lab 5-6 civi 381
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Concordia University *
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Course
381
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
docx
Pages
10
Uploaded by m_kina
EXPERIMENT 5: Flow through a Horizontal Contraction
EXPERIMENT 6 : Flow through a Horizontal Expansion
Date of submission : October 30, 2022
INTRODUCTION
When we evaluate flow that goes inside a horizontal contraction or expansion we
often use the continuity, energy and momentum equations. In this experiment we
will consider the cross section 1 (CS1) and throat cross section (CST). The
objectives of this experiment are : validate the energy relationship and to draw the
total energy gradient line and the hydraulic gradient line.
DESCRIPTION
EXPERIMENTAL
METHODS
In this experiment we got to let the flow in the flume and we have to keepthe flow depth around 12 inches. We have to pivot down the tailgate at the downstream to finish the flume in the experiment 5. But for experiment 6, we have to pivot in the up direction the downstream tailgate. Also, we have to take note of the flow depth, the discharge, the depth at the throat and the downstream depth.
OBSERVATIONS
Table
1
:
general
values
Length of the contraction (L
1
) (m)
0.208
Length of the expansion (L
2
) (m)
0.632
Length of the contraction/expansion transition (L) (m)
0.840
Flume width (B
1
) (m)
0.313
Throat width (B
t
) (m)
0.155
Table
2
:
Experiment
5
Run 1
Run 2
Run 3
Discharge (Q) (m
3
/s)
0.0151
0.0212
0.0269
Initial reading of depth gauge at CS1 (y
1i
) (m)
0
0
0
Final reading at CS1 (y
1f
) (m)
0.141
0.177
0.208
Flow depth at CS1 (y
1
) (m)
0.141
0.177
0.208
Initial reading of depth gauge at CST (y
ti
) (m)
0
0
0
Final reading at CST (y
tf
) (m)
0.882
0.400
0.136
Flow depth at CST (y
t
) (m)
0.882
0.400
0.136
Initial reading of depth gauge at CS2 (y
2i
) (m)
0
0
0
Final reading at CS2 (y
2f
) (m)
0.346
0.406
0.447
Flow depth at CS2 (y
2
) (m)
0.346
0.406
0.447
Stagnation pressure head (cm)
21.6
26.4
29.56
Static pressure head (cm)
10.6
11.1
11.9
Table
3:
Experiment
6
Run 1
Run 2
Run 3
Discharge (Q) (m
3
/s)
0.0268
0.0216
0.0103
Initial reading of depth gauge at CS1 (y
1i
) (m)
0
0
0
Final reading at CS1 (y
1f
) (m)
0.207
0.180
0.146
Flow depth at CS1 (y
1
) (m)
0.207
0.180
0.146
Initial reading of depth gauge at CST (y
ti
) (m)
0
0
0
Final reading at CST (y
tf
) (m)
0.133
0.116
0.106
Flow depth at CST (y
t
) (m)
0.133
0.116
0.106
Initial reading of depth gauge at CS2 (y
2i
) (m)
0
0
0
Final reading at CS2 (y
2f
) (m)
0.142
0.119
0.132
Flow depth at CS2 (y
2
) (m)
0.142
0.119
0.132
Sample
calculations
Continuity :
B
1
v
1
y
1
= B
t
v
t
y
t
= B
t
v
c
y
c
Energy :
y
+ z
+ 𝑣1
2 = y + z
+ 𝑣?
2
1
1
2?
t
t
2?
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Momentum :
0.5*B
1
y*y
1
^2 - 0.5*B
t
y*y
t
^2 - F
w
= Qp*(v
t
– v
1
)
Flow velocity :
v =
√
??
?
Discharge per unit width :
q =
√??
3
Experiment
6
run
#1
q = (Q/B
t
) = (0.0268/0.155) = 0.173 m^3/s
V
1
= (Q/B
1
*y
1
) = (0.0268/(0.313*0.207) = 0.414 m/s
Vt = (Q/B
t
*yt) = (0.0286/(0.155*0.133) = 1.300 m/s
V
2
= (Q/B
1
*y
2
) = (0.0268/(0.313*0.142) = 0.603m/s
E1 = y1 + v1^2/(2*g) = (0.207 m) + (0.414^2)/(2.9.81) = 0.216 m Et = yt + vt^2/(2*g) = (0.133 m) + (1.300^2)/(2*9.81) = 0.219 m E2 = y2 + v2^2/(2*g) = (0.142 m) + (0.603^2)/(2*9.81) = 0.203 m
Yt = yc
Yt theory = ((q^2)/(9.81))^(1/3) = ((0.173^2)/9.81))^(1/3) = 0.145 m
?
Difference with Yt experimental
0.145 – 0.133 = 0.012
In % = 0.012/0.145 = 8.26%
Fw = 0.5*B
1
y*y
1
^2 - 0.5*B
t
y*y
t
^2 - Qp*(v
t
– v
1
)
= (0.5*(0.313*9810*(0.207^2)) – (0.5*9810*(0.133^2)) –
(0.0268*1000*(1.300-0.414)
= 28.58 N
Table
4
:
Calculations
of
given
table
(see
excel
sheet
for
details
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DISCUSSION
a)
Table
5
:
Evaluation
of
Yt
(exp)
and
Yt
(theory)
Variable
Experiment 5
Experiment 6
Run
#1
#2
#3
#1
#2
#3
q (m^3/s)
0.097
0.137
0.174
0.173
0.139
0.066
Yt (experimental) (m)
0.882
0.400
0.136
0.133
0.116
0.106
Yt(theory) (m)
0.099
0.124
0.145
0.145
0.126
0.077
difference (m)
0.783
0.276
0.009
0.012
0.010
0.029
difference in %
88.79
69.00
6.43
8.26
7.62
27.70
b)
In experiment 5, the difference in % of the Yt theory and experimental
are 88.79% for run 1, 69% for run 2 and 6.43% for run 3. In experiment
6, the difference in % of the Yt theory and experimental are 8.26% for
run 1, 7.62% for run 2 and 27.70% for run 3. We see the huge
differences in percentage specially for run 1 and 2 for experiment 5 and
run 3 of experiment 6. These differences can be due of wrong gauges
used or human error such as someone not reading the manometer
properly.
c)
Figure 1 : experiment 5
Figure 2 : experiment 6
Experiment 5
1
0.9
0.8
0.7
0.6
Yc line
0.5
0.4
Total energy line
water surface profile
0.3
0.2
0.1
0
0.0000.2000.400
E (m)
0.600
0.800
1.000
0.250
0.200
0.150
E (m)
0.100
0.050
0
0.000
0.05
Yc line
total energy line water surface profile
0.15
0.1
0.2
0.25
Experiment 6
y (m)
y (m)
d)
Table
6 :
Values
of
Fw
Variable
Experiment 5
Experiment 6
Run
#1
#2
#3
#1
#2
#3
Fw (N)
-557.41
-72.68
29.15
28.58
21.84
20.05
We can see huge values and negatif values for run 1 and run 2 for experiment 5. These were probably cause by human error.
e)
With table number 2 we can see that the more the stagnation pressure head is high (run 1 : 21.6 run 2: 26.4 run 3 : 29.56) the v2 is going to be higher (0.139 , 0.167 and 0.192).
CONCLUSION
To conclude, all the objectives were made, we verified the energy equation and we drew the total energy gradient and hydraulic gradient line.
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REFERENCES
Civi lab manual