UEL SCHOOL OF COMPUTING, INFORMATION TECHNOLOGY & ENGINEERING CE2206 Hydraulics
Dr R.Jayaratne
Laboratory Report on sluice gate and hydraulic jump
Contents Page Aim........................................................................................................3 Research methodology.............................................................................4 Apparatus............................................................................................4 Figure 1.1.......................................................................................4 Procedures..........................................................................................5 Table 1.1.........................................................................................6 Table 1.2.........................................................................................7 Table 1.3.........................................................................................7 Table 1.4.........................................................................................8 Table 1.5.........................................................................................8 Table 1.6.........................................................................................9 Critical depth..................................................................................9 Comparison and discussion....................................................................11 Possible Machine/materials errors.........................................................11 Graph 1.2.....................................................................................12 Fig 1.2..........................................................................................13 Comments on health and safety...............................................................14 Conclusions..........................................................................................15 References...........................................................................................16
Aim The aim of the experiment proposed is to study and calculate the hydraulic jump and his specific energy curve in a sluice gate and then try to compare the results obtained with the Theoretical values.
Research methodology Apparatus 1 Open channel flow tanks –The tanks are used to allow the flow to fluid between them by the force of gravity and pressure. 2 Sluice gate- is a mechanism used to control amount of flow going from on tank to another. 3 Depth Gauge with Vernier Scale- is a measuring apparatus that is used to measure the high of the liquid at different parts of the hydraulic jump experience. 4 Discharge Meter- is used to measure and display the discharge flow value of the experience. 5 Water Pump: is a pump used to control the speed of the flow. 6 Ruler: a measuring scale that is used to measure the distance of the xaxis of the hydraulic jump experience.
Figur e 1: Drawing of all apparatus and apparatus location represented by numbers1 to 6.
Procedures
First the water pump was turned on. Water started to flow from one tank to another tank through the open channel.
After a couple of minutes of wait the channel was complete with water and start establishing the hydraulic jump .
The Depth gauge attached to the channel was released into the tank “A” to measure the high of the water in the tank. The lower tip of the point gauge was put on the surface of the water and a reading was taken as an upstream section (Section “A” in the shown Fig.1.2) both in y-axis and x-axis, the xaxis was measured by the use of a ruler.
The next reading was taken by the same method when the water was in downstream section (Section “B” in the shown Fig.1.2) both in y-axis and xaxis.
The next reading was taken in the starting point of hydraulic jump (section “C” in the shown Fig.1.2) and the measures were taken by horizontally and vertically.
The last point of reading was taken in the transition point of the hydraulic jump, where it changes from the jump to normal flow (Section “D” in the shown diagram Fig.1.2) and measures were taken in the x-axis and y-axis.
While the measures were taken in each section the Flow rate was noted, to afterwards calculate an average of it.
Fi g 1.2: Drawing of analyzed section of the experiment.
Analysis
Symbols Q=Channel Discharged flow b=Chanel Width y=Channel Depth V= Velocity Ec=Specific energy Fr=Froude number Dc=Critical depth Sector
Distanc
Water
e along Depth y/cm Channel x-/cm 1
38.0
22.0
2
57.0
0.9
3
113.0
1
4
135.6
6.55
Table 1.1: Lab results in a tabular form
Calculation for new Q Average Q=110 l/min Q=
110 ×(0.001 cubic meters) =0.00183 m/ second (60 seconds)
Average Q =110 l/min =0.00183 m/s Average Channel Width b=104 mm=0.104 m
Locatio
Description
n
Water
Distance
Depth-y (m)
along Channel-x (m)
1
Upstream of sluice gate
0.220
0.380
2
Downstream of sluice
0.009
0.570
gate 3
Start of hydraulic jump
0.01
1.130
4
End of hydraulic jump
0.0655
1.356
Table 1.2: Table with water depth and distance converted from centimeters Locatio
Description
to Area=width × Depth=b × y
n
meters. Area ( m2 )
1
Upstream of sluice gate
0.104 × 0.22=0.0228
0.0228
2
Downstream of sluice
0.104 × 0.009=0.0009
0.0009
gate
3
Start of hydraulic jump
4
End of hydraulic jump
0.104 × 0.01=0.001
0.0010
0.104 × 0.0655=0.0068
0.0068
Table 1.3: Table with calculated Area
Locatio
Description
Q Area
Velocity
V=
0.00183 0.0228
0.0802
V=
0.00183 0.0009
2.0333
V=
0.00183 0.001
1.83
V=
n 1
Upstream of sluice gate
2
Downstream of sluice gate
3
Start of hydraulic jump
4
End of hydraulic jump
V=
(m/s)
0.00183 0.0068
0.2691
Table 1.4: Table with the calculated Velocity Locatio
Description
n
1
Upstream of sluice gate
(
Ec = y +
(
V 2g
Ec = 0.22+
Specific
)
0.0802 2 × 9.8
energy
)
0.2203
2
Downstream
of
(
Ec = 0.009+
sluice gate 3
Start of hydraulic
(
Ec = 0.01+
jump 4
End of hydraulic
(
2.0333 2× 9.8
1.83 2× 9.8
Ec = 0.0655+
jump
0.2199
)
0.1808
)
0.2691 2× 9.8
)
0.0691
Table 1.5: Table with calculated specific energy and Froude’s number.
Locatio
Description
Fr=
n 1
Upstream
of
sluice
V √( g . y )
Downstream of sluice
0.0546
2.0333 √(9.8 ×0.009)
6.846
1.83 √(9.8 ×0.01)
5.845
0.2691 √(9.8 ×0.0655)
0.3359
Fr=
gate 3
Start of hydraulic jump
4
End of hydraulic jump
Fr=
Fr=
Table 1.6: Table with calculated froude number Critical depth
Q b√g
( )
Dc =
(
Dc =
2 3
0.00183 0.104 ×√ 9.8
)
2 3
Dc
number
0.0802 √(9.8 ×0.22)
Fr=
gate 2
Froude
=0.0316 m
Critical specific energy Ec =
( 32 )× Dc
Ec =
( 32 )× 0.0316
Ec =0.0474
Depth ratio Calculation for Hydraulic Jump
y4 y3 Figure 1.5: Diagram of hydraulic jump with respect to y3 and y4 Calculated value of the hydraulic jump y 4 −1+ √ 1+8 Fr23 = y3 2 y 4 −1+ √ 1+8 ×5.8452 = =7.781 y3 2 Observed value of the hydraulic jump y 4 0.0655 = =6.55 y3 0.01
Relative Error:
Relative Error: Error= 18%
Actual−theoretical ×100 Theoretical 7.781−6.55 ×100=18 6.55
Length of the Jump: Length of the jump consists in a subtraction of the length end of the jump with the length of the start (results taken by table 1.2). Actual value of the jump=L4-L3 1.356-1.130=0.226 m Theoretical Length of the jump is calculate by the high of the end of the jump subtracted by the high of the start of the jump times 5.5. Theoretical value of the jump=5.5 x (y4-y3) 5.5 x (0.0655-0.01)=0.305 Relative Error:
0.226−0.305 ×100=25 0.305
Comparison and discussion The experiment results indicates clearly hydraulic jump occur when there is flow that suddenly change from supercritical to subcritical flow. It’s established that the decreasing of the area of the water increases the velocity of the water and the Froude number and by the large change of area by the sluice gate changes the velocity and with the change of velocity the hydraulic jump is formed. This can be discuss by observing the tables 1.3,1.4 and 1.6, its clearly observed the change of area in location 1 to 2 and then from location 3 to 4, that cause the change in the velocity and also cause the change in the Froude number. The table 1.5 making a relation of points locations with the table 1.2 it´s clearly observed that the there’s energy loss along the channel and a large drop in the hydraulic jump. For the type of jump occurred in the experiment it was assumed to be the steady jump shown in the figures 1.2 and 1.3
The Results that were expected to have are slightly different by the results obtained and by comparing with other results made, Errors of 10% to 20% are respectfully, but in case of errors of more than 20% are very different in magnitude is cause for alarm. The calculated comparison of the hydraulic jump is 18% error from the actual value to the theoretical value that means it was 18% close to the supposed value. This error is assumed to be by the bad accuracy of the apparatus that can contribute to a large relative error.
Possible Machine/materials errors: Water temperature and density- Is an error mentioned because it exists, but has little effect upon the jump behavior and therefore is ignored in the analysis. Machine channel width with different measures-The width measured in the channel had different values so I was made an average of the width, one of the assumed causes of the errors results. Water pump and the flow meter with errors- It’s not very likely to one of the main reasons for the error but could happen. Accumulative dust or material in the channel-The constant change of the water of the equipment, brings always water waist and it gets attached to channel changing the measures of the channel.
water depth 0.25
0.2
0.15 Specific energy2 0.1
0.05
0 0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
Graph 1.1: Graph shown above consists in water depth in the y-axis and Specific energy in the x-axis, with Dc (Critical depth) and Ec (Critical Specific energy) shown in red color. Specific energy 0.25 0.2 0.15
Length along the channel
0.1 0.05 0 0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Graph 1.2: Graph shown above consists in specific energy in the y-axis and length along the channel in the x-axis,and is also shown the number of the
location points and the water movement, it’s notice that the energy is loss along the channel with a big drop of energy when the hydraulic jump is formed.
Open Channel Flow Tank
Sub Critical Critical depth
Sub Critical
Super Critical depth
Super
Fig 1.2- The image shown above represents the open channel with the critical depth line, above the line the water flow is sub-critical and below the line the water flow is supercritical.
Fig 1.3- Image of a hydraulic jump with the Froude number between 4,5 to 9, jump consider a steady jump, information taken from B.S.Massey (1989) Mechanics of Fluids,
6th
edition.
Fig 1.4- Drawing of the Lab hydraulic jump, Froude number 5.8, is assumed as “steady jump” by the use of previous studies, the jump above (Fig 1.3) was the jump more similar to the jump obtained in the experiment.
Comments on health and safety
The health and safety problems in the lab experiment are very small to occur, the experiment doesn’t contain sharp elements or flammables components, and the safety problems that may occur is to slip on the floor due to the using of tanks of water, or an electrical shock for the reason of the use of electrical devices. For the protection of this safety problems is advised that check if the machine is not pouring water and use the proper type of shoes.
Conclusions To conclude is clear that apparatus errors were influents in the final results and just demonstrates that for this particular report the need for the devices to be very accurate is crucial, is also concluded that to a hydraulic jump to be performed a change in the water area has to be performed, it was also determined that the hydraulic jump create a large energy loss.
References
B.S.Massey, (1989) Mechanics of Fluids,
6th
edition, (Pages:
393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408) Video loaded by “Djkjjudi” available on http://youtu.be/5etwhZ0d2GU [23 Jun 2012] Video loaded by “GEJOKER” available on [21 Jun 2012] Les Hamill, Understanding of hydraulics 2011, third Edition, (Pages: 263,264,267,268,269,270) Sarah Catmur,(2012) Module handbook CE2206 Hydraulics,(Section 5 hydraulic jump)
