PART A: THE HYDRAULIC JUMPS
1.0 1.0 INTR INTROD ODUC UCT TION ION
A hydraulic jump is a fluid shockwave shockwave created at the transition between laminar and turbulent flow. One common example of a hydraulic jump can be seen in the water radiating outward when the stream of tap water strikes the horizontal surface of a sink. The water initially flows in a smooth sheet with consistent current patterns. In this region the speed of the water exceeds the local wave speed. !riction against the sink surface slows the flow until an abrupt change occurs. At this point the depth increases as water piles up in the transition region and flow becomes turbulent. The motion of individual water molecules becomes erratic and unpredictable. The interruption of flow patterns also reduces the kinetic energy of the water. In addition to the kitchen sink example hydraulic jumps are also typical features of river rapids where the water swirls and foams around rocks and logs.
2.0 OBJ OBJECTIVE
To investigate the characteristic a standing wave "the hydraulic jump# produced when waters beneath an undershot weir and to observe the flow patterns obtained.
3.0 3.0 LEAR LEARNI NING NG OUTC OUTCOM OMES ES
At the end of the course course students students should be able able to apply apply the knowledge knowledge and skills skills they have learned to$ a. %nderstand the concept and characteristics characteris tics of hydraulic jump. b. %nderstand the factors which influence the hydraulic jump.
4.0 THEORY
&hen water flowing rapidly changes to slower tran'uil flow a hydraulic jump or standing wave is produced. This phenomenon can be seen where water shooting under a sluice gate mixes with deeper water downstream. It occurs when a depth less than critical changes to a depth which is greater than critical and must be accompanied by loss of energy. An andular jump occurs when the change in depth is small. The surface of the water undulates in a series of oscillations which gradually decay to a region of smooth tran'uil flow. A direct jump occurs when the change in depth is great. The large amount of energy loss produces a zone of extremely turbulent water before it settles to smooth tran'uil flow. (y considering the forces acting within the fluid on either side of a hydraulic jump of unit width it can be shown that$ 2 vb ∆ H = d a + − d b + 2 g 2 g
va
2
va
*)
&here
is the total head loss across jump "energy dissipated# "m#
is the mean
da
velocity before jump "m+s#
vb
is the depth of flow before hydraulic jump "m#
is the
db
mean velocity after hydraulic jump "m# and
is the depth of flow after hydraulic jump
da ≈ d,
"m#. (ecause the working section is short ∆ H =
( d
3
− d 1
)
3
db ≈ d -
and
. Therefore simplifying
4 d 1d 3
the above e'uation
.
5.0 EQUIPMENTS USED
lear/acrylic rectangular open channels supported by steel frames "1.-m width#
0ump tank
0witch pump with water meter
2ectangular sluice gate "1.-m width#
ontrol valve 3 pump
4 units measurement gauges
, meter long steel ruler
5lasticine
6.0 EPERIMENTAL METHODS 6
,. 6nsure the flume is level with the downstream tilting overshot weir
at the
b
bottom of its travel. 7easure and record the actual breadth
"m# of the
undershot weir. Install the undershot weir towards the inlet end of the flume and ensure that it is securely clamped in position. 4. Adjust the undershot weir to position the sharp edge of the weir 41 mm above the bed of the channel. Increase the height of the tilting overshot weir until the downstream level just start to rise.
-. 8radually open the flow control valve and adjust the flow until an andular jump is created with small ripple decaying towards the discharge end of the working section. Observe and sketch the flow pattern. 9. Increase the height of water upstream of the undershot weir by increasing the flow rate and increase the height of the tilting overshot weir to create a hydraulic jump in the center of the working section. Observe and sketch the flow pattern. d1
:. 7easure and record the values of
dg
d3
q
and dg
q rates
. 2epeat this for other flow
"upstream head# and heights of the gate
.
!.0 SAMPLE DATA
hannel &idth b;1.-1m
Weir Openi ng,
Upstre am Flow Depth,
"g $m%
"o $m%
0.20
0.3145
0.21
0.3184
0.22
0.3085
0.23
0.2625
0.24
0.2508
Flow Flow Dept Dept h h Abov Belo e w Jump, Jump, " "# $m% $m% 0.017 0.094 3 4 0.015 0.091 5 8 0.016 0.094 6 3 0.017 0.094 1 1 0.021 0.093 0 8
Flow Rate,
∆H
V
∆H!"
"#!"
4.055 4 5.035 1 4.513 1 4.147 9 2.331 8
5.456 6 5.922 6 5.680 7 5.502 9 4.466 7
& $m#!s% 0.011
0.0702
0.1833
0.011
0.0780
0.1746
0.011
0.0749
0.1667
0.011
0.0709
0.1594
0.011
0.0490
0.1528
Table <.,. The )ydraulic =umps <., alculate >, and plot dg against > , <.4 alculate ?)+d, and plot ?)+d , against d -+d, <.- alculate dc and verify d ,@dc@d-
".0 ANALYSIS O# RESULTS$ EQUATIONS USED
8.1 6'uation used for V 1
Q=AV V=Q/A
A=d g x b ;1.41 x 1.-1 ;1.11m 4
A=d g x b ;1.4, x 1.-1 ;1.1-m 4
A=d g x b ;1.44 x 1.-1 ;1.1m 4
A=d g x b ;1.4- x 1.-1 ;1.1Cm 4
A=d g x b ;1.49 x 1.-1 ;1.1<4m 4
V=Q/A ;1.1,,+1.1 ;1.,B--m+s
V=Q/A ;1.1,,+1.1 ;1.,<9m+s
V=Q/A ;1.1,,+1.1 ;1.,
V=Q/A ;1.1,,+1.1C ;1.,:C9m+s
V=Q/A ;1.1,,+1.1<4 ;1.,:4Bm+s
'raph ()) "g against V 0.25 0.24 0.23 "g ,
dg/V1
0.22 0.21 0.20 0.15 0.16 0.16 0.17 0.17 0.18 0.18 0.19 , V
B.4 6'uation used for ∆H = (d 3-d 1 )3 / 4d 1d 3
?) ; "1.1C99/1.1,<-# 9"1.1,<-#"1.1C99# ; 1.1<14m
?) ; "1.1C9,/1.1,<,# 9"1.1,<,#"1.1C9,# ; 1.1<1Cm
?) ; "1.1C,B/1.1,::# 9"1.1,::#"1.1C,B# ; 1.1
?) ; "1.1C-B/1.14,1# 9"1.14,1#"1.1C-B# ; 1.19C1m
?) ; "1.1C9-/1.1,# 9"1.1,#"1.1C9-# ; 1.1<9Cm
B.- alculations for ∆H / d 1
; 1.1<14 1.1,<; 9.1::9
; 1.1
; 1.1<9C 1.1, ; 9.:,-,
; 1.1<1C 1.1,<, ; 9.,9
; 1.19C1 1.14,1 ; 4.--,B
B.9 alculations for d 3 / d 1
; 1.1C99 1.1,<; :.9:
; 1.1C,B 1.1,:: ; :.C44
; 1.1C9 1.1, ; :.B1<
; 1.1C9, 1.1,<, ; :.:14C
; 1.1C-B 1.14,1 ; 9.9<
'raph ()*) ∆H!" against "#!" 5.5 5.0 4.5 4.0
∆H!" , 3.5
d3/d1
3.0 2.5 2.0 4
5
6
7
, "#!"
B.: alculations for ritical depth d c = (q2 /g)1/3
, where q = Q/b
; "1.1-< 4+C.B,# ,+; 1.1:,m and acceleration due to grativy g = 9.81m2 /s
; 1.1,,+1.; 1.1-
%& V'()*)&+,)-/$ )* % 1%&%3
1.41m 1.1,<
[email protected]:,@1.1C99 1.4,m 1.1,::@1.1:,@1.1C,B 1.44m 1.1,@1.1:,@1.1C91.4-m 1.1,<,@1.1:,@1.1C9, 1.49m 1.14,
[email protected]:,@1.1C-B
.0 QUESTIONS
,# >erify the force of the stream on either side of the jump is the same and that the specific energy curve predicts a loss e'ual to ?)+d c. F befoe = F !f"e 4# 0uggest application where the loss of energy in hydraulic jump would be desirable. )ow is the energy dissipatedD #$e $%d!&'c &m* f'o+ *ocess c! be ''&s"!"ed b% &se of "$e s*ecfc eeg% coce*". q&!"o 'oss eeg% c! be +""e "em of "$e s*ecfc eeg% = d o V 2 / 2g
0$ee do !d !e fee". ec!&se of "$e $e!d 'oss !coss "$e &m*, "$e &*s"e!m !'&es of !e dffee". Abo&" "$e g!*$, (1) "o s"!"e (2) "$e f'&d does o" *oceed !'og "$e s*ecfc eeg% c&e !d *!ss "$o&g$ "$e c"c!' cod"o. #$e eeg% dss*!"es +$e +!"e f'o+ !" +e o*eg !d "$e eeg% bec!me bec!&se d !d d 3 $!s !e foce fom !dese. !me '5e "$e eq&!"o, F befoe = F !f"e . 6!c"c!' !**'c!"os of $%d!&'c &m*s 7ss*!"o of eeg% of +!"e f'o+g oe d!ms !d +es "o *ee" •
•
• •
*ossb'e eoso !d sco&g d&e "o $g$ e'oc"es. !sg +!"e 'ee's c!!'s "o e$!ce g!"o *!c"ces !d ed&ce *&m*g $e!ds. ed&cg &*'f" *ess&e &de "$e fo&d!"os of $%d!&'c s"&c"&es. :e!"g s*ec!' f'o+ cod"os "o mee" ce"! s*ec!' eeds !" co"o' sec"os g!gg s"!"os, f'o+ me!s&eme", f'o+ eg&'!"o.
10.0 COMPARISON ITH THEORY$ DISCUSSION
11.0 CONCLUSIONS
