Flow Through Pipes, Head Loss in Pipes, Minor Head Loss, Major Head Loss, Darcy's Formula, Chezy's Formula, Hydraulic Gradient Line, Total Energy Line, Energy Gradient Line... By Engr. M. Jalal Sarwar

2. FLOW THROUGH PIPES
•A pipe is a closed conduit, generally of circular cross-section.
•Used to carry water or liquid.
•They are made of Galvanized Iron, Steel & PVC (Polyvinyl
Chloride) etc.
•When the pipe is running full, the flow is under pressure.
•If the pipe is not running full, the flow is not under pressure.
•In such case, the atmospheric pressure exists inside the pipe.
BY ENGR. M. JALAL SARWAR

3. HEAD LOSS IN PIPES
•When water is flowing in a pipe, it experiences some resistance
to its motion, whose effect is to reduce the energy (Velocity
etc.) of water.
•This reduction in the energy of water is called Head Loss.
•If the Head Loss became equal to total energy, then the flow will
stopes.
•Head Loss is divided into two groups:
1. Minor Head Loss
2. Major Head Loss
BY ENGR. M. JALAL SARWAR

4. HEAD LOSS IN PIPES
1. MINOR HEAD LOSS:
These are the smaller losses during flow of water. For smaller pipelines,
these losses are important to calculate. Smaller pipelines means, a
pipeline having length less than 1000 times of its dia. Minor losses with
formulas are given as:
a) Head Loss due to sudden enlargement ℎ 𝑒 =
(𝑣1 −𝑣2 )2
2𝑔
b)Head Loss due to sudden Contraction ℎ 𝑐 = 0.375
𝑣2
2
2𝑔
c) Head Loss at the Entrance of pipe ℎ𝑖 = 0.5
𝑣1
2
2𝑔
d)Head Loss at the Exit of Pipe ℎ 𝐸 = 0.375
𝑣2
2
2𝑔
BY ENGR. M. JALAL SARWAR

5. HEAD LOSS IN PIPES
1. MINOR HEAD LOSS:
e)Head Loss due to Bend of Pipe ℎ 𝑏 =
𝐾𝑣2
2𝑔
(where k = Co-efficient of bend)
f) Head Loss at Pipe Fittings ℎ 𝑝 =
𝐾𝑣2
2𝑔
where k = Co-efficient of pipe fitting, 0.5 – 0.9
g) Head Loss due to Obstruction ℎ 𝑜 =
𝐾𝑣2
2𝑔
(
𝐴−1
𝐶(𝐴−𝑎)
)2
where a = Maximum area of obstruction
C = Co-efficient of contraction that may be taken as 0.66.
g = Gravitational Acceleration (9.8 m/sec2)
v = Velocity of flow
A = Area of Pipe
BY ENGR. M. JALAL SARWAR

6. HEAD LOSS IN PIPES
2. MAJOR HEAD LOSS:
Head Loss in a pipe due to friction is called Major Head Loss. This
friction is in between the surface of pipe and the liquid. To find out the
Major Head Loss, following two formulas are used.
a)Darcy’s Formula:
ℎ 𝑓 =
4𝑓𝑙𝑣2
2𝑔𝑑
𝑶𝑹 ℎ 𝑓 =
𝑓𝑙𝑄2
3𝑑5
Where
hf = Head Loss in Pipe due to Friction, v = Mean Velocity of flow,
f = Co-efficient of friction, Q = Discharge,
d = Diameter of Pipe, g = Gravitational Acceleration
BY ENGR. M. JALAL SARWAR

7. HEAD LOSS IN PIPES
2. MAJOR HEAD LOSS:
b)Chezy’s Formula:
𝑣 = 𝐶 𝑚𝑖
Where
m = Hydraulic mean depth = 𝑎
𝑝 OR 𝑑
4 for circular pipe, where d = dia of pipe.
i = Loss of head per unit length
C = Chezy’s Constant
•Head Loss in total length of pipeline “L” is determined by
ℎ 𝑓 = 𝑖 × 𝐿
BY ENGR. M. JALAL SARWAR

8. HYDRAULIC GRADIENT LINE (H.G.L)
•If pressure head of a liquid flowing in a pipe be plotted as vertical
ordinates on the centerline of the pipe, then the line joining the tops of
such ordinated is known as Hydraulic Gradient Line.
BY ENGR. M. JALAL SARWAR
TOTAL ENERGY LINE (T.E.L)
•If the sum of pressure heads and velocity heads of a liquid flowing in a
pipe be plotted as vertical ordinates on the centerline of the pipe, then
the line joining the tops of such ordinates is known as Total Energy Line
OR Energy Gradient Line.

9. H.G.L & T.E.L (E.G.L)
BY ENGR. M. JALAL SARWAR