lab2.docx

EXPERIMENT 2 IMPACT  OF JET  OF  JET 

Objectives •

 To investigate the validity of theoretical expressions for the force exerted by a jet on targets of various shapes.

Background / Theory  Water turbine are useful in generating power which is applying the principle of conservation of linear theorem. The momentum equation relates the sum of the forces acting on a uid element to its acceleration. A theoretical model for the force necessary to hold the impact surface stationary is obtained by applying the integral forms of the continuity and momentum equations. The details of the model depend on whether or not the uid stream leaving the impact surface is symmetric relative to the vertical axis of the surface. When a jet of uid strikes a solid surface of the target plate at any angle a force will be produced by the pressure of the uid at high velocity of the uid. !t will not be rebounded from the surface but a stream of uid is formed which moves over the surface. When the surface area is larger than the stream hitting it the liquid will ow away from the normal.  The components of force can be obtained by applying the momentum principle. There are some assumptions which is required in order to ful"ll this principle. #irstly the uid should be incompressible and in viscid. $econdly the surface tension forces are very small so it can be negligible. Thirdly the ow of the uid is steady. %astly the velocity distribution across the cross section is uniform.  The momentum principle states that the force is the rate of change of  momentum. &y applying this principle the impact force of the jet can be determined. The vertical velocity force F  y  applied to the surface of the target is therefore' F  y  (

∫ v ( ρ v dA )  A

 )

∫ v cos θ ( ρ v dA )  A

( ρv 2 A *+ ) cos θ ,

According to the volumetric ow rate equation - ( Av where v is the velocity and  A  is the cross)sectional area of water jet the equation above can be simpli"ed as equation +' F  y  ( ρvQ *+ ) cos θ ,)))*+,

From the equation 1,

 ρ

 and Q represent the density of the fluids and volumetric flow

rate respectively. θ  is the flow deflection angle. In this experiment, flat target, 120 °  target and hemispherical target are used. esides, the vertical velocity force!

F  y

" is related to the flow deflection angle! θ " which is

shown in equation 1. #herefore, there will $e different equation for different target. For the flat plat, the deflection angle is equal to %0

°

, so su$stituting the value inside

the equation 1, the equation for flat target will $e& Q ° , where v(  A F  y  ( ρvQ *+  cos/0

Q ρQ ( 1  A  *+)0,

(

 ρQ  A

2

 and therefore the vertical velocity force!

  ))))))))*2,

F  y

" is produced $y 120 °  target will $e

shown in equation '& Q ° F  y  ( ρvQ *+  cos+20 , where v(  A

(

Q  ρQ 1  A 3+)*)

1 2

,4

3 ρ Q

(

For the vertical velocity force!

2

  )))))))*5,

2 A

F  y

" which is produced $y the hemispherical target will

 $e shown in equation (& Q F  y  ( ρvQ *+  cos+60 ° , where v(  A

(

(

2 ρ Q

 A

 Q  ρQ X  [ 1−(−1 )]  A

2

  )))))))*7,

From the equation 2,' and (,the maximum force that a )et can exert will $e produced when a hemispherical target is used, then it is followed $y 120 °  target and flat target. #he reason why the vertical velocity force will $e maximum when the hemispherical target is used $ecause the flows are completely reversed in direction when they deflected  $y this *ind of target.

#ig +' the shape of the water after striking di8erent targets.

Procedures 1. +hec*ing whether the spirit level is in the suita$le range otherwise need to ad)ust the feet.

 The suitable range of the spirit level

Fig2&pirit level is in the suita$le range 2. #he top plate and the transparent casing were removed so that the no--le diameter  !mm" can $e measured and the flat target !%0 ° " was placed on the rod attached to the weight pan. '. #he apparatus was assem$led and the inlet pipe was connected to the $ench with the apparatus in the open channel. (. #he $ase of the apparatus was levelled with the top plate loosely assem$led and the top plate was screwed down to datum which is a silver line on the spirit level. /. #he level gauge was ad)usted to suit the datum on the weight pan and a load was  placed on the weight pan. #he water was allowed to flow $y operating the control valve on the ydraulic ench.

%evel 9atum on the weight

Fig'&weight pan and level gauge . #he flow rate was then ad)usted until the weight pan was read)acent to the level gauge. #he weight pan should $e oscillated to minimi-e the effect of friction when testing for level. 3. 4ecording down the readings of volume and time to find the flow rate. #he mass which is placed on the weight pan also need to $e noted. . #he experiment was repeated $y increasing the masses!/0g2/0g" on the weight  pan.

%. +hanging the 120 °  and hemispherical target to repeat the experiment.

Fig(& the mass which is provided

Fig/& ' different targets !120 ° ,flat,hemisphere"

Calculation/ Result  In this part, the result of each target will $e ta$ulated in ta$le 1 until ta$le '. #he m against

Q

2

 will also $e plotted.

5iameter of no--le&  mm 6 !+ross sectional area of the water )et" 7 +ross sectional area of no--le 7 7

π 

r 2

π 

 !0.00("2

7 /.02/810/ m2 6ssuming that  Ρ  !5ensity of water" 7 1000 *g9m'  g  !:ravitational acceleration" 7 %.1 m9s2

!i"

flat plate Flow rate Q !m'9s"

;ass on weight  pan m !*g"