Assignment on the Importance of Hydro graph

Introduction
Hydrograph are used to determine surface runoff from uniform excess rainfall that would be
distributed temporally and spatially over the whole watershed for the excess rainfall duration.
Therefore, unit hydrograph would be used to determine surface runoff from a unit uniform
excess rainfall that would be distributed temporary and spatial over the whole watershed for the
excess rainfall duration. A unit hydrography will be called instantaneous when the excess rainfall
duration would be infinitely small (Aricò, Corato, Tucciarelli, Meftah, Petrillo and Mossa, 2010).
The method of hydrograph would be used when considering temporal and spatial variation of
rainfall or storage/routing effects. The design of detention of storm water, pump stations,
facilities of water quality and drainage system of large storm water would mainly relay on flow
routing.
The flood wave movement down a channel would exhibit a storage discharge loop relation,
where it would be simulated using Muskingum model. The nonlinear three parameters of
Muskingum model were appraised by Gill, Singh and Tung. Gill applied a method of segmented
curve to assess the three parameters and determined an optimal value of N = 1/2.347. Tung
applied concept of four parameters and determined an optimal value of N that was varying
between 1/1.7012 and 1/2.3470. Singh determined a higher moderate value of N of about 0.2 and
realized that the accuracy of the model would depend on parameter c scale.
The kinematic wave equation could be modified in order to simulate its hysteretic phenomenon
(Harman, Reeves, Baeumer and Sivapalan, 2010);
q = cN * sN – c1(ds/dt)
Where; c1 = constant
Substitution of ds/dt to the above equation;
s = 1/c[c1i + (1 + c1)q]1/N
Where; N = 1, therefore it would reduce to form a model of Muskingum

Terms used in determine unit flow rate
a. Storm duration, intensity and frequency
The rainfall depth normally would be determined by storm duration design. Time concentration
would be defined when the design of the duration would produce an maximum peak runoff.
Rainfall intensity would represent an average intensity of rainfall a specific duration time (t)
b. Spatial distribution
Its characteristic would depend on the large size of the catchment.
c. Temporary distribution
It would be used to distribute rainfall within the storm designed area. It has a significant shape
effect of the hydrograph runoff and peak discharge.
d. Rainfall excess
Rainfall excess is the amount of rainfall that would remain when rainfall losses that include
infiltration, evaporation and depression storage would be subtracted from it. This would be the
capacity of rain that would produce a runoff.
Kinematic wave method
The method of kinematic waves is regarded as the method of hydraulic routing that helps in
routing runoff through pipes and channels and across planar surface. It is only valid when
applied on one dimensional planar surface overland flow. Its application is not enhanced on
urban drainage.
Importance of kinetic wave
1. It offers nonlinear responses without involving in costly solution and excessively
complicated procedure.
2. It has considerable adjusted parameters of ∝∧β that helps in accounting for basin and
flows complexities
3. The simulated river flows and overland would be approximated to the actual responses
due to complexity nature of the drainage basin and mathematic simplification to enable
the model be economical to execution. This has been proven to be efficient and accurate
method for water runoff simulation

The features of kinematic wave would dominate dynamic wave considering flows having less
Froude number than or equal to 2 (F ≤ 2).
Kinematic wave momentum equation;
S0 = Sf ................................................... (1)
The momentum equation would be equivalent to the relationship below between area of low, A
and discharge Q.
A = α Qβ .............................................. (2)
Applying Manning equation
Q = √Sf
n R
2
3 A (metric units) .............. (3a)
Q = 1,49∗√Sf
n R
2
3 A (English units) .............. (3b)
A = [ n P
2
3
√Sf ]3
5
¿ Q
3
5 or ∝= [ n P
2
3
1.49∗√ Sf ]3
5
∗Q
3
5 ........................ (4)
Therefore;
β= 5
3 =1.667 ........................... (5)
The relationship can also be represented as;
q = α y β
Where; q = flow rate per unit width and y = water depth
Therefore, velocity, V = α y β−1