Open Channel Flow Profile Calculation and Analysis: Civil Engineering

This project investigates open channel flow characteristics in a trapezoidal channel, considering varying bed roughness and channel bends. The assignment involves developing an Excel program to calculate gradually varied flow profiles for a steady flow rate of 14.5 m3/s, considering three downstream hydraulic control conditions: a free overfall, a sharp-crested weir, and a vertical sluice gate. The analysis includes determining key parameters such as y, A, R, u, H, Sf, and Fr, and generating flow profiles for each case. The project also involves comparing the computed profiles, discussing the results, and explaining the impact of different hydraulic controls on flow velocity, available head, and Froude number. The results indicate that sluice gates offer the best performance in terms of surface profile and flow velocity, often leading to a hydraulic jump.

OPEN CHANNEL FLOW CHARACTERISTICS
INTRODUCTION
The scenario
In this case, I consider the following given scenario where a trapezoidal channel is considered
such that it gets watered by a river and meanders through to the downstream. Along the channel,
there are physical characteristics such as roughness of the bed and its slopes. The channel seems
to be clean in the upstream section but it gets rough as it approaches its downstream end hence
Manning’s equation of surface roughness is considered. Additionally, due to the bends along the
channel, the profile (which is to be determined) will be affected and that will have to be
accommodated. Meanwhile, the roughness results from the vegetative growth more prevalent at
the downstream end. Otherwise, the other sections of the river are all free of vegetation. Notably,
for the given scenario, the following shall be undertaken:
(A) Deriving a program in excel to calculate gradually-varied flow profiles along this canal
for a steady flow rate of 14.5 m3 /s at the downstream control.
(B) Determining the profile that would occur for each of the three downstream hydraulic
control conditions that are under consideration for this canal:
(1) A free over fall into a drain at the downstream end of the canal reach
(2) Free flow over a rectangular sharp-crested weir at the downstream end of the canal
reach, having a crest length of 7 m and a crest elevation at 1.5 m above the canal bed
("Sharp Crested Iir 2")
(3) Free flow under a 3.5-m-wide vertical sluice gate with the gate set at 0.95 m above
the canal bed at the downstream end of the canal reach
Furthermore, in consideration of the cross-section for a given length of the channel, the profile
will be broken down into those sections hence the following is considered:
(1) The 20-m spacing between cross sections for the first 500 m upstream from the
downstream control
(2) 50-m spacing for the next 1000 m upstream, and
(3) 100-m spacing for the last 4500 m upstream.
Therefore, from the above-given scenario, I present the following as the requirements:
(1) Step by step procedure used in arriving at the final results. Hence the following output
parameters are provided in the program: y, A, R, u, H, Sf, and Fr (Jfccivilengineer No
“page”).
(2) A plot of the profiles for the three cases.
(3) A comparison of the three computed profiles
(4) Discussion of the results and explanation for the same

Notably, the aim of the above-given case is to establish flow profiles for all the given case
conditions by considering normal depth only Yn ()
CALCULATION
Procedure Description
Firstly, I assume the flow is constant along the channel hence the following governing equation
(based on energy and mass conservation) to describe the various profiles given the conditions
(Defina, and Bixio No “page”):
The following equations will come in handy for the given parameters:
(i) H= Z+Y+αU2/2g
(ii) Sf= n2U2/R4/3
(iii) OHe= Cb(αU2/2g)
(iv) H’ = H+average Sf+0’He
(v) Fr= Q/A2g
(vi) U= qX where X is the distance between cross section i and i+1
(vii) A= by +my2
1st Condition: Consider the rectangular weir
But first, I must establish an iterative formula for determining the normal depth and this is given
as (best on specific energy):
Y= (nQ/bs0.5)3/5x(1+2h/b)2/5…(i)
Hence substituting appropriately I end up with this iterative formula :
Yn= y0(1+2yo/b)2/5…..(ii)
Equation (ii) will therefore be used in generating the various values of y
With an increment of h= (2.7987-1.8128)= 0.9859/90=0.010954
2nd Condition: Consider the free overfall
Where the flow is assumed critical hence Fr= 1.0
And the parameters are determined accordingly

3rd Condition: Flow under the sluice gate
Dy/dx= (So-n2Q2/A2R4/3)/ 1-F2 … (4)
Now, using equation (4) above and the fact that the channel is trapezoidal, I can undertake
various calculations to arrive at the profile:
The trapezoidal section:
From Manning’s Equation, I find the average velocity:
V= R2/3S1/2/n
Hence substituting when n=0.06: v= 0.54392/30.00051/2/0.06= 0.2483= 0.25m/s
And when n=0.02, v= 0.54392/30.00051/2/0.02= 0.7449 = 0.74m/s
Froude Number, Fr= αV2/gR cosϕ
= 1.1 x 0.252/9.81 x 0.5439x1 = 0.01289
.
For the friction slope, Sf, I can determine from equation 3
Hence: dy/dx= 1/cos ϕ {(So-Sf)/1-F2=0.033006
5x10-4- Sf= -0.033006(1-0.012892)
Sf= 0.033499

And the available head for the free fall, only velocity head is assumed available (Abdullah and
Faruque 400):
H=v2/2g= 0.252/2x9.81= 3.186x10-3m
Finally, I can replicate the procedure for the three special cases with a slight modification on the
flow rate equations hence this is provided in the excel file
PROFILES
Figure 1: Flow Profile of a free overfall case
Figure 2: Flow Profile of a sharp-crested rectangular Iir
Figure 3: Flow Profile of a vertical sluice gate
DISCUSSION
Looking at the slopes for the three profiles, it can be seen that the sluice gate one has the steepest
slope. There is a marked increase in velocity when sluice gate is placed instead of the free fall
over-fall case. This is due to the narrow constriction considering the area of the sluice gate
making velocity to increase given flow rate is constant. There is also a remarkable increase in the
available head; the least head is provided by the free fall case. Meanwhile, Froude number has
increased by 0.14241 when free-fall case is replaced by the sluice gate. Therefore, it can be
concluded that sluice gates offer the best performance as far as the surface profile and the flow
velocity is concerned. The sluice gate being used is normally accompanied by a transition from
subcritical to supercritical flow, a phenomenon that is technically referred to as a hydraulic jump
(Iahrmedialibrary.Net No “Page”).

CONCLUSION
Finally, this brief report has provided fundamental work on the study of the open channel flow
under different hydraulic conditions. The obtained results provide a sneak preview into further
study of the open channel flows to aid in more economical fluidic system design.
References
Md Abdullah Al Faruque. "Open Channel Flow Velocity Profiles for different Reynolds
Numbers and Roughness Conditions". International Journal Of Research In Engineering And
Technology, vol 03, no. 01, 2014, pp. 400-405. Esat Publishing House,
doi:10.15623/ijret.2014.0301069. Accessed 1 Mar 2018.
Jfccivilengineer. "Sharp Crested Iir 2". 2018,
http://www.jfccivilengineer.com/sharp_crested_Iir_2.htm. Accessed 1 Mar 2018.
Iahrmedialibrary.Net "Vertical Sluice Gate Flow | IAHR Media Library"., 2018,
http://www.iahrmedialibrary.net/776/. Accessed 1 Mar 2018.
Defina, Andrea, and Anna Chiara Bixio. "Mean Flow And Turbulence In Vegetated Open
Channel Flow". Water Resources Research, vol 41, no. 7, 2005. Wiley-BlackIll,
doi:10.1029/2004wr003475. Accessed 1 Mar 2018.