Hydraulic Design for Gravity-Driven Piping System: Calculations, Pipe Selection, and Friction Analysis

Hydraulic Design Calculations 1
Hydraulic Design for Gravity driven Piping System
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Hydraulic Design Calculations 2
Task 1
Compute the following
i. Diameter of the pipe
Give the following:
V =1.0 m
s ; Q=355 l
s ; H=14.2 m; L 1=1450 m; L 2=6300 m; Bd=0.81 m; Bh=1.25 m;
Bm=45.5 kg
The discharge is calculated using the following formula:
Q= Area x velocity= π d2
4 x v
Then substituting for all the known values:
d2= Q 4
πv = 4 x 0.355
3.142 x 1
The diameter is then found to be
d=0.452 m
d=452 mm ≈ 500 mm
The standard pipe to be used in this scenario will be 500 mm diameter pipe.
ii. Pipe material
The pipe material selected for this case will be High density polyethylene (HDPE) pipe.
Considering a head of 14.2 m, the expected pressure in the pipes would be 142 bar. Considering

Hydraulic Design Calculations 3
a safety factor of 1.5, the maximum pressure expected in the system would be 213 bar.
Therefore, the pipe to be selected would be HDPE PN25.
iii. Gradient
Using the Hazen Williams Formula, the gradient of the pipe would be:
Gradient=162,000,00 x (Design flow/ HWC)1.85 x ( Internal Diameter
10 )
−4.87
Where
Gradient - m/km
Diameter to be internal in mm (Given as 500 mm)
Hazen William Coefficient (140 for plastic pipes)
Design Flow in l/s ( Given as 355 l/s)
Therefore:
Gradient=162,000,00 x (355 /140)1.85 x ( 500
10 )
−4.87
Gradient=4.2 m/ km
iv. Compute pipe friction coefficient, λ and friction losses
Frictional losses along the pipe and fittings can be calculated using the following formulas:
Friction loss∈ pipe, hLPipe=4 λLV 2
D 2 g
Friction loss∈ fittings , hLFittings= ∑ K Fittings V 2
2 g

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Where
V - Velocity
D - Inner diameter of pipe
L - Pipe Length
g – Gravity
K - Resistance coefficient for fittings
λ - Pipe friction coefficient
hL - Pressure drop;
To determine the kind of flow we would have, we compute the Re number:
ℜ=ρ cd
μ
Where
ρ – Density of water = 1000 kg/m3
c – Velocity (Given 1 m/s)
μ - coefficient of dynamic viscosity (Given as 1.4 x 10-3 NS/m2)
d – Diameter (given as 500mm)
Therefore:
ℜ=1000 x 1 x 0.5
1.14 x 10−3
ℜ=438596; Therefore the flow is turbulent
For the turbulent flow, the λ - Pipe friction coefficient will be calculated using the Blasius equation:
f = 0.079
ℜ1 / 4 = 7.204 x 10-7
Friction loss in pipe is given by:
Friction loss∈ pipe, hLPipe=4 x 7.204 x 10−7 x 7750 x 12
0.5 x 2 x 9.81