Head Loss In Backwashing

During the backwashing process filter media undergoes expansion due to the heavy pressure of the air wash and water wash pumps. Therefore, head lost in the backwashing is the sum of the head loss in the expanded bed, under drains (nozzles) and in the pipes, valves and rate controller.
The equation of head loss in the backwashing process is written as:

H = hf + hu + hp

Where:
hf = Head loss in the expanded bed
hu = Head loss in the under drains (nozzles)
hp = Head loss in the pipe, valves & rate controllers

Head Loss in the Expanded Bed

During the backwashing process, 50 % expansion of the bed takes place as a result porosity of the unexpanded sand bed which is 0.42 increases. The porosity of the expanded bed is worked out from the following relation given Water Treatment Principles & Design by MWH (P -896)

Le/L = 1-e / 1-ee
Where:

Le = Depth of expanded bed
e = Porosity of the unexpanded bed (0.42)
ee = Porosity of the expanded bed

Since provision for 50 % bed expansion has been made, therefore

Le = 1.5 L
1.5 = 1 - 0.42 / 1 - ee
ee = 0.613

Head loss in the expanded bed is given by the following expression:

hf = Le (1 - ee)( Ss - 1)

Le = Depth of expanded bed (1.5 x 4.5 Ft)
P = Porosity of the unexpanded bed (0.42)
Ss = Specific Gravity of the Filtering Media (2.65)

hf = 1.5 x 4.5 (2.65 - 1.0) (1.0 - 0.613)
= 4.3 Ft

Head Loss in the Under Drains (Nozzles)

Head loss in the under drains (nozzles) and is given by the following expression:

hu = (Vb / αβ)2 x 1/2g

Vb = Backwash velocity
α = Orifice Coefficient (0.61)
β = Ratio of the orifice to bed area (normally 0.2 to 0.7 percent)
Area of Orifice = 0.2

g = Acceleration due to gravity

Kawamura (2000) P - 237 has given a head loss range of 4 - 7 Ft for filter nozzles placed 6 - 8 inches apart having orifice size of 0.25 to 0.75 mm.

Therefore, instead of going for detailed calculations upper limit i.e 7.0 Ft given above has been selected as the head loss through nozzles.

Hudson (1981) has reported 1.0 m (3.25 Ft) headloss in the filter under drains (Nozzles) for a backwashing rate of 36 m/h.

Head Loss in Pipe, Valves & Rate Controller

Head loss in the pipe, valves and controller is given by the following expression:

hp = f l/ 2gd x ( 4 Qb/ л d2)2
f = Friction factor (0.01)
l = Equivalent pipe length
d = Pipe diameter (1.5’)
Qb = Backwash flow rate (14 Cusecs)

Calculations of equivalent length of pipe is worked out from the following expression (Ref Wastewater Treatment by Syed R. Qasim:

L = 55.4 C D1.2
L = Equivalent length of pipe fittings for pipe diameter D
C = Factor for equivalent length of pipe

Equivalent length is calculated in the following table:

Fittings
No of Fittings
C value for equivalent pipe length
Equivalent Length
Gate Valve
2
0.25
45.0
Bends
5
0.33
150.0
Tee
1
1.33
120.0
Non Return Valve
1
0.90
81
Length of Pipe


120


Total
516.0 ~ 520

hp = 0.01 x 520 x ( 4 x 14/ 3.14 (1.5)2)2/ 2 x 32.2 x 1.5
= 4.50 Ft

Total Headloss = 4.3 + 7.0 + 4.5
= 15.8 Ft
Delivery Head ( 1034.75 - 1021.5) = 13.25 Ft
Suction Lift = 2.5 Ft
Drawdown = 3 Ft
Total Headloss = 15.8 Ft
Total Head = 34.55 Ft