Headrace Pressure Flow in Steel Pipes
Headrace pipe can also serve the same function as that of Headrace tunnels, depending upon the site location, geological and topographical constraints. as discussed earlier that tunnels can be divided into two types on the basis of type of flow
 Pressure Flow Tunnels
 Gravity Flow Tunnels.
Similarly headrace pipes can also be divided into two categories pressure flow and gravity flow. Following are the design examples of the two types:
Hydraulic Design of Pressure Flow in Headrace Pipes (STEEL)
Let suppose a 50 cumecs needs to be passed through 4.0m diameter steel pipe with a total length of 1000m, longitudinal slope of 1/1000 m, Mannng’s coefficient of 0.014 (steel) and with a gross head of 100m.
Hydraulic Design Calculations of Headrace Pipe (Pressure Flow)
BASIC DATA 




Pipe invert elevation at Start 
I.L.1 
= 
100.00 
m a.s.l. 
Design discharge 
Q 
= 
50.0 
m3/s 
Internal diameter of pipe 
D 
= 
4.00 
m 
Flow velocity 
V 
= 
4.0 
m/s 
Hydraulic radius 
R 
= 
1.00 
m 
Maximum Gross Head 
H 
= 
100.00 
m 
Effective head from center of pipe 
he 
= 
10.0 
m 
Max. possible flow velocity (orifice flow) 
VOmax 
= 
8.40 
m/s 
Max. possible discharge (orifice flow) 
QOmax 
= 
105.61 
m3/s 
Alternatively Using another equation 




Max. possible discharge (conduit flow) 
QCmax 
= 
147.1 
m3/s 
Check QOmax ≥ Q 

= 
O.K. 

Total length of pipe (Δx) 
L 
= 
1000.0 
m 
Longitudinal slope 
S 
= 
0.0010 
m/m 
HazenWilliams roughness coefficient 
C 
= 
120 

Mannings friction factor (steel) 
n 
= 
0.0140 

Friction factor (Moody) 
f 
= 
0.0130 

FRICTION FACTOR 




Using Reynolds number 




Kinematic viscosity of water at 20oC 
ν 
= 
1.0E06 
m2/s 
Reynolds number 
Re 
= 
15915494 

Check Re ≤ 2000 

= 
TURBULENT 

Roughness height (welded steel) 
e 
= 
0.600 
mm 
Ratio 
e/D 
= 
0.00015 


1 
= 
1.00 

Friction factor (Moody) 
f 
= 
0.01304 

SUBMERGENCE REQUIREMENTS 




Minimum submergence (by Knauss) 
Smin 
= 
9.84 
m 
" " " " (by Rohan) 
Smin 
= 
8.20 
m 
" " " " (by Gordon) 
Smin 
= 
5.77 
m 
Minimum submergence 
Smin 
= 
7.94 
m 
Provided submergence 
SPr 
= 
10.00 
m 
Check SPr ≥ Smin 

= 
O.K. 

HEADLOSSES 




FRICTION LOSS 




Headloss (Manning) 
hf 
= 
3.10 
m 
Headloss (HazenWilliams) 
hf 
= 
2.46 
m 
Headloss (DarcyWeisbach) 
hf 
= 
2.63 
m 
Using Colebrook  White equation 
1 
= 
1.00 

Friction loss (ColebrookWhite) 
hf 
= 
2.63 
m 
Maximum friction headloss 
hfmax 
= 
3.10 
m 
BEND LOSS 




No. of bends 
nB 
= 
10 
no. 
Headloss in bends 
hLB 
= 
1.21 
m 
ENTRANCE LOSS 




Velocity at pipe bellmouth 
vE 
= 
0.46 
m/s 
Entrance headloss 
hLE 
= 
0.0011 
m 
Total headloss in headrace pipe 
hLT 
= 
4.31 
m 
WALL THICKNESS 




Bulk modulus of water 
k 
= 
2.1E+09 
N/m2 
Modulus of elasticity of pipe material 
E 
= 
2.1E+11 
N/m2 
Wall thickness (provided) 
ts 
= 
25.0 
mm 
Hydrostatic pressure 
Pw 
= 
10.00 
kN/mm2 
Weld efficiency 
kf 
= 
0.95 

Allowable tensile stress 
σf 
= 
1400 
kN/mm2 
Corrosion allowance 
cs 
= 
1.5 
mm 
Wall thickness (required) 
ts 
= 
15.04 
mm 
Wall thickness (provided) 
ts 
= 
25.0 
mm 
Density of steel 
ρs 
= 
7850.0 
kg/m3 
Minimum thickness of steel sheet 
tmin 
= 
11.25 
mm 
Effective thickness of pipe 
te 
= 
23.50 
mm 
Check te ≥ tmin 

= 
O.K. 

Hoop stress 
σH 
= 
851.06 
kgf/cm2 
Check σH ≤ 1.5yield stress 

= 
O.K. 

STEEL QUANTITY 




Xsectional area of steel 
As 
= 
0.316 
m2 
Volume of steel 
Vs 
= 
316.12 
m3 
Weight of steel 
Ws 
= 
2481.56 
tons 
Weight of steel (5% increse for joints) 
Ws 
= 
2605.64 
tons 
Width of steel sheet 
w 
= 
12.72 
m 
Length of steel sheet 
l 
= 
6.0 
m 
No. of steel sheets 
n 
= 
167 
no. 
BASIC DATA 




Pipe invert elevation at Start 
I.L.1 
= 
100.00 
m a.s.l. 
Design discharge 
Q 
= 
50.0 
m3/s 
Internal diameter of pipe 
D 
= 
4.00 
m 
Flow velocity 
V 
= 
4.0 
m/s 
Hydraulic radius 
R 
= 
1.00 
m 
Maximum Gross Head 
H 
= 
100.00 
m 
Effective head from center of pipe 
he 
= 
10.0 
m 
Max. possible flow velocity (orifice flow) 
VOmax 
= 
8.40 
m/s 
Max. possible discharge (orifice flow) 
QOmax 
= 
105.61 
m3/s 
Alternatively Using another equation 




Max. possible discharge (conduit flow) 
QCmax 
= 
147.1 
m3/s 
Check QOmax ≥ Q 

= 
O.K. 

Total length of pipe (Δx) 
L 
= 
1000.0 
m 
Longitudinal slope 
S 
= 
0.0010 
m/m 
HazenWilliams roughness coefficient 
C 
= 
120 

Mannings friction factor (steel) 
n 
= 
0.0140 

Friction factor (Moody) 
f 
= 
0.0130 

FRICTION FACTOR 




Using Reynolds number 




Kinematic viscosity of water at 20oC 
ν 
= 
1.0E06 
m2/s 
Reynolds number 
Re 
= 
15915494 

Check Re ≤ 2000 

= 
TURBULENT 

Roughness height (welded steel) 
e 
= 
0.600 
mm 
Ratio 
e/D 
= 
0.00015 


1 
= 
1.00 

Friction factor (Moody) 
f 
= 
0.01304 

SUBMERGENCE REQUIREMENTS 




Minimum submergence (by Knauss) 
Smin 
= 
9.84 
m 
" " " " (by Rohan) 
Smin 
= 
8.20 
m 
" " " " (by Gordon) 
Smin 
= 
5.77 
m 
Minimum submergence 
Smin 
= 
7.94 
m 
Provided submergence 
SPr 
= 
10.00 
m 
Check SPr ≥ Smin 

= 
O.K. 

HEADLOSSES 




FRICTION LOSS 




Headloss (Manning) 
hf 
= 
3.10 
m 
Headloss (HazenWilliams) 
hf 
= 
2.46 
m 
Headloss (DarcyWeisbach) 
hf 
= 
2.63 
m 
Using Colebrook  White equation 
1 
= 
1.00 

Friction loss (ColebrookWhite) 
hf 
= 
2.63 
m 
Maximum friction headloss 
hfmax 
= 
3.10 
m 
BEND LOSS 




No. of bends 
nB 
= 
10 
no. 
Headloss in bends 
hLB 
= 
1.21 
m 
ENTRANCE LOSS 




Velocity at pipe bellmouth 
vE 
= 
0.46 
m/s 
Entrance headloss 
hLE 
= 
0.0011 
m 
Total headloss in headrace pipe 
hLT 
= 
4.31 
m 
WALL THICKNESS 




Bulk modulus of water 
k 
= 
2.1E+09 
N/m2 
Modulus of elasticity of pipe material 
E 
= 
2.1E+11 
N/m2 
Wall thickness (provided) 
ts 
= 
25.0 
mm 
Hydrostatic pressure 
Pw 
= 
10.00 
kN/mm2 
Weld efficiency 
kf 
= 
0.95 

Allowable tensile stress 
σf 
= 
1400 
kN/mm2 
Corrosion allowance 
cs 
= 
1.5 
mm 
Wall thickness (required) 
ts 
= 
15.04 
mm 
Wall thickness (provided) 
ts 
= 
25.0 
mm 
Density of steel 
ρs 
= 
7850.0 
kg/m3 
Minimum thickness of steel sheet 
tmin 
= 
11.25 
mm 
Effective thickness of pipe 
te 
= 
23.50 
mm 
Check te ≥ tmin 

= 
O.K. 

Hoop stress 
σH 
= 
851.06 
kgf/cm2 
Check σH ≤ 1.5yield stress 

= 
O.K. 

STEEL QUANTITY 




Xsectional area of steel 
As 
= 
0.316 
m2 
Volume of steel 
Vs 
= 
316.12 
m3 
Weight of steel 
Ws 
= 
2481.56 
tons 
Weight of steel (5% increse for joints) 
Ws 
= 
2605.64 
tons 
Width of steel sheet 
w 
= 
12.72 
m 
Length of steel sheet 
l 
= 
6.0 
m 
No. of steel sheets 
n 
= 
167 
no. 