Summary Formula For Hydraulic & Hydrology

DCC6213
– HYDRAULIC & HYDROLOGY

FORMULA

JKA, POLITEKNIK PORT DICKSON

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CONTENT / NO. PAGE

TOPIC FLUID CHARACTERISTICS ........................................................................................................... 2
TOPIC OPEN CHANNEL FLOW ................................................................................................................. 3

Open Channel Section Type................................................................................................................. 3
Manning Equation ................................................................................................................................. 4
Best Hydraulic Cross Section .............................................................................................................. 4
Non-Uniform Flow in Channel ............................................................................................................ 4
Type of Flow ........................................................................................................................................... 5
Hydraulic Jump...................................................................................................................................... 5
TOPIC PUMP ............................................................................................................................................... 7
Single Pump............................................................................................................................................ 7
Pumps in Series Arrangement............................................................................................................ 8
Pumps in Parallel Arrangement......................................................................................................... 8
Analysis Graph – Optimum Point ....................................................................................................... 9
Analysis Graph – Operation Point...................................................................................................... 9
TOPIC HYDROLOGICAL CYCLE & WATER BALANCE ......................................................................... 10
TOPIC RAINFALL DATA ANALYSIS ....................................................................................................... 12
Presentation Data ............................................................................................................................... 12
Mean Areal Precipitation................................................................................................................... 12

Arithmetic Mean Method ............................................................................................................... 12
Thiessen Polygon Method ............................................................................................................. 12
Isohyetal Method............................................................................................................................. 13
Missing data.......................................................................................................................................... 13
Arithmetic Mean Method ............................................................................................................... 13
Normal Ratio Method ..................................................................................................................... 13
Quadrant Method ............................................................................................................................ 14
Double Mass Curve.............................................................................................................................. 15
TOPIC STREAMFLOW MEASUREMENT................................................................................................ 16
Velocity Area Method ......................................................................................................................... 16
Mean Method........................................................................................................................................ 17
Mid Method........................................................................................................................................... 17
TOPIC URBAN DRAINAGE DESIGN........................................................................................................ 18

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TOPIC FLUID CHARACTERISTICS S = ( ) Sg = ( )
 
S = Relative density (no. unit)
= ∀
Sg = Specific gravity (no. unit)
 = Density (kg/m3)
m = mass (kg)  = Density (kg/m3)
 = volume (m3)
= =
W = mg
∀
W = weight (N @ kgm/s2)
m = mass (kg) ω = specific weight
g = acceleration gravity (9.81 m/s2) W = weight (N @ kgm/s2)

 = volume (m3)

 = Density (kg/m3)
g = acceleration gravity (9.81 m/s2)

= μ=ρ

 = Dynamic viscocity (kg/ms @ Ns/m2)
Vs = specific volume (m3/kg)  = kinematic viscosity (m2/s)
 = Density (kg/m3)
 = Density (kg/m3)

Specific Weight of water,  = 9.81 kN/m3
 = @ 9.81x103 kN/m3

 = kinematic viscosity (m2/s) ρ water = 1000 kg/m3
 = Dynamic viscocity (kg/ms @ Ns/m2) s water = 1
 = Density (kg/m3)
ρ mercury = 13.6 x 103 kg/m3
s mercury = 13.6

N = kg m/s2 1 m3 = 1000 dm3
Pa = N/m2 1 m3 = 1000 liter
1 kN = 1000 N 1 liter = 1000 ml

1 MN = 106 N 1 year = 365 days
1 GN = 109 N 1 day = 24 hour
1 kg = 1000 g 1 hour = 60 minute
1 g = 1000 mg 1 hour = 3600 second

1 m = 100 cm 1 minute = 60 second
1 m = 1000 mm 1 cm = 10 mm

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TOPIC OPEN CHANNEL FLOW

Open Channel Section Type

Hydraulic gradient, i slope at the bottom or base of the channel
Base slope, So
= tan Ɵ

Wet perimeter, P = − = ∆
Hydraulic radius @
hydraulic mean depth, R
@M
Perimeter of the liquid surface and container cutting in
Depth of flow section, d contact with the liquid
Ratio area of the wet section with a perimeter of the
channel

R =



A = cross sectional area of liquid
P = wet perimeter
depth of flow normal to the direction of flow.

Top width, T width of channel section at the free surface.

Hydraulic depth, D Ratio area of the wet section with a top width of the
channel

D =



A = cross sectional area of liquid
T = Top width

Freeboard Vertical distance between the highest water level
Side Slope, z anticipated in the design and the top of the retaining banks.
It is a safety factor to prevent the overtopping of
structures.

The ratio of the horizontal to vertical distance of the sides
of the channel

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Manning Equation

= / / Q = Discharge (m3/s)
A = Area (m2)
v = Flowrate (m/s)
= . / / N = Manning roughness coefficient
R = Hydraulic radius = A / P
i = Slope gradient

Best Hydraulic Cross Section Trapezoidal section
Rectangular section

y 1 y 1
b n b n

ny ny

b = 2y Q max = ½ [b +2zy] = y √(1+z2)

Non-Uniform Flow in Channel Contuinity equation
Q=AV Q = Discharge (m3/s)
A = Area of pipe (m2)
H = + + y v = Velocity (m/s)
Bernoulli equation
 H = Total energy (m)
P = Pressure head (N/m2)
= +  = Density (N/m3)
v = Velocity (m/s)
y = Flow depth (m)
E = Specific Energy (m)
= + v = Velocity (m/s)
y = Flow depth (m)

Rectangular section q = Discharge per unit width (m3/s/m @ m2/s)
Q = Discharge (m3/s)
= ( rectangular channel) v = Velocity (m/s)
y = Flow depth (m)


q = y1 v1 = y2 v2

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Fr = Froude number
= = v = Velocity (m/s)
√ √ y = Flow depth (m)
yc = Critical depth (m)
/ q = Discharge per unit width (m3/s/m @ m2/s)
= ( )
Emin = Minimum specific energy (m)
= . yc = Critical depth (m)
v = Velocity (m/s)
= + y = Flow depth (m)


Type of Flow Flow Velocity Froude Number Type of flow
Flow Depth < √ <
= √ = Sub Critical, slow
> < √ > Critical
= Super Critical, fast
<

Hydraulic Jump
√
= √ = Fr1 = Froude number before jump (upstream)
v1 = Velocity before jump (upstream) (m/s)
= = y1 = Flow depth before jump (upstream) (m)
√ √ q = Discharge per unit width (m3/s/m @
m2/s)
= √ + −
Fr2 = Froude number after jump
(downstream)
= √ + − v2 = Velocity after jump (downstream) (m/s)
y2 = Flow depth after jump (downstream) (m)
q = Discharge per unit width (m3/s/m @
m2/s)

Fr1 = Froude number before jump (upstream)
Fr2 = Froude number after jump
(downstream)
y1 = Flow depth before jump (upstream) (m)
y2 = Flow depth after jump (downstream) (m)

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= + E1 = Specific Energy before jump (upstream)
(m)
= + = + E2 = Specific Energy after jump (upstream)
√ (m)
hL = Energy loss (m)
= + = +
√ hL = E = Energy loss (m)
) y1 = Flow depth before jump (upstream) (m)
= ∆ = − = ( − y2 = Flow depth after jump (downstream) (m)


∆ = − hj = Height of hydraulic jump (m)
y1 = Flow depth before jump (upstream) (m)
y2 = Flow depth after jump (downstream) (m)

P =  g Q E P = Power loss (watt @ N/m2)

 = Density (N/m3)
g = Acceleration gravity (9.81 m/s2)
Q = Discharge (m3/s)

E = Energy loss (m)

Type of Hydraulic Jump

No Froude Jump Type

1 – 1.7 Undulur jump (mengalun)
1.7 – 2.5 Weak jump (lemah)
2.5 – 4.5 Oscillating jump (berayun)
4.5 – 9.0 Steady jump (tetap)
Strong jump (kuat)
>9.0

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TOPIC PUMP Hsystem = Pressure Head (m)
Hs = Head static (m)
Hsystem = Hs + HL HL = Head loss (m)
HL= 4 f L v2
Major Losses
2gd HL = Head losses (m)
HL= f L Q2 f = Friction coefficient
L = Pipe length (m)
3 d5 v = Velocity (m/s)
POut = p g H Q d = Pipe diameter (m)
Q = Flowrate (m3/s)
=
POut = Power of pump (watt)
 = Density (N/m3)
g = Acceleration gravity (9.81 m/s2)
H = Pump head (m)
Q = Flow rate (m3/s)

η = Efficiency of pump (%)
Pout = Power output = power of pump (watt)
Pin = Power input (watt)

Single Pump

= 1
= 1
= 1

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Pumps in Series Arrangement

= 1 = 2 = 3
= 1 + 2 + 3
= 1 + 2 + 3

Where
Q = Discharge (m3/s)
H = Head (m)
P = Power (watt)

Pumps in Parallel Arrangement

= 1 + 2 + 3
= 1 = 2 = 3
= 1 + 2 + 3

Where
Q = Discharge (m3/s)
H = Head (m)
P = Power (watt)

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Analysis Graph – Optimum Point
Analysis Graph – Operation Point

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TOPIC HYDROLOGICAL CYCLE & WATER BALANCE

ΔS = Changes in storage, m3
= − Δt = Duration of time, s
I = Inflow, m3/s
O = Outflow, m3/s

= [( + ) − ( + )] ΔS = Changes in storage, m3
Δt = Duration of time, s
ΔZ = Changes in elevation, m
I = Inflow, m3/s
O = Outflow, m3/s

= + S1 = Volume before changes in storage, m3
S2 = Volume after changes in storage, m3
ΔS = Changes in storage, m3

ΔZ = Changes in elevation, m
= ΔS = Changes in storage, m3
= − A = Area, m2

L = Volume of losses, m3
P = Volume of precipitation, m3
R = Volume of runoff, m3

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G = Ground water
P = Precipitation
R = Runoff or excess rainfall
P – DRO – E – T- G = ∆S DRO = direct runoff

@ B = Subsurface flow
I = Infiltration
ET = Evapotranspiration
P – ( R + E + T + G) = ∆S E = Evaporation
T = Transpiration
S = Change in storage in the saturated zone
- soil or groundwater

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TOPIC RAINFALL DATA ANALYSIS

Presentation Data Hydrograph

Hyetograph

Mean Areal Precipitation
Arithmetic Mean Method

= + + ⋯ + P = Mean areal precipitation
P1, P2, Pm = Precipitation at surrounding x
station.
M = No. of rain gauge

Thiessen Polygon Method

wi = , ratio area sub-catchment
A
Ai = Total area of catchment
Pi = Precipitation station (rain gauge)
AA, AB, AC…..AM = Area of polygon each sub-
catchment

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Isohyetal Method

Max = Maximum no. between range Isohyet line = 5.0
Isohyet line = 4.0
Min = Smallest no. between range
Pi = Precipitation station (rain gauge)
Ai = Total area of catchment A1, A2, A3…..AM = Area between isohyet line

wi = , ratio area sub-catchment
A

Missing data
Arithmetic Mean Method

= + + ⋯ + Px = Precipitation station x (missing data)
P1, P2, Pm = Precipitation at surrounding x
station.
M = No. of rain gauge

Normal Ratio Method

[ ( + + ⋯ + )] Px = Precipitation station x (missing data)

= P1, P2, PM = Precipitation at surrounding x
station.
Nx = normal annual precipitation at station
x

N1, N2, NM = Normal annual precipitation at
surrounding x station.
M = No. of rain gauge

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Quadrant Method

2 = 2 + 2
1/ 2

= Σ(1/ 2)
di2 = distance from origin
x, y = coordinate rain gauge
wi = ratio distance

PROCEDURE

i. Plot the location of all stations
ii. Build x-y axis through the gauge which

missing data as the origin
iii. Select the four rain gauge stations from

each quadrant and the closest to the
origin
iv. Calculate the distance from each station
of origin

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Double Mass Curve M0 = gradient line1= y
M1 = gradient line2 = xy
Case 1 x

M0 = M1 = Corection, F = M0 (>1.0)

M1

Estimate new data = F x Pyear after changes

Case 2 y
xy
M0 = gradient line1= x
M1 = gradient line2 =

M1 = Corection, F = M0 (< 1.0)
M0 =
M1

Estimate new data = F x Pyear after changes

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TOPIC STREAMFLOW MEASUREMENT
Velocity Area Method

Basic, Q = A V

Q = Discharge (m3/s)
A = Area (m2)
V = velocity (m/s)
Ai = segment width x average vertical depth
= − − ( − + )
Discharge cross section, qi = Segment area Ai x Average velocity Vi
If measure depth at 0.6D, average velocity at vertical depth = velocity stream
If measure depth at 0.2D & 0.8D, average velocity at vertical depth = . + .



Q =  (Ai x Vi)

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Mean Method

Basic, Q = A V

Q = Discharge (m3/s)
A = Area (m2)

V = velocity (m/s)

Discharge cross section, qi = Mean Velocity section Vi x Segment area Ai
= Mean Velocity section Vi x Mean depth section x width

= ( − + ) ( − + ) ( − − )
Q =  (Ai x Vi)

Mid Method

Basic, Q = A V

Q = Discharge (m3/s)
A = Area (m2)

V = velocity (m/s)

Discharge = Velocity section Vi x Segment area Ai
cross section, qi

= Velocity section Vi x depth section di x average width section bi

= (( − + ) − ( + + ))

Q =  (Ai x Vi)

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TOPIC URBAN DRAINAGE DESIGN

1. Return period, T ? years Note:
minor system design ARI ? years (Refer table
major system design ARI 4.1(page 1)

2. Time to travel over surface, to (minute) Note:
(Refer chart
Length of overland flow (m) 14.1 (page
Average surface slope (%) 10))
Type of surface
Note:
Form chart, to = ? minute Equation
14.5 (Page
3. Time in open drain, td (minute) 9)
L (length of open drain)

= V (assume velocity = 1 m/s)

= ? 1 minute = ? minutes

60

4. Time of concentration ,tc

= + d

5. Design average rainfall Intensity, I Note:
i. for i <30 min, used the t = 30 minutes and t = 60 minutes (mm/hour) (Refer
ii. for i >30 min, used the t = tc (mm/hour) Appendix
13.A (page
In (RIt) = a + b In (t) + c (In (t))2 + d (In (t))3 4, 5, 6 ,7))

Fitted coefficient for IDF (a, b, c, d) Location : ?
a=
b=
c=
d=

In (RI30) = a + b In (30) + c (In (30))2 + d (In 30))3 =

(RI30) = mm/hr (shift ex)

In (RI60) = a + b In (60) + c (In (60))2 + d (In 60))3 =

(RI60) = mm/hr (shift ex)

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6. Design intensity, RPt Note:
Equation
= = 13.4 (Page
( ) 2)
= ?
Note:
= = (Refer
( ) Figure 13.3
= ? (page 3)
values of
7. Adjustment factor for storm duration, FD 2 24ℎ)
Data :- (Table 13.3
(Page 2))
Duration: t0 minute
Note:
Depth, P = Equation
13.3 (Page
West coast East coast 2)
Note:
<100 120 150 >180 All Equation
13.4 (Page
Interpolation FD = if not equal value 2)
FD = ? Note:
(Refer
8. Design rainfall depth, for 30 minutes and 60 minutes (mm) chart 14.3
(page 11))
RPd = P30 – FD (P60 – P30)
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9. Rainfall Intensity,

= ( ) = ? mm/hr

9. Runoff coefficients, C
Rainfall intensity, (mm/hr)
Land Category

C=

10. Peak flow, Q ? m3/s

Qd = C x RId x A =
360

RIt – mm/hour
A – hectar

Note:
How to write RId @ RPd

Where;
R = Return period
d = tc (time concentration)
Example:
If return period for 10 year and time concentration for 12 minute
write it 10I12 for intensity & 10P12 for depth
for option design rainfall for 30 minutes and 60 minute
write it 10I30 @ 10I60 for intensity & 10P30 @ 10P60 for depth

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