DESIGN

OF

WEIR AND BARRAGES

HYDROLOGY

3

Hydrology Cycle

HYDROLOGY

4

Hydrology

Hydraulic Structure

5

Thiessen Polygon Method

PRECIPITATION AND ITS MEASUREMENT

Procedure

Join the adjacent rain gauge stations A,B,C,D,E etc. of the area

dividing the entire area in a series of triangles as sown in figure.

Draw the perpendicular bisector of each of these lines, as shown

by firm lines in figure.

The area enclosed by these perpendicular bisectors is served by

respective rain gauges. Thus these perpendicular bisectors form

a series of polygons around the Rain-gauge stations and

containing one and only one Rain-gauge station in each polygon.

The entire area within any polygon is nearer to the Rain-gauge

station contained there in than any other.

Find the area of each polygon and multiply it with the rainfall of

the respective Rain-gauge.

Continued….

6

Thiessen Polygon Method

PRECIPITATION AND ITS MEASUREMENT

The Calculations

If P1, P2, P3, P4, P5, and P6 are the rainfalls in station and

A1,A2,A3,A4,A5 and A6 are the areas respectively then average

rainfall of the catchment is;

Pav = (P1A1+P2A2+P3A3+P4A4+P5A5+P6A6+…+PnAn)

A1+A2+A3+A4+A5+A6 +…+An

P = (∑n

i=lPiA1 )/ A

7

Thiessen Polygon Method

PRECIPITATION MEASUREMENT

8

The Calculation

Let the isohyets represent the rainfall P1, P2,…… Pn and areas

between the successive isohyets A1, A2,…… Pn-1 Average

precipitation is then calculated as;

Pav = A1[P1+P2/2]+A2[P2+P3/2]+….+An-1[Pn-1+Pn/2]

A1+A2+A3+A4+….+An-1

P = A1[P1+P2/2]+A2[P2+P3/2]+….+An-1[Pn-1+Pn/2]

A Continued….

PRECIPITATION AND ITS MEASUREMENT

Procedure

From the rain fall data prepare the isohyetal map as shown infigure.

Measure the areas between two successive isohyets with the helpof a planmeter.

Multiply each area by the mean rainfall between the isohyets.

Calculate the average rainfall by the following equation

9

Isohyetal Method

PRECIPITATION MEASUREMENT

10

STREAM FLOW MEASUREMENT

Mean Section Method

In the mean section method, averages of the mean velocities

in the verticals and of the depths at the boundaries of a

section sub-division are taken and multiplied by the width of

the sub-division, or segment.

Q = ∑qi = ∑V.a = ∑ni=1 (Vi-1 + Vi)/2 (di-1 + di)/2

(bi – bi-1)

11

STREAM FLOW MEASUREMENT

Mid Section Method

In the mid section method, the mean velocity and depth

measurement at a sun-division point are multiplied by the

segment width measured between the mid points of

neighboring segments.

Q = ∑qi = ∑V.a = ∑ni=1 Vi.di (bi + 1– bi-1)/2

Empirical Formulae

S. N.

Author Formula in inch units

Formula in Centimeter Unit

1. Ingles formula for Ghat Area R=0.85 P-12 R=0.85 P-30.5

2. Ingles formula for non-Ghat Area

R= (P-7) x P100

R= (P-17.8) x P254

3. Lacey’s formula R = P(1+120F)/PS

R = P(1+304.8F)/PS

4. Khosla’s formula R= P – (T-32)9.5

R= P – (T-32)3.74

5. Parker’s formula for British Isles R = 0.94 P – 14 R = 0.94 P – 35.6

6. Parker’s formula for Germany R = 0.94 P – 16 R = 0.94 P – 40.6

RUN-OFF MEASUREMENT

HYDROGRAPH ANALYSIS

Estimation of Maximum Discharge

i) Physical Indication of past floods

ii) Flood Discharge Formula

iii) Rational Formula

iv) Unit Hydrograph

Flood Discharge Formula

Q = CAn

Q = Flood Discharge

A = Catchments Area

C = Flood Coefficient

n = Flood index

Both ‘C’ and ‘n’ depends upon; (i) catchments characteristics,

(ii) intensity and duration of rainfall and its distribution pattern of

storm over the basin.

14

Rational Formula

Qp = CIA (FPS)

Qp = 1 CIA (MKS)

3.6

Qp = Peak Discharge (m3/sec),

‘I’ = Intensity of Rainfall (mm/hr) for duration more than time of

concentration

‘A’ = Area of drainage basin (km2)

‘C’ = constant (0.3 – 0.8)

RUN-OFF MEASUREMENT

15

Hydrograph Segment

HYDROGRAPH ANALYSIS

Unit Hydrograph

Unit Hydrograph (UH) is “defined as the Hydrograph of surface

runoff of a catchment area resulting from unit depth

(usually 1 cm) of rainfall excess or net rainfall occurring uniformly

over the basin and at uniform rate for a specified duration”.

Unit Hydrograph is a linear model of the catchment which is used

to find out the volume of DSR due to 1 cm of direct surface runoff

or 1 cm of rainfall excess. This is always constant for the

catchment since area of the catchment is constant.

If rainfall comes to the catchment producing 2 cm of rainfall

excess, “the ordinates of the DSR will be twice as great of the

Unit Hydrograph (UH) ordinates and volume of DSR will be two

time the volume of DSR of unit hydrograph”.

HYDROGRAPH ANALYSIS

Derivation of UH from a simple Flood Hydrograph –

(Isolated Storm)

Step 1 From the given flood Hydrograph, “separate the base flow” by

any one of the methods. Most commonly used method to

draw a straight line without much error for simplicity (Figure

enclosed)

Step 2 Determine the volume of DSR Hydrograph by the formula;

“Volume of DSR = ∑QΔt”

A

Step 3 Divide this volume by “known Area of Catchment” to get DSR

volume (depth in cm) i.e., “net rainfall or rainfall excess”.

Step 4 Divide the ordinates of DSR by the depth of DSR Hydrograph

to obtain ordinates of UH.

Step 5 Plot the ordinates of UH of the catchment as per enclosed

figure.

HYDROGRAPH ANALYSIS

Unit Hydrograph Derivation

HYDROGRAPH ANALYSIS

S-Hydrograph (S-Curve)

S-Hydrograph or S-Curve is a Hydrograph which is produced by a

“continuous effective rainfall at a constant rate for indefinite

period”.

It is a “continuous rising curve”, in the form of letter ‘S’, till

equilibrium is reached. At the time of equilibrium, “it will

represent a constant rate of continuous effective rainfall, say Ro

cm per hour”.

At the time of equilibrium, “the S-Curve will represent a runoff

discharge as under”;

Qo = (A x 100 x 100) Ro

100 x 3600

= A Ro cumec

36

(Where A is the catchment area in hectares)

HYDROGRAPH ANALYSIS

Contd…

If the catchment area ‘A’ is in “square kilometers”, the discharge

represented by S-Curve, at the time of equilibrium is given by;

Qo = (A x 1000 x 1000) Ro

100 x 3600

=(AR0) x 100 (cms)

36

= 2.778 A Ro (cms)

(‘A’ = Area of catchment in km2 and Ro = Constant rate of

continues effective Rainfall.)

The S-Hydrograph or S-Curve is constructed by “adding together

number of Unit Hydrographs of unit time duration (T0) spaced at a

unit time duration (T0) (i.e., duration of effective rainfall).

“This is illustrated in the enclosed example were in S-Curve has

been drawn for 6 hours Unit Hydrograph. Area of basin is 311

km2”.

HYDROGRAPH ANALYSIS

HYDROGRAPH ANALYSIS

Computation of S-Hydrograph from Successive Unit Hydrograph

Contd…

HYDROGRAPH ANALYSIS

This discharge of 144 cumecs will be achieved in the above table at 36

hours (which is equal to base period – T0 hours.)

HYDROGRAPH ANALYSIS

Derivation of S-Hydrograph from Series of Unit Hydrograph