research design para sa hydraulics. bahala kayo I have no involvement in any action you do in this design...make credits always.:-)

1. TABLE OF CONTENTS
1. PROBLEMS AND ITS BACKGROUND
1.1. INTRODUCTION
1.2. BACKGROUND OF THE STUDY
1.3. STATEMENT OF THE PROBLEM
1.4. SIGNIFICANT OF THE STUDY
1.5. OBJECTIVES
2. REVIEWS AND RELATED LITERATURES AND STUDIES
3. RESEARCH AND METHODOLOGY
4. DOCUMENTATION, ANALYSIS AND PRESENTATION OF DATA
5. CONCLUSION

2. CHAPTER 1: PROBLEMS AND ITS BACKGROUND
This chapter discusses the background ofthe study as well as the objectives, significance ofthe study
set by the group.
1.1 INTRODUCTION
Chezy and Manning equations, the foundation of our presentscience ofopen channel hydraulics, are
not dimensionally homogeneous. The author presents a new derivation of these equations that reveals the
constituent parts of these coefficients, allowing for calculation of more accurate values. Open channel
hydraulics was undoubtedly the first subjectstudied under the broad category offluid mechanics. The Law of
Continuity was the first relation to be developed. Published in 1628 by a Benedictine monk named Bene detto
Castelli,1 who was a pupil of Galileo Galilei, this fluid law is formulated today as:
Equation 1
Q = AV
where:
- Q is volumetric flow rate in ft3 per second;
- A is flow cross-sectional area in ft2; and
- V is average velocity over a cross-sectional area perpendicular to the flow in feetper second.
In the 1760s, French engineer Antoine Chezy compared flow behavior between two streams having similar
characteristics and formulated his observations as:
Equation 2
Vaverage = C(R1/2)So1/2
where:
- C is Chezy's coefficientin ft1/2 per second;
- R is hydraulic radius or area/wetted perimeter in feet; and
- So is the slope ofthe channel bottom (the conceptofan energy slope was notyetin use).

3. After that, numerous investigators - including Strickler, Gauckler,Kutter, Ganguilletand Hagen - sought
to devise other formulas and coefficients by finding analytical expressions thatreplicated observed stream flow
behavior.
Finally, in 1889, Irish engineer Robert Manning postulated a formula that was an average of all the
previous formulas1 and is written as:
Equation 3
Vaverage = (1.486/n)R2/3So1/2
where:
- 1.486/n is Manning's coefficient, in ft1/3/sec.
Chezy's C equals (1.486/n)R1/6 in Manning's equation. Therefore, Manning's coefficient, 1.486/n, has
units of ft1/3/sec. (In the metric system, 1/n is the coefficientso that the numerical value ofn is the same in both
systems). It has always been known that both coefficients, C and n, are numerically variable. They appear to
vary with roughness ofthe channel boundaries and for very shallow and very steep slopes.Further,it is unclear
how seemingly similar channels could have different coefficients. Therefore, investigators had long sought to
learn the componentmakeup ofthe coefficients in order to improve the accuracy ofthe two equations. Both of
these formulae are in common use today. Both equations refer to a single point of measurement along the
course ofthe channel. Thus, they do not explicitly contain a parameter of head loss. Further their applicability
has been clarified; they are for use only with normal flow. In open channel hydraulics, normal flow refers to
where the slope ofthe channel bottom,So,slope ofthe water surface, Sw, and friction slope (orenergy gradient
or energy line), Sf, are all the same. In other words, steady state, where the hydraulic depth is notchanging. In
contrast, if the flow conditions are changing, they would be characterized as gradually varied flow or rapidly
varied flow. The velocity profile ofnormal flow in an open channel is not restricted to being everywhere equal.
In pipes, however, normal flow is defined as the condition where the velocity profile perpendicular to the flow
cross-sectional area is everywhere equal over the area.

4. 1.2 BACKGROUND OF THE STUDY
RobertManning was born in Normandy, France, in 1816, a year after the battle of Waterloo, in which
his father has taken part. He died in 1897. In 1826, he moved to Waterford, Ireland, and worked as an
accountant. From 1855 to 1869, Manning was employed by the Marquis ofDownshire, while he supervised the
construction of the Dundrum Bay Harbor in Ireland and designed a water supply system for Belfast. After the
Marquis' death in 1869, Manning returned to the Irish Office ofPublic Works as assistant to the chiefengineer.
He became chiefengineer in 1874, a position he held it until his retirement in 1891. Manning did not receive
any education or formal training in fluid mechanics or engineering.His accounting background and pragmatism
influenced his work and drove him to reduce problems to their simplest form. He compared and evaluated
seven bestknown formulas ofthe time: Du Buat (1786), Eyelwein (1814), Weisbach (1845), St. Venant (1851),
Neville (1860), Darcy and Bazin (1865), and Ganguillet and Kutter (1869). He calculated the velocity obtained
from each formula for a given slope and for hydraulic radius varying from 0.25 m to 30 m. Then, for each
condition, he found the mean value of the seven velocities and developed a formula that best fitted the data.
The first best-fit formula was the following:
V = 32 [RS (1 + R 1/3 )] ½
However, in some late 19th century textbooks, the Manning formula was written as follows:
V = (1/n) R 2/3 S 1/2
Through his "Handbook ofHydraulics," King (1918) led to the widespread use ofthe Manning formula as we
know it today, as well as to the acceptance that the Manning's coefficient C should be the reciprocal ofKutter's
n. In the United States, n is referred to as Manning's friction factor, or Manning's constant. In Europe, the
Strickler K is the same as Manning's C, i.e., the reciprocal of n.
Antoine Chézy was born at Chalon-sur-Marne, France, on September 1, 1718, and died on October 4,
1798. He retired in 1790 under conditions of extreme poverty. It was not until 1797, a year before his death,
that the efforts of one of his former students, Baron Riche de Prony, finally resulted in Chézy's belated
appointmentas directorofthe Ecole des Ponts etChaussées.Chézy was giventhe task to determine the cross
section and the related discharge for a proposed canal on the river Yvette, which is close to Paris, but at a
higher elevation. Since 1769, he was collecting experimental data from the canal of Courpalet and from the
river Seine. His studies and conclusions are contained in a reportto Mr. Perronetdated October 21, 1775. The
original document, written in French, is titled "Thesis on the velocity ofthe flow in a given ditch," and itis signed

5. by Mr. Chézy,GeneralInspectorofdes Ponts etChaussées.Itresides infile No.847, Ms.1915 ofthe collection
of manuscripts in the library of the Ecole.
In 1776, Chézy wrote another paper, entitled: "Formula to find the uniform velocity that the water will have in
a ditch or in a canal ofwhich the slope is known." This documentresides in the same file [No. 847, Ms. 1915].
It contains the famous Chézy formula:
V = 272 (ah/p)1/2
in which h is the slope, a is the area, and p is the wetted perimeter. The coefficient272 is given for the canal
of Courpaletin an old system ofunits. In the metric system, the equivalentvalue is:
V = 31 (ah/p)1/2
For the river Seine, the value ofthe coefficientis 44. Herschel Clemens translated into English the two
Chézy papers. He was the first person to translate the original documents into English in an accurate way. In
the library of the Ecole, there is another document, without a date, but apparently written after 1775, which
shows that Chézy had applied his formula on the flow in the pipe that conveyed water to the city of Rennes,
France. In this case, the number 17 is the value given to the coefficient.
Current knowledge aboutChézy's work is due to Girard and De Prony. Pierre-Simon Girard was chief
engineer atPonts etChaussées and a member ofthe scientific mission to Egyptsend by Napoleon Bonaparte.
Baron Riche de Prony was one of Chézy's former students. De Prony was the first person to use the Chezy
formula. Later, in 1801, in Germany, Eytelwein used both Chézy and De Prony's ideas to further the
development of the formula. He gave the value of 50.9 [metric] to the coefficient.

6. 1.3 STATEMENT OF THE PROBLEM
1. What is the relationship between Manning’s and Chezy’s roughness coefficient.
2. Who is the mostaccurate formula in a very wide range ofchannels.
1.4 SIGNIFICANCE OF THE STUDY
The study in this subjectand specifically inHydraulics is still essentialuponconducting the experiment.
This study will also be beneficialto the students.This researchis intended to enrich and upgrade criticalthinking
in Hydraulics course by College ofCivil Engineering students and also by motivating ourselves and promoting
good work environment in the workplace when we apply or engage in effective learning and strategies
particularly in different concepts related to the relationship ofMannings and Chezy’s formula. By understanding
the needs ofstudents and the benefits of quality education, students be assured of a competitive advantage.
Moreover, this research will provide recommendations on how to evaluate the performance of a certain
institution in accordance to the study of Manning’s and Chezy’s roughness coefficient.
This experiment addressed itself to: educators, specifically civil engineering students that they
may gain valuable insights on the relationship of Mannings and Chezy’s formula, and by developing the skills
of the students in conceptualizing problems related to the Mannings and Chezy’s formula. This study was a
great opportunity to as students to have an idea on how to proceed to determine the Mannings and Chezy’s
formula correlating each other.
1.5 OBJECTIVES
The activity aims:
 To study the variation of “n “ & “c” as a function of velocity .
 To investigate the relation between “n” & “c”
DEFINITION OF TERMS
 FLUMES:
are specially shaped, engineered structures that are used to measure the flow of water in open
channels. Flumes are static in nature - having no moving parts - relying on restricting the flow of
water in such a way so as to develop a relationship between the water level in the flume at the pointof
measurement and the flow rate.

7.  OPEN CHANNEL FLOW:
is a type of liquid flow within a conduitwith a free surface, known as a channel. The other type offlow
within a conduit is pipe flow. These two types of flow are similar in many ways, but differ in one
important respect: the free surface. Open-channel flow has a free surface, whereas pipe flow does not.
 UNIFORM FLOW:
A uniform flow is one in which flow parameters and channel parameters remain same with
respectto own distance b/w two sections. this type offlow only possible in prismatic channel.
 PRISMATIC CHANNEL:
channel with defined cross section and bed slope.
 NON-UNIFORM FLOW:
A non-uniform flow is one in which flow parameters and channel parameters not remain same with
respect to distance b/w two sections.
 STEADY FLOW:
A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from
point to point but DO NOT change with time.
 UN STEADY FLOW:
If at any point in the fluid, the conditions change with time,the flow is describedas unsteady (In practice
there are always slight variations in velocity and pressure, butif the average values are constant, the
flow is considered steady.
 STEADY UNIFORMM FLOW:
Conditions do not change with position in the stream or with time. An example is the flow ofwater
in a pipe of constant diameter at constant velocity.
 STEADY NON-UNIFORMM FLOW:
Conditions change from point to point in the stream but do not change with time. An example is flow
in a tapering pipe with constant velocity at the inlet - velocity will change as you move along the
length of the pipe toward the exit.

8.  STEADY UNIFORMM FLOW:
At a given instant in time the conditions at every point are the same, but will change with time. An
example is a pipe of constantdiameter connected to a pump pumping ata constantrate which is then
switched off.
 UNSTEADY NON-UNIFORMM FLOW:
Every condition of the flow may change from point to point and with time at every point. For
examples waves in a channel.

9. CHAPTER 2: REVIEW OF RELATED LITERATURE AND STUDIES
In this Chapter an attempt has been made to presenta review ofpastworks by differentresearchers
on the relevant topic. The study ofMannings and Chezy’s roughness coefficientare reported in the following
section.
(J. T. Limerinos in cooperation with the California department of water resources).” Determination of the
Manning Coefficient from Measured Bed Roughness in Natural Channels ”. This report presents the results
of a study to test the hypothesis that basic values of the Manning roughness coefficientof stream channels
may be related to (1) some characteristic size ofthe streambed particles and to (2) the distribution ofparticle
size. These two elements involving particle size can becombined into a single element by weighting
characteristic particle sizes. The investigation was confined to channels with coarse bed material to avoid the
complication ofbed-form roughness thatis associated with alluvial channels composed of fine bed material.
(Fu-Chun Wu; Hsieh Wen Shen;and Yi-Ju Chou).” Variation of Roughness Coefficients for Unsubmerged and
Submerged Vegetation ”. This paper investigates the variation ofthe vegetative roughness coefficientwith the
depth of flow. A horsehair mattress is used in the experimental study to simulate the vegetation on the
watercourses. Test results reveal that the roughness coefficient reduces with increasing depth under the
unsubmerged condition. However, when fully submerged, the vegetative roughness coefficient tends to
increase at low depths but then decrease to an asymptotic constant as the water level continues to rise. A
simplified model based on force equilibrium is developed to evaluate the drag coefficient of the vegetal
element; Manning's equation is then employed to convertthe drag coefficientinto the roughness coefficient.
The data of this study are compared with those of selected previous laboratory and field tests. The results
show a consistenttrend of variation for the drag coefficientversus the Reynolds number. This trend can be
represented by a vegetative characteristic number k. Given information such as the bed slope,the height of
vegetation, and k, one can apply the proposed model to predictthe roughness coefficientcorresponding to
different flow depths.
(John E. Gilley, University of Nebraska - Lincoln and S. C. Finkner, University of Nebraska - Lincoln).”
Hydraulic Roughness Coefficients as Affected by Random Roughness”. Random roughness parameters are
used to characterize surface microrelief. In this study, random roughness was determined following six
selected tillage operations. Random roughness measurements agreed closely with values reported in the
literature. Surface runoff onupland areas is analyzed using hydraulic roughness coefficients.Darcy-Weisbach
and Manning hydraulic roughness coefficients were identified in this investigation on each soil surface where

10. random roughness values were determined. Hydraulic roughness coefficients were obtained from
measurements of discharge rate and flow velocity.

11. CHAPTER 3: RESEARCH AND METHODOLOGY
In this chapter, detailed experimentprocedures have been imposed in order to determine the following data:
1. Flow Rate
2. Bed Slope
3. Area of Flow
4. Wetted Perimeter
5. Hydraulic Radius
6. Flow Velocity
For us to discover the above characteristics, the procedure of determining the manning’s and roughness
coefficient must be performed.
CHEZY’S FORMULA:
Chezy formula can be used to calculate mean flow velocity in conduits and is expressed as
Where
v = mean velocity (m/s, ft/s)
c = the Chezy roughness and conduitcoefficient
R =hydraulic radius of the conduit(m, ft) S
= slope ofthe conduit(m/m, ft/ft)
MANNING’S FORMULA:
The Manning formula states
where
v = mean velocity (m/s, ft/s)
n = manning’s roughness coefficient
R = hydraulic radius ofthe conduit(m,ft)
S = slope ofthe conduit(m/m, ft/ft)

12. HYDRAULICS RADIUS:
The hydraulic radius is a measure ofchannel flow efficiency.
Where:
R = hydraulic radius,
A = cross sectional area of
flow.
P = wetted perimeter.
The greater the hydraulic radius, the greater the efficiency ofthe channel and the less likely the river
is to flood. For channels of a given width, the hydraulic radius is greater for the deeper channels.
ROUGHNESS:
Roughness Is Actually Resistance to Flow
COMPOSITE OR EQUILENT ROUGHNESS:
when the bed & side material and condition are differentthen we use equivalentroughness.
PROCEDURE:
1. switch on the apparatus
2. Wait to stabilize the water in the flume
3. Set the slope of the flume
4. Note the discharge reading.
5. Measure the depth at three different location for one discharge reading.
6. Then change the discharge and measure the depth reading again.

13. APPARATUS:
 S6 glass sided Tilting lab flume with manometric flow arrangement and slope adjusting scale.
 Point gauge (For measuring depth of channel)
RELATEDTHEORY:
FLUME:
Open channel generally supported on or above the ground.

14. CHAPTER 4:
DOCUMENTATION, ANALYSIS AND PRESENTATION OF DATA
OBSERVATION & CALCULATION
SR
#
CHANNEL
BED
SLOPE
FLOW
RATE
Depth of Flow (y)
AREA OF
FLOW
WETTED
PERIMETER
HYDRAULI
C
RADIUS
FLOW
VELOCITY
MANNINGS
ROUGHNESS
COEFFICENT(n
)
CHEZYS
ROUGHNESS
COEFFICENT(c
)y1 y2 y3 Yavj.
m3/sec mm mm mm Mm m2 m m m/sec
1 0.0020 0.007998 30.3 47.5 51 42.93 0.01288 0.385867 0.033379 0.620963 0.007466 75.99959
2 0.0020 0.009795 39.3 53.7 57 50.00 0.015 0.4 0.0375 0.653 0.007673 75.40195
3 0.0020 0.011311 42.3 59.6 61 54.30 0.01629 0.4086 0.039868 0.694352 0.007517 77.75952
4 0.0020 0.012646 46.1 59.4 64.7 56.73 0.01702 0.413467 0.041164 0.743008 0.007176 81.88778
5 0.0020 0.013853 49.6 70 70.4 63.33 0.019 0.426667 0.044531 0.729105 0.007706 77.25788
6 0.0020 0.015996 54.3 66.6 72.8 64.57 0.01937 0.429133 0.045137 0.825813 0.006865 86.91567

15. GRAPHS:

17. CHAPTER 5: CONCLUSION OF THE EXPERIMENT
◦ value of chezy's co-efficientincreases with increase in discharge.
◦ Manning’s co-efficientdecreases with increase in discharge.
◦ There is an inverse relation between manning’s coefficient& velocity.
◦ There is a directrelation between chezy’s coefficient& velocity
◦ There is inverse relationb/wmanning’s co-efficientand chezy’s co –efficienttaken manometric
reading when flow is steady.
◦ If the bed and sides material and conditions are differentthen we take equivalent
roughness coefficient.
◦ The manning formula is simple, accurate and values of for a very wide range ofchannels
are available

18. REFERENCE MATERIALS:
Websites:
1. http://manningsn2.sdsu.edu/manning_history.html
2. http://chezy.sdsu.edu/
3. Experiment# 1, FAISAL SARDAR 2009-CIV-122
http://www.hydroworld.com/articles/hr/print/volume-33/issue-3/articles/dimensionally-
homogeneous-form-of-the-chezy-and-manning-equations.html