sample calcualtions for hydraulic

1. ASSIGNMENT
CIVIL HYDRAULICS
MODULE 1
JOSE CARLOS PONCE
STUDENT NO. 1050313
01/09/2019

2. JCPONCE
1050313
1
Contents
TASK 1............................................................................................................................................... 2
Assumptions and General Calculations .......................................................................................... 2
Cross Sections Approximation........................................................................................................ 3
Water Depth and Velocities Comparisons...................................................................................... 4
Relevant Equations and Result Discussion...................................................................................... 5
TASK 2............................................................................................................................................... 6
Part a: Calculating the height of the gates opening ........................................................................ 6
Assumptions and General Information....................................................................................... 6
Free Flow assumption................................................................................................................ 6
Part b: Flow at 10% less ................................................................................................................. 8
Part c: Possible effects of this alteration ........................................................................................ 8
Water levels in the weir pool and the flow in the old Thomson river.......................................... 8
TASK 3............................................................................................................................................... 9
Part A: Comparing calculation methods ......................................................................................... 9
Part B: Characterizing the Flow...................................................................................................... 9
Part C: HEC-RAS Model analysis................................................................................................... 10
Part D: Rainbow Creek flow analysis ............................................................................................ 10

3. JCPONCE
1050313
2
TASK 1
Assumptions and General Calculations
By comparing the flow depths and velocities at the Old Thomson river and Rainbow creek, before and
after the implementation of flow regulation structures (Cowwarr Weir), an impact assessment can be
generated to report the weir performance.
The Section 4b and 4a data is presented in the briefing shows the typical flow rate values and slope of
each body of water. Table 1 summarises this data.
Table 1. Provided Data
BODY OF
WATER
Q NATURAL
(ML/D)
Q NATURAL
(M3/S)
Q CURRENT
(ML/D)
Q CURRENT
(M3/S)
CHANNEL
SLOPE
OLD
THOMSON
378 4.38 118 1.37 0.0011
RAINBOW
CREEK
189 2.19 59 0.68 0.0020
To generate an adequate analysis is necessary to state some practical assumptions that would not
only made possible the work but more practical for the purposed of the activity. Table 2 shows a
summary of this statements and their use during the analysis.
Table 2. Necessary Assumptions
ASSUMPITONS PRACTICAL APPLICATION
UNIFORM FLOW
By defining uniform flow is possible to apply
manning’s equation 𝑄 =
1
𝑛
∙ 𝐴 ∙ 𝑅2/3
∙ 𝑆1/2
and
express the flow in terms of the unknown
variable that is the depth 𝑦.
THE BED-SLOPE AND CROSS-SECTION
MAINTAIN CONSTANT ON BOTH CHANNELS
ALONG THEIR WHOLE LENGTH
With this condition, the uniform flow statement
is reinforced and is possible to establish a
constant manning’s n value.
GEOMETRICAL APPROXIMATION TO
CALCULATE THE AREA
Because both cross-sections are irregular, is
necessary to approximate them to a possible
array of know geometrical figures such as
trapezoids, triangles and squares.
VALUE OF MANNING’S N IS THE SAME IN THE
WHOLE CHANNEL
By stating the same value of manning’s n, the
complexity of the analysis is reduced because it
is assuming that the energy dissipate due to
friction is constant through the whole channel.
CHANNEL WATER LEVELS ARE NOT GOING TO
EXCEED THE LEVEE MARKS.
The provided data shows two station points
were the typical levee water depth values in the
channels maintain. Assuming the flow would not
increase further than the median, the cross
section necessary to uphold it would be close to
this marks. This would simplify the geometrical
analysis.

4. JCPONCE
1050313
3
Before commencing the geometrical analysis, is necessary to calculate the Manning’s coefficient for a
natural channel in each cross-section. The modified Cowan method for determining channel
roughness is going to be applied. The equation for it is:
𝑀𝑎𝑛𝑛𝑖𝑛𝑔; 𝑠 𝑛 = (𝑛𝑏 + 𝑛1 + 𝑛2 + 𝑛3 + 𝑛4)𝑚
Were:
𝑛𝑏 = 𝐶ℎ𝑎𝑛𝑛𝑒𝑙 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
𝑛1 = 𝐷𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑖𝑟𝑟𝑒𝑔𝑢𝑙𝑎𝑟𝑖𝑡𝑦
𝑛2 = 𝑉𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛
𝑛3 = 𝐸𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑜𝑏𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛𝑠 𝑒𝑥𝑐𝑙𝑢𝑑𝑖𝑛𝑔 𝑣𝑒𝑔𝑒𝑡𝑎𝑡𝑖𝑜𝑛
𝑛4 = 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑉𝑒𝑔𝑒𝑡𝑎𝑡𝑖𝑜𝑛
𝑚 = 𝐷𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑚𝑒𝑎𝑛𝑑𝑒𝑟𝑖𝑛𝑔
Table 3. Manning's Coefficient Calculation
CHANNEL NB N1 N2 N3 N4 M MANNING’S
N
OLD
THOMSON
0.024 0.012 0.003 0.005 0.025 1.0 0.07
RAINBOW
CREEK
0.024 0.006 0.003 0.005 0.01 1.0 0.05
Table 3 Shows the typical Manning’s n to be used during the flow rate calculations for each channel.
This values are derived from the case study briefing and photos that show the state of each body of
water.
Cross Sections Approximation
The areas shown in figure 1.A are the geometrical assumptions made. The use of trapezoidal figures,
triangles and squares were used.
A1
A2
A3
A4
Figure 1. Old Thomson Cross Section (A) Geometrical Approximation (B)

5. JCPONCE
1050313
4
The areas shown in figure 2.A are the geometrical assumptions made. The use of trapezoidal figures
were used.
Table 4. Old Thomson Flow calculation per Geometrical Section
Table 5. Rainbow Creek Flow calculation per Geometrical Section
Tables 4 and 5 shows the values of flow each section provide considering each geometry. With this
information is possible to estimate a value of water depth, by knowing approximately the section were
the amount of flow needed would be supplied.
Water Depth and Velocities Comparisons
Table 6. Flow regulation impact results
VARIABLES OLD THOMSON RIVER RAINBOW CREEK
Y NATURAL (M) 1.16 0.75
Y CURRENT (M) 0.62 0.31
VELOCITY NATURAL (M/S) 0.37 0.44
VELOCITY CURRENT (M/S) 0.29 0.40
AREA NATURAL (M2) 11.78 4.97
AREA CURRENT (M2) 4.72 1.68
Areas Area(m2) Perimeter (m) Q(m3/sec)
A1 Trapezoid 1 24.405 5.019 33.669
A2 Trapezoid 2 2.478 1.263 1.867
A3 Trapezoid 3 3.372 5.502 1.169
Triangle 1 0.345 2.319 0.047
Triangle 2 0.282 1.904 0.038
Square 1 0.510 1.700 0.110
A4
Figure 2. Rainbow Creek Cross Section (A) Geometrical Approximation (B)
A1 A1
A2
A3
A4

6. JCPONCE
1050313
5
Relevant Equations and Result Discussion
To obtain the value for each water depth level, an expression in terms of y was necessary. The
following is the flow rate expression in terms of y, for a trapezoid channel. The values of theta were
obtain from the coordinate system.
𝑄 =
1
𝑛
∙
[𝑦 (
𝑏
2 +
𝑦
tan 𝜃1
) + 𝑦 (
𝑏
2 +
𝑦
tan 𝜃2
)]
5/3
[𝑏 + (
𝑦
sin𝜃1
+
𝑦
sin 𝜃2
)]
2/3
∙ 𝑆1/2
To obtain the value of 𝑦 , the first step is to calculate the value of the flow for each defined area, to
then know which section is the one to be analysed. This value of flow to be iterated is equal to the
difference between the median flow and the accumulated in the previous sections.
The values showed on table 6 verifies that the used of the Cowwarr weir is dissipating energy, thus
the values of water depth and velocities are decreasing on both channels.
Figure 3. Water depth Level Old Thomson Natural (A) Water depth Level Old Thomson Current (b)
Figure 4. Water Depth Level Rainbow Creek Natural (A) Water Depth Level Rainbow Creek Current (B)

7. JCPONCE
1050313
6
TASK 2
Part a: Calculating the height of the gates opening
Assumptions and General Information
As stated in the briefing, the environmental flow to be controlling the Old Thomson River is equal to
2.0 𝑚3
𝑠−1
. With this information to preserve the upstream flow of the weir pool, the value expected
for the Rainbow Creek need to be 3.0 𝑚3
𝑠−1
.
Due to the fact that is only on gate that control the downstream flow for both of the channels, the Old
Thomson river rating curve provides a water surface elevation in function of the total flow rate. So
checking for 2.0 𝑚3
𝑠−1
the estimated water surface 𝑦1 = 94.24 − 93 = 1.24 𝑚 where 93 is the
channel’s bed DATUM. A practicle
Table 7 summarises the assumptions needed to estimate a value for the gate opening.
Table 7. Task 2 Assumptions
ASSUMPTIONS PRACTICAL APPLICATION
THE 3 GATE DOORS CAN BE TAKEN AS ONE
WITH A WIDTH O B= 6M
This is important because its going to maintain
the flow distribution as previously stated
THE CHANNEL BEHAVES AS A MAN MADE
CHANNEL A FEW METERS AFTER THE GATE
WITH THE SAME SLOPE AS UPSTREAM
To prove that the flow is going to behave in
accordance of the sluice gate equations and the
use of Froude number
ASSUME FREE FLOW INITIALLY This helps because it enables the use of the
hydraulic jump equations.
ASSUME A SQUARE CROSS SECTION FOR THE
CHANNEL A FEW METERS UPSTREAM
To simplify the flow calculations and the normal
depth.
FRICTIONAL EFFECTS ARE NEGLIGIBLE The changes in water depth are in a short
distance
FLOW UPSTREAM IS STEADY The weir pool has an almost static flow.
Free Flow assumption
Figure 5. Free flow assumption and Hydraulic Jump
To calculate a value of a in this context, the following equations are used:
𝑄 = 𝐶𝑑 ∙ 𝑏 ∙ 𝑎 ∙ √2 ∙ 𝑔 ∙ 𝑦1
𝑦2 = 0.61 ∙ 𝑎
(E.Q1-Flow on a sluice gate)
(E.Q-2water depth after the gate)

8. JCPONCE
1050313
7
𝑣2 =
𝑄
𝑏 ∙ 𝑦2
𝐹𝑟2 =
𝑣2
√𝑔 ∙ 𝑦2
𝑦3
𝑦2
=
−1 + √1 + 8𝐹𝑟2
2
2
𝑄 =
1
𝑛
∙
[𝑏𝑦𝑛]5/3
[𝑏 + 2𝑦𝑛]2/3
∙ 𝑆1/2
The general idea is to prove that with the gate opening calculated, the conjugated height 𝑦3 is bigger
than the normal depth to show that a free flow is occurring. If its smaller then the flow is drowned.
For the value of discharge coefficient 𝐶𝑑, it is assume a value of 0.58 as provided in figure 6. This is the
maximum value shown in figure 6. Then its possible to calculate gate opening a from equation 1
3 = 𝐶𝑑 ∙ 𝑏 ∙ 𝑎 ∙ √2 ∙ 𝑔 ∙ 𝑦1 = 0.58 ∙ 6 ∙ 𝑎 ∙ √2 ∙ 9.81 ∙ 1.24
𝑎 = 0.175𝑚
Then calculate 𝑦2, 𝑣2 and 𝐹𝑟2
𝑦2 = 0.61 ∙ 0.175 = 0.1067𝑚
𝑣2 =
3
6 ∙ 0.1067
= 4.68 𝑚/𝑠
(E.Q-3velocity for y2)
(E.Q-4Froude Number)
(E.Q-5Hydraulic Jump)
(E.Q-6Manning’s equation)
Figure 6. Discharge Coefficient for free and Drowned outflows. Obtained from Cengel and Cimbala.

9. JCPONCE
1050313
8
𝐹𝑟2 =
4.68
√9.81 ∙ 0.1067
= 4.57 > 1 𝑡ℎ𝑒𝑛 𝑖𝑠 𝑠𝑢𝑝𝑒𝑟𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑓𝑙𝑜𝑤
With this values and the hydraulic jump equation (E.Q-5) is possible to calculate a conjugated depth.
Once obtained is possible to compare it against the normal depth that its obtained by iterating E.Q-6
in terms of y.
𝑦3
𝑦2
=
−1 + √1 + 8𝐹𝑟2
2
2
= 5.98
𝑦3 = 5.98 ∙ 0.1067 = 0.64 𝑚
𝑦𝑛 = 0.43𝑚
𝑦3 > 𝑦𝑛 ∴ 𝑓𝑟𝑒𝑒 𝑓𝑙𝑜𝑤 𝑎𝑠𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑖𝑠 𝑐𝑜𝑟𝑟𝑒𝑐𝑡
Part b: Flow at 10% less
The flow registered is 10% less than the environmental ones because the calculations are based on a
no energy loss assumption. Some factors of the phenomena may be frictional loss on the channel’s
bed, the energy dissipation caused by the sluice gate and other environmental factors that generate
changes in the energy heads. Nonetheless the flow initiates at the projected ones but then due to the
previous factors their value start lowering.
Part c: Possible effects of this alteration
Water levels in the weir pool and the flow in the old Thomson river
The water level on the weir pool should increase due to the conservation of mass principle. Because
the reduction in the rainbow creek flow does not alter the upstream flow, the actual effect would be
presented in the downstream of the Old Thomson river. This increase in flow is going to increase the
water depth level thus the weir pool height.

10. JCPONCE
1050313
9
TASK 3
Part A: Comparing calculation methods
Table 8. Old Thomson River Comparison
OLD THOMSON RIVER COMPARISON FLOW RATE 2 M3/S
METHOD Water Level (m) Velocity (m/s) Area (m2) FROUDE
GEOMETRICAL ANALYSIS 0.86 0.25 7.8 0.1
HEC-RAS 1.03 0.24 8.27 0.1
Table 9. Rainbow Creek Comparison
RAINBOW CREEK COMPARISON FLOW RATE 3 M3/S
METHOD Water Level (m) Velocity (m/s) Area (m2) FROUDE
GEOMETRICAL ANALYSIS 0.81 0.49 6.09 0.18
HEC-RAS 0.97 0.49 6.09 0.21
The geometrical analysis used in tables 8 and 9 is the same used in task1. So is important to clarify
that the same geometrical distribution shown in figures 1 and 2 was used. From the table is possible
to see that the geometrical analysis was a good estimation. Even though it varies 17 cm for the Old
Thomson and 16 for Rainbow creek in de normal depths, velocities and areas are almost identical on
both cases.
This differences may be caused by several reasons. A quite significant is the difference in parameters
between both methods, such as the manning’s coefficient. also the geometrical analysis plots a single
normal depth on a typical section while HEC-RAS is generating a whole water surface profile along the
totality of the stations. In addition the inaccuracy of generating an exact geometric approximation
alters the values of the wetted perimeter and the cross section area, both directly proportional to the
water depth, this meaning that when the values of the perimeter and area are smaller the water level
would also get lower.
Part B: Characterizing the Flow
The Froud number shown on tables 9 and 8 was calculated through the next equation:
𝐹𝑟 =
𝑣
√𝑔 ∙ 𝐷𝑚
The hydraulic depth 𝐷𝑚 is used instead of the water depth because is an irregular cross-section.
𝐷𝑚 =
𝐴
𝐵
Were B is the water surface level width, A is the total area of the cross-section. For the Old Thomson
B is equal to the trapezoid 1 base. For the rainbow creek the water surface is estimated graphically
based on figure 2. The total areas are tabulated on tables 9 and 8.
VALUES OLD THOMSON RIVER RAINBOW CREEK
AREA (M2) 7.8 6.09
B (M) 12.39 8.3
DM (M) 0.63 0.73
FLOW CHARACTERISATION 0.1< 1 thus Subcritical 0.18< 1 thus Subcritical

11. JCPONCE
1050313
10
Part C: HEC-RAS Model analysis
i. The HEC-RAS data for downstream water depths probably based its calculation on a normal
depth approach. this can be supported by comparing the values of the water surface elevation
and the energy gradient elevation. In station 0.97 both values are the same. This can only be
possible if the channel was consider long enough for the flow to reach from sub critical to
normal depth as shown in the Froude number.
ii. To consider this approach not suitable, the flow should not behave as one of the following:
• If the flow isn’t uniform of steady, there would not be possible to approximate the
depth to normal depth, due to the constant change in energy.
• Another situation would be if the flow is supercritical. As stated in the briefing, the
Old Thomson river slope is mild one so if the case is presented that the flow is
supercritical, the water depths would constantly be increasing until a hydraulic jump
is generated.
iii. It can be a good approach to try and find a critical depth through the channel. It can be
measured on points were the slope change from mild to steep on a considerable distance
between two stations. A good idea could be to construct a dissipation structure such as a
broad crested weir. This is because it is know that the water depth on top of the weir is equal
to the critical depth. This does not depend on the channel being sufficiently long or the flow
being uniform.
Part D: Rainbow Creek flow analysis
Analysing the graphical representation of the results, is possible to estimate that the station that
present the closes depth too the critical one would be 220.62. this is also supported by the head loss
between the energy gradient elevation and the water surface elevation. This means that at this point
there is more kinetic energy than potential one. To support this statement the velocity at this point is
the highest in the whole creek and also the Froude number is the closest to 1.