanical work can be produced from uids by pressurizing pressurizing the uid thereby accelerating accelerating them to very high velocities in a jet. This is directed directed to turbine wheels where force is generated due to the momentum change that occurs when the jet strikes the wheel. In reality, these water turbines produce around !!!!! k" with a very high e#ciency of $!%. &onsidering the vertical direction as y'a(is, the rate of momentum change of the uid along the y'a(is is e)ual to the force applied on the vane by the t he uid. *or a horizontal vane +along the y'a(is Momentum before impact -u ! Momentum after impact - ! *or a hemispherical cup +along the y'a(is Momentum before impact - u ! Momentum after after impact - ' u! /o, momentum change - 0 u! u- 12 u0! - u0 3 04g4h /ince acceleration acceleration due to gravity slows down down the uid uid by the above amount. "here ,

 u!- velocity of the uid just before impact u - velocity of the uid just after leaving the jet  - rate of change of mass of the uid h - distance between the center of the vane to jet 5iven values, 2!- 67.8mm0 m- !.9 kg h - !.!:8m +;aw- !!! kg1m: &onsidering the *<= of the lever before and after impact and e)uating moments of the forces about the pivot, we get the following, >et *s be the spring force, " be the weight load. >et ?a@ be distance between spring and pivot. ?b@ be distance between spring and impact point ? (i @ be the distance between impact point and weight without the jet. ?(@ be distance between impact and load. et, y- ('(i aAb-8 cm *-B4g4y

DESCRIPTION OF APPARATUS: *igure shows the arrangement in which the bench supple is led to a vertical pipe terminating in a tapered nozzle.  This produces a jet of water which impinges on the vane in the form of a at plate, hemispherical cup. The nozzle and vane are contained within a transparent cylinder, at the base of the cylinder there is an outlet by which the ow may be directed to the weighing tank. 2s indicated in the Cgure, the vane is supported by a pivoted beam, which carries a jockey weight and is restrained by a light spring. This lever may be set to a balanced position +as indicated by the tally suspended from it by placing the  jockey weight at its zero position and then adjusting the knurled nut above he spring . 2ny force generated by impact of the jet on the vane may now be measured by moving the jockey weight along the lever until the tally shows that the lever has been restored to its original balanced position. PROCEDURE: •

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 The apparatus is Crst levelled and the lever set to the balanced position +as indicated by the tally with the  jockey weight at its zero position. "ater is admitted through the bench supply valve and the rate of ow is then increased to the ma(imum.  The position of the jockey weight which restores the lever to the balanced position is noted while the discharge is weighed.

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 The e(periment is repeated with diDerent ow rates and respective readings are noted down.  The readings have the same )uantity of water +8kg. E(periment is repeated with at plate or hemispherical cup.

SAMPLE CALCULATIONS: Flat vane : t-0.:B s F-! liters  - !10B.:B - !.B96 Gg1s u -  1+raw42 - !.B961+!!!467.84!'9  - 8.$6 m1s u!0-u0 3 04$.74!.!:8 - u 0 3 !.976 u! - √  −0.687 - √ 5.97 −.687 -8.$ m1s 2

2

u

u! - 0.66 H y-6! mm *e(p - B 4 $.7 4 6! 4!': -0.68 H

Hemispherial C!p : t- 00.9: s F- ! liters  - !100.9: - !.BB0 Gg1s u -  1 +raw42 - !.BB01+!!!467.84!'9  - 8.9: m1s u!0-u0 3 04$.74!.!:8 - u 0 3 !.976 u! - √  −0.687 - √ 5.63 −.687 2

u

2

-8.86 m1s

 u! - 0.B9 H y-98 mm *e(p - B4 $.7 4 98 4 !': -8. H Ta"les:# Flat Fae : # Fua ntity ! ! ! ! ! ! !

 J  t +m +Gg1s +s m  0. !.B9 :B 6! 79!B 00. !.BB 90 9! 0!76 08. !.:$ 8: 8! 9$9 07. !.:B $B B! 88B: ::. !.0$ 89 :! 6$6B B!. !.0B 0: 0! 786 8:. !.7 78 ! 86!

u +m1s 8.$9 $B60 8.9: 966 B.$7 $68$ B.B! 78 :.6$ 87BB :.9 98!9 0.:9 897

u! +m1s 8.$ 968 8.86 !:69 B.$0 !B99 B.:0 : :.6! B079 :.!8 98 0.0 8607

4u ! +H 0.66 !0:0 0.B9 087$ .$0 6:06 .B$ :77 .! :67 !.68 $96 !.B B9:

* +H 0.6 B97 0.: 8BB .$ 90 .8 9$9 . 660 !.6 7B7 !.: $0B

Hemispherial !p :# Fuan t tity +s 00. ! 9: 0:. ! 8$

 J +m m : !  8

 +Gg1s  !.BB 7$ !.B0: $!7

u +m1s 8.90$ 77 8.B!! !6

u! +m1s 8.896 79 8.::9 B6

4u! +H 0.B9! :7$ 0.090 !:7

* +H 8. !0 B.8 09

!

08

!

09 0$. B6 :B. 07 :7. 99 BB. BB 99. BB

! ! ! ! !

! ! 78 6! 88 B! 08 !

!.B !.:7B 98 !.::$ :07 !.0$ 68 !.087 998 !.008 !0: !.8! 80

8.!$8 8B B.7$$ 88$ B.:00 98 :.69 7 :.0$8 !$$ 0.799 80$ .$6 :B6

8.!06 6!6 B.707 $6: B.0B0 B66 :.900 8B8 :.7$ $6 0.6BB :6 .60$ !0:

0.! !7: .786 0$6 .B:$ 8$0 .!89 680 !.70B $:8 !.96 B$: !.09! 0:7

:.$ 0B :.: :8B 0.6 B97 0. 870 .8 9$9 !.$ 7 !.: $0B

ON A NE$ PA%E Res!lt:# •

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F&r 'at plateK /lope of *theoretical vs rate of change of momentum - /lope of *e(perimental vs rate of change of momentum-!.$7 F&r hemispherial !p: /lope of *theoretical vs rate of change of momentum 0 /lope of *e(perimental vs rate of change of momentum-0.

In(erene:

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It is clear that the force produced on each of the vanes is directly proportional to the rate of momentum transfer from the jet.  The force generated for the hemispherical cup will be more than the force generated by the at vane. This is because the momentum change is more in the hemispherical case. *or at plate percentage of error in slope - 0% *or hemispherical cup percentage of error in slope 8%

SOURCES OF ERRORK •

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 The noting down of time in stopwatch may not be very accurate.  Laralla( error may e(ist in adjusting the lever to be e(actly horizontal by comparing it with the groove on the tally. Error may occur while recording the reading.