Formula Sheets: Treatment of Water | Environmental Engineering - Civil Engineering (CE) PDF Download

 Page 1


GA TE CE 2026 F orm ula Sheet: W ater and W aste W ater Qualit y
and T reatmen t
1. W ater Qualit y Index (W QI)
• General form of W QI (w eigh ted arithmetic index):
W QI =
n
?
i=1
W
i
·q
i
where:
– q
i
=
(
Ci
Si
)
×100 , qualit y rating for the i -th parameter
– C
i
: Measured concen tration of the i -th parameter
– S
i
: Standard p ermissible v alue for the i -th parameter
– W
i
=
k
Si
, w eigh t of t he i -th parameter
– k : Prop ortionalit y constan t (often tak en as 1 for simplicit y)
–
?
W
i
= 1
2. W ater Requiremen t
• P er capita w ater demand:
Q
total
=P ·q
where:
– Q
total
: T otal w ater demand (liters/da y)
– P : P opulation
– q : P er capita demand (liters/capita/da y)
• Maxim um daily demand:
Q
max daily
= 1.8·Q
a vg daily
• P eak hourly demand:
Q
p eak hourly
= 2.7·Q
a vg daily
3. W ater Distribution System
• Con tin uit y equation for pip e flo w:
Q =A·v
where:
– Q : Flo w rate (m
3
/s)
– A : Cross-sectional area of pip e (m
2
)
– v : V elo c it y of flo w (m/s)
• Hazen-Williams form ula for head loss:
h
f
= 10.67·
L·Q
1.852
C
1.852
·D
4.87
where:
– h
f
: Head loss (m)
– L : Pip e length (m)
– Q : Flo w rate (m
3
/s)
– C : Hazen-Williams co e?icien t (dimensionless)
– D : Pip e diameter (m)
1
Page 2


GA TE CE 2026 F orm ula Sheet: W ater and W aste W ater Qualit y
and T reatmen t
1. W ater Qualit y Index (W QI)
• General form of W QI (w eigh ted arithmetic index):
W QI =
n
?
i=1
W
i
·q
i
where:
– q
i
=
(
Ci
Si
)
×100 , qualit y rating for the i -th parameter
– C
i
: Measured concen tration of the i -th parameter
– S
i
: Standard p ermissible v alue for the i -th parameter
– W
i
=
k
Si
, w eigh t of t he i -th parameter
– k : Prop ortionalit y constan t (often tak en as 1 for simplicit y)
–
?
W
i
= 1
2. W ater Requiremen t
• P er capita w ater demand:
Q
total
=P ·q
where:
– Q
total
: T otal w ater demand (liters/da y)
– P : P opulation
– q : P er capita demand (liters/capita/da y)
• Maxim um daily demand:
Q
max daily
= 1.8·Q
a vg daily
• P eak hourly demand:
Q
p eak hourly
= 2.7·Q
a vg daily
3. W ater Distribution System
• Con tin uit y equation for pip e flo w:
Q =A·v
where:
– Q : Flo w rate (m
3
/s)
– A : Cross-sectional area of pip e (m
2
)
– v : V elo c it y of flo w (m/s)
• Hazen-Williams form ula for head loss:
h
f
= 10.67·
L·Q
1.852
C
1.852
·D
4.87
where:
– h
f
: Head loss (m)
– L : Pip e length (m)
– Q : Flo w rate (m
3
/s)
– C : Hazen-Williams co e?icien t (dimensionless)
– D : Pip e diameter (m)
1
• Darcy-W eisbac h equation for head loss:
h
f
=f ·
L
D
·
v
2
2g
where:
– f : F riction factor (dimensionless)
– v : Flo w v elo c it y (m/s)
– g : A cceleration due to gra vit y (9.81 m/s
2
)
4. Drinking W ater T reatmen t
• Sedimen tation - Settling v elo cit y (Stok es’ La w):
v
s
=
g·(?
p
-?
w
)·d
2
18·µ
where:
– v
s
: Settling v elo cit y (m/s)
– ?
p
: Densit y of particle (kg/m
3
)
– ?
w
: Densit y of w ater (kg/m
3
)
– d : P article diameter (m)
– µ : Dynamic viscosit y of w ater (kg/m·s)
• Surface loading rate (o v erflo w rate) for sedimen tation tanks:
v
o
=
Q
A
where:
– v
o
: Ov erflo w rate (m³/m²·da y)
– Q : Flo w rate (m³/da y)
– A : Surface area of tank (m²)
• Coagulation - Jar test for optim um coagulan t dose:
Dose =
Mass of coagulan t
V olume of w ater
• Filtration rate:
v
f
=
Q
A
where:
– v
f
: Filtration rate (m³/m²·hr)
– Q : Flo w rate through filter (m³/hr)
– A : Filter b ed area (m²)
5. Unit Pro cesses and Op erations
• Disinfection - Chic k-W atson La w:
ln
(
N
t
N
0
)
=-k·C
n
·t
where:
– N
t
: Num b er of surviving organisms at time t
2
Page 3


GA TE CE 2026 F orm ula Sheet: W ater and W aste W ater Qualit y
and T reatmen t
1. W ater Qualit y Index (W QI)
• General form of W QI (w eigh ted arithmetic index):
W QI =
n
?
i=1
W
i
·q
i
where:
– q
i
=
(
Ci
Si
)
×100 , qualit y rating for the i -th parameter
– C
i
: Measured concen tration of the i -th parameter
– S
i
: Standard p ermissible v alue for the i -th parameter
– W
i
=
k
Si
, w eigh t of t he i -th parameter
– k : Prop ortionalit y constan t (often tak en as 1 for simplicit y)
–
?
W
i
= 1
2. W ater Requiremen t
• P er capita w ater demand:
Q
total
=P ·q
where:
– Q
total
: T otal w ater demand (liters/da y)
– P : P opulation
– q : P er capita demand (liters/capita/da y)
• Maxim um daily demand:
Q
max daily
= 1.8·Q
a vg daily
• P eak hourly demand:
Q
p eak hourly
= 2.7·Q
a vg daily
3. W ater Distribution System
• Con tin uit y equation for pip e flo w:
Q =A·v
where:
– Q : Flo w rate (m
3
/s)
– A : Cross-sectional area of pip e (m
2
)
– v : V elo c it y of flo w (m/s)
• Hazen-Williams form ula for head loss:
h
f
= 10.67·
L·Q
1.852
C
1.852
·D
4.87
where:
– h
f
: Head loss (m)
– L : Pip e length (m)
– Q : Flo w rate (m
3
/s)
– C : Hazen-Williams co e?icien t (dimensionless)
– D : Pip e diameter (m)
1
• Darcy-W eisbac h equation for head loss:
h
f
=f ·
L
D
·
v
2
2g
where:
– f : F riction factor (dimensionless)
– v : Flo w v elo c it y (m/s)
– g : A cceleration due to gra vit y (9.81 m/s
2
)
4. Drinking W ater T reatmen t
• Sedimen tation - Settling v elo cit y (Stok es’ La w):
v
s
=
g·(?
p
-?
w
)·d
2
18·µ
where:
– v
s
: Settling v elo cit y (m/s)
– ?
p
: Densit y of particle (kg/m
3
)
– ?
w
: Densit y of w ater (kg/m
3
)
– d : P article diameter (m)
– µ : Dynamic viscosit y of w ater (kg/m·s)
• Surface loading rate (o v erflo w rate) for sedimen tation tanks:
v
o
=
Q
A
where:
– v
o
: Ov erflo w rate (m³/m²·da y)
– Q : Flo w rate (m³/da y)
– A : Surface area of tank (m²)
• Coagulation - Jar test for optim um coagulan t dose:
Dose =
Mass of coagulan t
V olume of w ater
• Filtration rate:
v
f
=
Q
A
where:
– v
f
: Filtration rate (m³/m²·hr)
– Q : Flo w rate through filter (m³/hr)
– A : Filter b ed area (m²)
5. Unit Pro cesses and Op erations
• Disinfection - Chic k-W atson La w:
ln
(
N
t
N
0
)
=-k·C
n
·t
where:
– N
t
: Num b er of surviving organisms at time t
2
– N
0
: Initial n um b er of organisms
– k : Disinfection rate constan t
– C : Disinfectan t concen tration (mg/L)
– n : Co e?icien t of dilution
– t : Con tact time (min)
• CT v alue for disinfection:
CT =C·t
where:
– CT: Disinfectan t concen tration-time pro duct (mg·min/L)
3