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MAAE 2300 - Flow Through a Sluice Gate and Hydraulic
Jump Report
Fluid Mechanics I (Carleton University)
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- CARLETON UNIVERSITY -
Experiment 3:
Flow Through a Sluice Gate and Hydraulic Jump
Summary:
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This laboratory report analyzes Experiment 3: Flow Through a Sluice Gate and Hydraulic
Jump, during which a hydraulic jump was created by the flow of water passing from a sluice
gate, through a channel, and contacting an end barrier. The experiment was performed by
measuring the water flow heights at three different points along the channel, that is, before, at,
and after the jump. Before the jump, the flow of the water was classified as supercritical and
after the jump, it was classified as subcritical. This ultimately demonstrated that the flow type
conversion was induced by the jump. The purpose of this laboratory is to verify the course
techniques of flow prediction as discussed throughout MAAE 2300.
Nomenclature:
V1
=
Upstream velocity, inside tank (m/s)
VT2
=
Theoretical downstream velocity, preceding jump (m/s)
VA2
=
Experimental downstream velocity, preceding jump (m/s)
V3
=
Velocity after jump (m/s)
P1
=
Upstream flow pressure, inside tank (Pa)
P2
=
Downstream flow pressure, preceding jump (Pa)
Patm
=
Atmospheric pressure (101 325 Pa)
ρ
=
water
Density of water (1 000 kg/m3)
A1
=
Area of upstream cross section, inside tank (m2)
A2
=
Area of downstream cross section, preceding jump (m2)
Q
=
Flow rate (m3/s)
H1
=
Upstream head, inside tank (m)
H2
=
Downstream head, preceding jump (m)
H3
=
Downstream head, following jump (m)
h1
=
Upstream flow height, inside tank (m)
h2
=
Downstream flow height, before jump (m)
h3
=
Downstream flow height, following jump (m)
w
=
Channel width (6.25 in)
Flow Analysis:
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Bernoulli’s Equation relates the stagnation, static, and statics pressures of two given points
along a stream line of flow:
1
1
P1+ ρV 21 + ρg z 1=P2 + ρV 22 T + ρg z 2
2
2
(Eq. 1)
Conservation of momentum demonstrates that the mass flow rate of water at any given point
throughout the system is equivalent. This implies that, since the density is constant throughout
the system, the velocity of flow and area through which flow passes are inversely proportional:
ḿ1=ḿ2
(Eq. 2)
The following equation is used to calculate the total head, or total mechanical energy, at any
given point throughout the system:
(Eq. 3)
Volumetric Flow Equation:
Q= A 2 V 2
(Eq. 4)
Experimental Setup:
[3]
[1]
[2]
Experimental Procedure:
Executed procedure was consistent with instructed procedure from MAAE 2300 Fluid
Mechanics I Laboratory Exercises manual. No changes were made.
Results and Discussion:
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Flow 1
Flow 2
Position Flow
Flow Head Flow
Flow Head
Height (m) (m)
Height (m) (m)
V-Notch
0.140335 N/A
0.140462 N/A
[1] 0.4810125 0.4810125
0.180975 0.1825625
[2] 0.0277368
0.4191
0.048768
0.1524
[3]
0.173736
0.1778 0.1164336
0.13335
Refer to MAAE 2300 Fluid Mechanics I Laboratory Exercises, Analysis and Discussion section.
1.0 Determining the theoretical downstream velocity, preceding jump, VT2:
1.1.1 Conservation of Momentum Equation (Eq. 2) is expanded to find upstream velocity, inside
tank (V1):
ḿ1=ḿ2
ρw A 1 V 1 =ρw A 2 V 2
A2V 2
V 1=
A1
whV 2
V 1=
wh1
h2 V 2
V 1=
h1
1.1.2 Downstream velocity, following jump, V2, is unknown. This is found using Bernoulli’s
Equation (Eq. 1):
1
1
2
2
P1+ ρV 1 + ρg z 1=P2 + ρV 2 + ρg z 2
2
2
1
1
Patm + ρ V 21 +ρg z 1=Patm + ρ V 2T 2 + ρg z 2
2
2
1 2
1
V 1+ g z 1= V 2T 2 +g z 2
2
2
1.1.3 Variable substitutions are made; h1 and h2 for z1 and z2 respectively as well as V1 for the
above expression:
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2
1 h2 V 2
1
(
) + g h1 = V 2T 2 +g h2
2 h1
2
2
h V
2
−( 2 2 ) −2 g h1+2 g h2=−V 2
h1
(
)
h2 V T 2 2
2 g h 2−2 g h1 =
−V 2T 2
h1
( )
h2 2
2 g ( h2−h1 ) =V (
−1)
h1
2
T2
V T 2=
√( )
2 g ( h2−h1 )
h2 2
−1
h1
The known variables are substituted into the above equation to determine VT2 (refer to
Appendix B):
Flow 1:
VT2 = 2.99 m/s
Flow 2:
VT2 = 1.67 m/s
1.2 Determining the experimental downstream velocity, preceding jump, VA2:
1.2.1 Volumetric Flow Rate Equation (Eq. 4) is used to determine VA2:
Q= A 2 V A 2
1.2.2 MAAE 2300 Fluid Mechanics I Laboratory Exercises provides that Q=1.38 H 2.5 :
A 2 V A 2=1.38 H 2.5
V A 2=
1.38 H 2.5
A2
V A 2=
1.38 H
wh2
2.5
The known variables are substituted into the above equation to determine VA2 (refer to
Appendix B):
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Flow 1:
VA2 = 1.71 m/s
Flow 2:
VA2 = 0.054 m/s
Both Flow 1 and Flow 2 trials demonstrate the experimental downstream velocities, preceding
the jump, are lower than their theoretical values. This trend is to be expected due to the
unideal conditions in which this experiment was performed. Friction from the water’s contact
with the channel walls and floor would be the main factor here, as well as turbulent flow
throughout the system.
2. Determining and comparing the total heads measured inside tank and in supercritical flow, H1
and H2:
2.1 Determining total head of supercritical flow, H1:
2
P VT1
+h1
H 1= +
ρg 2 g
Flow 1:
H 1=1.22 m
Flow 2:
H 1=0.97
m
2.2 Determining total head of subcritical flow, H2:
2
P V
H 2= + T 2 +h2
ρg 2 g
Flow 1:
H 2=1.23 m
Flow 2:
H 2=0.99 m
The theoretical head totals are higher than the experimental head totals, however the trend
remains the same; there is only a slight increase of head totals before and after the sluice gate.
4. Calculating the total head change across the hydraulic jump for between each flow before
jump and the flow after the jump:
4.1 Total head of flow inside tank, H1:
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2
P V
H 1= + T 1 +h1
ρg 2 g
Flow 1:
H 1=1.23 m
Flow 2:
H 1=0.97
m
4.2 Total head of supercritical flow, H2:
H 2=
P V 2T 2
+
+h2
ρg 2 g
Flow 1:
H 2=1.22 m
Flow 2:
H 2=0.99 m
4.2 Total head of subcritical flow, H1:
H 3=
√
H2
h
2Q22
+ 3+
2
4 g w2 h2
Flow 1:
H 2=0.91 m
Flow 2:
H 2=0.64
m
4.4 The average total head change across the hydraulic jump:
Flow 1:
dH =0.315 m
Flow 2:
dH =0.34 m
Conclusions:
This laboratory experiment has demonstrated a directly proportional relationship
between head totals at any given point in a flow. However, assumptions made in order to use
the simplified equations developed in the MAAE 2300 course, such as frictionless surfaces and
laminar flow, result in inaccuracies between experimental and theoretical flow data.
Appendix A:
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Appendix B:
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