This 3-sentence summary provides the key information from the document: The document summarizes a lab experiment on the energy equation for open channel flows. Students derived the specific energy equation and showed that critical depth is a function of flow per width. Data tables show critical depths calculated for two different flow rates, and graphs plot the depth-energy relationships. Calculated critical depths matched theoretical values with small differences likely due to measurement errors.

1. CWR 4633: Water Resources Engineering II Lab
Lab 2 – Energy Equation
Date: June 10th
, 2015
Submitted by:
Group D
Armany Gonzalez
Juan Barrios
Shawn Smyth- shawn_smyth@knights.ucf.edu
Matt Nicastro
Cody Lasseigne
Katy Bradford
Lab Instructor: Hanieh Tabkhivayghan
Water Resources II Lab
CWR - 4633C
Course Instructor: Dr. Medeiros

2. Introduction
Energy conservation plays an integral role in the system; when dealing with open channel
flows. This week’s lab is dedicated to developing a better understanding of the Energy Equation.
The equation mst be slightly altered in order to allow the known components to be used. The
altered version of the energy equation is presented below:
𝑬 = 𝒚 +
𝒗 𝟐
𝟐𝒈
⟹ 𝑬 = 𝒚 +
𝑸 𝟐
𝟐𝒈𝑨 𝟐
⟹ 𝑬 = 𝒚 +
𝑸 𝟐
𝟐𝒈𝒃 𝟐 𝒚 𝟐
(𝟏)
𝐸 = 𝑦 +
𝑄2
2𝑔𝑏2 𝑦2
𝑦 = 𝐷𝑒𝑝𝑡ℎ
𝑄 = 𝑇𝑜𝑡𝑎𝑙 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒
𝑔 = 𝐺𝑟𝑎𝑣𝑖𝑡𝑦
𝑏 = 𝑊𝑖𝑑𝑡ℎ 𝑜𝑓 𝐶ℎ𝑎𝑛𝑛𝑒𝑙
𝐸 = 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦
The final equation above will be applied to both points A and B along the open channel
system. When solving this equation at point B, one can see that the yb value is not known and need
to be determined. In order to do so, a new equation must be introduced that relates the energy at to
different points. The equation that needs to be applied can be found below:
𝑬 𝟏 = 𝑬 𝟐 (𝟐)
An energy diagram can be generated when the discharge values are known. The diagram
displays the energy vs depth values that were calculated in the lab. In this experiment, the chosen
datum was the bottom of the channel. There is a supplementary critical depth value (yc) for every
value of unit discharge. When the discharge is flowing at a depth greater than the critical depth it
is considered to be subcritical. When the discharge is flowing at a depth lower than the critical
depth it is considered to be supercritical. The critical depth is the smallest energy value found on

3. a depth vs energy diagram. One can derive the energy equation with respect to depth in order to
determine the critical depth (dE/dy). The minimum value can then be found by setting the equation
equal to zero, which can be seen below:
𝝏𝑬
𝝏𝒚
= 𝟏 −
𝑸 𝟐
𝟑𝒃 𝟐 𝒈
( 𝟐)(
𝟏
𝒚 𝒄
𝟑
) = 𝟎 ⟹ 𝒚 𝒄
𝟑
=
𝑸 𝟐
𝒈𝒃 𝟐
⟹
𝒚 𝒄 = √
𝑸 𝟐
𝒈𝒃 𝟐
𝟑
(𝟑)
𝒚 𝒄 = √
𝑸 𝟐
𝒈𝒃 𝟐
𝟑
𝑦𝑐 = 𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝐷𝑒𝑝𝑡ℎ
𝑄 = 𝑇𝑜𝑡𝑎𝑙 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒
𝑔 = 𝐺𝑟𝑎𝑣𝑖𝑡𝑦
𝑏 = 𝑊𝑖𝑑𝑡ℎ 𝑜𝑓 𝐶ℎ𝑎𝑛𝑛𝑒𝑙
The objective of this experiment is to derive the specific energy equation and to show that
the critical depth is a function of the flow per width. This lab does an exceptional job in
exemplifying how to integrate the energy equation in channel flow.

4. Procedures and Equipment:
To perform lab #2, the following pieces of equipment were needed:
1. S16 Amrfield Hydraulic Flow Demonstrator (Pictured Below):
2. A timer
For procedure of the lab, the purpose is to change the water flow and the height of the
inflow gate to different heights and flow rates to calculate the changes that occur. Heights and flow
rates can be viewed easily with the measuring sticks pictured below (Picture #1) after adjusting
the gate and water flow.
Picture #1 (right): Amrfield
Hydraulic Flow Demonstrator

5. To begin our experiment, the Flow demonstrator was plugged in and the inlet valve was
opened to allow water to circulate and run through the channel. The depth of the upstream side
was adjusted to a height of 170mm’s while the sluice gate was lowered to 10mm’s. The flow was
then calculated by measuring the amount of time for 20 L of water to accumulate.
For the first series of tests, the changing variable was the height of the sluice gate. The
initial depth of the upstream side was kept constant at 170mm’s while the depth of the sluice gate
began at 10mm’s and increased in increments of three until 4 tests were performed. So in the end,
sluice gate heights of 9, 12, 15 and 18mm’s were tested and the flow channel height was recorded.
For the second series of tests the upstream height was set to 150mm’s and the gate was set
to 10mm’s and a new flow rate was calculated using a time lapse for 20L of water once again.
With a lower initial flow rate from the first series of tests, the sluice gate was again set to values
of 9, 12, 15, and 18 mm’s and the flow depth through the channel and new Y0 values were recorded.
After the collection of the following two data series and flow rates, calculations below can be done
to find energy levels and the critical depth.
Picture #1 (Left): The left side
measuring stick is upstream flow
height. The middle measuring stick
is the height of the sluice gate. The
far right hand measuring stick is
the measured height of water
flowing through the channel.

6. Data
Figure 1: Location of the depths, y0, yg, and y1 (Lab #2 Manual)
When the initial depth of water behind the gate, Y0,is 170 mm and the initial depth of water under
the gate, Yg, is 9mm, the volume of water in the basin reached 20 L after approximately 25 seconds.
𝑄1 (
𝐿
𝑠
) = (
20 𝐿
25 𝑠
)(
1,000,000 𝑚𝑚3
1 𝐿
) = 800,000
𝑚𝑚3
𝑠
Table 1: Recorded depths of flow corresponding to Q1 = 800,000 mm3
/s
yg (mm) y0 (mm) y1 (mm)
9 170 11
12 108 13
15 65 16
18 49 18
When the initial depth of water behind the gate, Y0,is 150 mm and the initial depth of water under
the gate, Yg, is 9mm, the volume of water in the basin reached 20 L after approximately 30 seconds.
𝑄2 (
𝐿
𝑠
) = (
20 𝐿
30 𝑠
)(
1,000,000 𝑚𝑚3
1 𝐿
) = 670,000
𝑚𝑚3
𝑠
Table 2: Recorded depths of flow corresponding to Q2 = 670,000 mm3
/s
yg (mm) y0 (mm) y1 (mm)
9 150 10
12 69 15
15 46 17
18 35 24

7. 𝐸𝑖 = 𝑦𝑖 +
𝑄2
2𝑔𝑏2 𝑦𝑖
2
= 𝑦𝑖 +
𝑄2
2(9810
𝑚𝑚
𝑠2 )(77 𝑚𝑚)2 𝑦𝑖
2
[Equation #]
𝑦𝑐 = √
𝑄2
𝑔𝑏2
3
= √
𝑄2
(9810
𝑚𝑚
𝑠2 )(77 𝑚𝑚)2
3
[Equation #]
Table 3: Critical depth of open channel flow when Q = Q1 = 800,000 mm3
/s
yg (mm) y0 (mm) y1 (mm) E0 (mm) E1 (mm) yc (mm)
9 170 11 170.190 56.469
22.242
12 108 13 108.472 45.555
15 65 16 66.302 37.491
18 49 18 51.291 34.981
Table 4: Critical depth of open channel flow when Q = Q2 = 670,000 mm3
/s
yg (mm) y0 (mm) y1 (mm) E0
(mm)
E1
(mm)
yc (mm)
9 150 10 150.245 65.017
19.762
12 69 15 70.156 39.452
15 46 17 48.600 36.037
18 35 24 39.491 33.552
Table 5: Depth and corresponding specific energy when Q = Q1 = 800,000 mm3
/s
y (mm) E (mm)
y0
170 170.19
E0
108 108.472
65 66.302
49 51.291
y1
18 34.981
E1
16 37.491
13 45.555
11 56.469

8. Table 6: Depth and corresponding specific energy when Q = Q2 = 670,000 mm3
/s
y (mm) E (mm)
y0
150 150.245
E0
69 70.156
46 48.600
35 39.491
y1
24 33.552
E1
17 36.037
15 39.452
10 65.017
Figure 2: Depth of flow plotted with corresponding values of specific energy for each tested discharge
(Q1=800,000 mm3
/s and Q2=670,000 mm3
/s)
0
10
20
30
40
50
60
0 10 20 30 40 50 60 70
Depth,y(mm)
Specific Energy (mm)
y-E Line for Each Value of Discharge
Q1
Q2

9. Figure 3: Critical depth and minimum specific energy for each discharge tested (Q1=800,000 mm3
/s and
Q2=670,000 mm3
/s)
Table 6: Critical depth and minimum specific energy for each value of discharge, Q, as determined from
Figure 3
Q (mm3
/s) yc (mm) Emin (mm)
800,000 22.9 33.4
670,000 17.1 34.9
10
15
20
25
30
35
40
45
50
30 35 40 45 50 55 60 65 70
Depth,y(mm)
Specific Energy (mm)
y-E Line for Each Value of Discharge
Q1
Q2

10. Conclusion
This lab allowed the students to derive the specific energy equation for an open channel
flow for different gate openings and channel depths. This lab also showed that the critical depth is
a function of the flow per width. Tables 3 and 4 above summarize the data collected and analyzed
from the lab. Table 3 shows that the critical depth of an open channel flow when Q = 800,000
mm3/s and a width of 77 mm is equal to 22.242 mm. Table 4 shows that at a slightly lower flow,
Q = 670,000 mm3/s, and the same width, the critical depth is equal to 19.762 mm. This shows that
at a lower flow rate, width held constant, the critical depth is shallower.
As is normally the case when comparing theoretical and calculated values, the calculated
critical depth differs slightly from the theoretical critical depth as shown in Table 6 which is the
critical depth taken from the y-E graph. This table shows that the critical depth for Q of 800,000
mm3/s is 22.9 mm (as compared to 22.242 mm) and for a Q of 670,000 mm3/s is 17.1 mm (as
compared to 19.762 mm). These differences may be because of human error in measurements, the
turbidity of the water flowing through the channel that wasn’t accounted for, or a potential
rounding/calculation error.

11. Lab Questions
1. How critical depth is affected by the Q?
As shown in the results, when the flow rate (Q) is lower, the critical depth is shallower. When the
flow rate (Q) is higher, the critical depth is deeper.
2. Theoretically, what should be the relation between E0 and E1? Do the calculated values
agree with the theory?
Theoretically, under ideal conditions, energy should be conserved (E0 = E1) at a given discharge.
This may be slightly different due to factors not taken into account such as Energy loss due to
Head Loss (friction) and systematic error. We caused the systematic error by measuring Y2 at the
wrong location. We had measured in the middle of the tank were you would have taken the
measurement for a hydraulic jump, however, our final values weren’t altered that drastically
because of this.
3. How do calculated values for critical depth agree with the corresponding values extracted
from the plotted curves? If not, what is the reason?
As stated earlier in the conclusion, the calculated value for the critical depth corresponding to a Q
value of 800,000 mm3/s is very close to the value taken from the graph (difference of .658 mm).
The calculated value for the critical depth corresponding to a Q value of 670,000 mm3/s shows
more of an error when compared to the value extracted from the graph (difference of 2.662 mm).
These differences can be attributed to different things such as human error, machine inefficiency,
additional friction not taken into account, or water turbidity.

12. References
Bedient, Huber, and Vieux. Hydrology and Floodplain Analysis, Fifth Edition. Pearson Education
Inc., 2013.
Finnemore and Franzini. Fluid Mechanics with Engineering Applications, Tenth Edition.
McGraw-Hill, 2002.