REPORT
Flow Chart of Report
I. Problem Statement
Design a system to supply water flow from the reservoir to the elevated tank shown in below at a discharge of Q= 1.0 m3/s.
II. Approach and Assumptions
Identifying the piping connections of the system and arranging all its auxiliaries from initial to the final discharge. Locating and calculating all the valves, gate valve and all head losses. Assuming, iterating and calculating for the achieving required flow rate at discharge of Q= 1.0 m3/s.
III. Result and Discussion
Pipe line Connection:
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As per calculation and iterations based on all head losses considering, to attain the flow rate at the discharge of 1 m3/s
Taking
pipe diameter as 15 inches = 0.381 m, the cross section area of pipe = 
For
required flow rate of 1 m3/s as per chosen pipe diameter, the flow
velocity = (1 m3/s)/ (
=
8.771m/s
Reynolds
number = 
= 
Referring Chart
For pipe roughness (e/d) =0.001, e= 0.00038m or 0.38mm f = 0.02, and head loss for 50 m pipe length is computed using Darcy-Weishbach equations
, 
= 131.6, head loss = 0.02*131.6*3.92 = 10.3 m
for pipe roughness 0.38 mm
For cast iron pipe (e/d) =0.0005, e= 0.00019m or 0.19mm f= 0.017,
Head loss = 8.8 m for pipe roughness 0.19 mm or 190 micron
For cost iron pipe Surface roughness is 0.26 mm (From table 14.2)
For longer pipe of 300m length, let us chose pipe with roughness under 260 micron, then e/d = 0.00068, and f is 0.017
If we choose cost iron 50 m pipe also, Head loss = 0.017*131.6*3.92 m = 8.77 m
With same cost iron pipe for 300m long pipe, head loss = 0.017*(300/0.38)*3.92 m = 52.6 m.
The head loss in 300 m long pipe is quite large with cast iron pipe.
Loss can be minimized if we choose Smooth pipe. From the chart the f will get reduced from 0.017 to 0.0095
With smooth pipe for 300m long pipe, head loss = 0.0095*(300/0.38)*3.92 m = 29.4 m.
The head losses considered are the entrance loss, 90 deg bend elbow losses, losses at half opened gate valve, pipe friction losses, globe valve losses and exit loss.
|
ID |
INTERFACES |
HEAD LOSS |
|
1 |
RESERVOIR TO PIPE: ENTRANCE LOSS |
1.92 |
|
2 |
GLOBE VALVE HEAD LOSS |
23.52 |
|
3 |
50 M LONG PIPE |
8.77 |
|
4 |
90 DEGREE ELBOW BEND |
1.02 |
|
5a |
300 M LONG PIPE( Cost iron) |
52.6 m |
|
5b |
3000 m long pipe ( smooth pipe) |
29.4 |
|
6 |
GATE VALVE |
8.23 |
|
7 |
90 DEGREE ELBOW BEND |
1.02 |
|
8 |
50 M LONG PIPE |
8.77 |
|
9 |
PIPE TO TANK: EXIT LOSS |
4.1 |
Primary head losses (Includes all the pipes, glove valve, and gate valve) = 23.52+ 8.77+ 29.4+8.23+8.77= 78.69
Secondary head loss (Includes entrance, elbow bend, exit) = 1.92+1.02+1.02+4.1 = 8.06
Total head loss = 86.75
% of secondary head loss is close to 10%
Head loss due to component are taken from class notes
After solving energy equation we can conclude that, we require a pump of 1339 KW/ 1796 HP when 15 inch (0.381 m) dia pipe and elbows are used.
To lower the Pump power requirements, we need to increase the pipe diameter. Doubling the pipe diameter reduces flow velocity by factor of 4 and thus Head loss will reduce by factor of 16.
With 30 Inches pipe diameter
Taking
pipe diameter as 30 inches = 0.762 m, the cross section area of pipe = 
For
required flow rate of 1 m3/s as per chosen pipe diameter, the flow
velocity = 
2.19/s
Reynolds
number = = 
For cost iron pipe Surface roughness is 0.26 mm (From table 14.2)
For longer pipe of 300m length, let us chose pipe with roughness under 260 micron, then e/d = 0.00034, and f is 0.017
With same cost iron pipe for 300m long pipe, head loss = 1.63 m
Total head loss will reduce by a factor of 32
Final design
Case 1:- By taking 300m Cast Iron Pipe
|
ID |
INTERFACES |
Material |
HEAD LOSS [M] |
|
|
|
Pipe Size 15” |
Pipe Size 30” |
|
|||
|
1 |
RESERVOIR TO PIPE: ENTRANCE LOSS |
|
1.92 |
0.06 |
|
|
2 |
GLOBE VALVE HEAD LOSS |
|
23.52 |
0.735 |
|
|
3 |
50 M LONG PIPE |
Cast Iron |
8.77 |
0.274063 |
|
|
4 |
90 DEGREE ELBOW BEND |
|
1.02 |
0.031875 |
|
|
5a |
300 M LONG PIPE( Cast iron) |
Cast Iron |
52.6 |
1.64375 |
|
|
6 |
GATE VALVE |
|
8.23 |
0.257188 |
|
|
7 |
90 DEGREE ELBOW BEND |
|
1.02 |
0.031875 |
|
|
8 |
50 M LONG PIPE |
Cast Iron |
8.77 |
0.274063 |
|
|
9 |
PIPE TO TANK: EXIT LOSS |
|
4.1 |
0.128125 |
|
|
|
|
Total Head Loss |
109.95 |
3.435938 |
|
|
|
|
Power Required |
1961387 Watt |
655258.2 Watt |
|
|
|
|
Power Required |
2630.22 HP |
878.7012 HP |
|
Case 2:- Taking 300m Smooth pipe
|
ID |
INTERFACES |
Material |
HEAD LOSS [M] |
|
|
|
Pipe Size 15” |
Pipe Size 30” |
|
|||
|
1 |
RESERVOIR TO PIPE: ENTRANCE LOSS |
|
1.92 |
0.06 |
|
|
2 |
GLOBE VALVE HEAD LOSS |
|
23.52 |
0.735 |
|
|
3 |
50 M LONG PIPE |
Cast Iron |
8.77 |
0.274063 |
|
|
4 |
90 DEGREE ELBOW BEND |
|
1.02 |
0.031875 |
|
|
5b |
3000 M LONG PIPE( Smooth) |
Smooth |
29.4 |
0.91875 |
|
|
6 |
GATE VALVE |
|
8.23 |
0.257188 |
|
|
7 |
90 DEGREE ELBOW BEND |
|
1.02 |
0.031875 |
|
|
8 |
50 M LONG PIPE |
Cast Iron |
8.77 |
0.274063 |
|
|
9 |
PIPE TO TANK: EXIT LOSS |
|
4.1 |
0.128125 |
|
|
|
|
Total Head Loss |
86.75 |
2.710938 |
|
|
|
|
Power Required |
1676897 |
646367.9Watts |
|
|
|
|
Power Required |
2248.719 |
866.7793 HP |
|
IV. Summary
a. Component List
|
ID |
COMPONENTS INVOLVED |
DESCRIPTION/RESULT |
LENGTH |
MATERIAL |
|
1 |
RESEVOIR |
ELEVATION = 450 M |
*** |
Tank |
|
2 |
GLOBE VALVE |
FULLY OPEN |
*** |
Cast Iron |
|
3 |
PUMP |
786 KW/ 1054 HP |
*** |
Cast Iron |
|
4 |
PIPE |
DIA 0.381 M (15 INCH) |
50 |
Cast Iron |
|
5 |
90 DEGREE ELBOW BEND |
DIA 0.381 M (15 INCH) |
*** |
Cast Iron |
|
6 |
PIPE |
DIA 0.381 M (15 INCH) |
300 |
SMOOTH PIPE |
|
7 |
GATE VALVE |
HALF OPENED |
*** |
Cast Iron |
|
8 |
90 DEGREE ELBOW BEND |
DIA 0.381 M (15 INCH) |
*** |
Cast Iron |
|
9 |
PIPE |
DIA 0.381 M (15 INCH) |
50 |
Cast Iron |
|
10 |
TANK |
ELEVATION = 500 M |
*** |
Tank |
b. Head Losses
|
ID |
INTERFACES |
HEAD LOSS |
|
1 |
RESERVOIR TO PIPE: ENTRANCE LOSS |
1.92 |
|
2 |
GLOBE VALVE HEAD LOSS |
23.52 |
|
3 |
50 M LONG PIPE |
8.77 |
|
4 |
90 DEGREE ELBOW BEND |
1.02 |
|
5a |
300 M LONG PIPE( Cost iron) |
52.6 |
|
5b |
3000 m long pipe ( smooth pipe) |
29.4 |
|
6 |
GATE VALVE |
8.23 |
|
7 |
90 DEGREE ELBOW BEND |
1.02 |
|
8 |
50 M LONG PIPE |
8.77 |
|
9 |
PIPE TO TANK: EXIT LOSS |
4.1 |
V. Appendix
Formulae:
For all head losses:
hL = KL*((1/2g)*v2)
Where, hL= Head loss, m
KL= Loss factor,
g= Acceleration due to gravity= 9.81 m/s2,
v= Flow velocity, m/s
i. For Entrance Loss,
KL= 0.5.
ii. For Globe Valve,
KL= 6; Ref: Fluid Mechanics by Frank M. White. (Table 6.5)
iii. Pipe Friction Loss:
hf = f (L/d) (v2/2g).
Where, hf = Head loss in m due to Pipe Friction Loss
f= Friction factor; Friction factor depends on a) Pipe roughness b) Pipe diameter c) Flow velocity
Value taken from Ref: Fluid Mechanics by FM White (Equation 6.48)
L= Length of Pipe;
d= Diameter of Pipe;
g= Acceleration due to gravity= 9.81 m/s2,
v= Flow velocity, in m/s
iv. Elbow 90o Bend:
KL= 0.26.
v. Gate Valve:
KL= 2.1; from lecture notes.
vi. Energy Equation:
*The Mechanical Energy Equation in Terms of Energy per Unit Mass
The mechanical energy equation for a pump or a fan can be written in terms of energy per unit mass where the energy into the system equals the energy out of the system.
Epressure,in + Evelocity,in + Eelevation,in + Eshaft = Epressure,out + Evelocity,out + Eelevation,out + Eloss
(1)
Where,
p = static pressure (Pa, (N/m2))
ρ = density (kg/m3)
v = flow velocity (m/s)
g = acceleration of gravity (9.81 m/s2
hin= elevation height at inlet (m)
hout= elevation height at outlet (m)
Eshaft= net shaft energy per unit mass for a pump, fan or similar (J/kg)
Eloss = hydraulic loss through the pump or fan (J/kg)
The energy equation is often used for incompressible flow problems and is called the Mechanical Energy Equation or the Extended Bernoulli Equation.
Efficiency
According to (1) more loss requires more shaft work to be done for the same rise of output energy. The efficiency of a pump or fan process can be expressed as:
*The Mechanical Energy Equation in Terms of Energy per Unit Volume
The mechanical energy equation for a pump or fan (1) can also be written in terms of energy per unit volume by multiplying (1) with the fluid density - ρ:
(2)
Where,
γ = ρ g =specific weight (N/m3)
The dimensions of equation (2) are
Energy per unit volume
The Mechanical Energy Equation in Terms of Energy per Unit Weight involving Heads
The mechanical energy equation for a pump or a fan (1) can also be written in terms of energy per unit weight by dividing with gravity - g:
(3)
= net shaft energy head per unit mass
for a pump, fan in (m)
= loss head due to friction (m)
The dimensions of equation (3) are energy per unit weight (Nm/N = m)
E shaft = shaft power (W)
m = mass flow rate (kg/s)
Q = volume flow rate (m3/s)
VI. Actual Calculations:
To attain discharge Flow Rate Q= 1 m3/s discharge,
Assume Diameter of Pipe/ Valve d= 0.381 m (15 inch);
Velocity of Fluid v= Q/ (pi*d2/4)
v= 1/ (3.14*0.3812/4)
v= 8.77 m/s
Reservoir to Pipe: Entrance loss he=
= 
=1.96 m
Globe valve head loss: Globe valve is fully open
hL=
=
=
=23.52 m
1. Pipe Friction Loss:
Length L= 50 m
Reynolds No. = (rho*v*d/ Dynamic Viscosity (µ)) = (998*8.77*0.381/0.001 Pa-s) =3335152
è Implies the flow is turbulent.
àPipe Material= Cast Iron à Roughness = 0.26
As per FM White Moody Chart,
f= 0.017
hf = f(L/d)(v2/2g)
= 0.017* (50/0.381)(8.772/2*9.81)=8.8 m
2. 90o Elbow Bend 1 Loss:
hL=0.2=
=1.0 m
3. Pipe Friction Loss:
Length L= 300 m
Reynolds No. = (rho*v*d/ Dynamic Viscosity (µ)) = (998*8.77*0.381/0.001 Pa-s) =3335152
è Implies the flow is turbulent.
àPipe Material= Cast Iron à Roughness = 0.26
As per FM White Moody Chart,
f= 0.017
hf =
* 
= 
* 
= 52.6 m ( With cast iron pipe)
With doubling of pipe diameter to 30”, Velocity gets reduced to 2.19m/s, Re Number 0.9 Million and head loss gets reduced to
hf
= * = 
* 
= 1.63 m
( With cast iron pipe), quite low so we do not need to go for smooth pipe.
4. Gate valve head loss: Gate valve is half closed
hL=
2.1*((1/2g)*v2) = 
= 8.23 m
5. 90o Elbow Bend 2 Loss:
hL= 0.26*((1/2g)*v2) = 0.26* ((1/2*9.81)*(8.77) =1.019 m
6. Pipe Friction Loss:
Length L= 50 m
Reynolds No.= (rho*v*d/ Dynamic Viscosity(µ))= (998*8.77*0.381/0.001 Pa-s) =3335152
è Implies the flow is turbulent.
àPipe Material= Cast Iron à Roughness = 0.26
As per FM White Moody Chart,
f= 0.017
hf = f(L/d)(v2/2g)
= 0.017* (50/0.381)(8.772/2*9.81) = 8.8 m
7. Pipe to tank :Exit loss
hL=
= 
= 4.1 m
i. Sum of head loss= 114.20 m
ii. Gain of Elevation (Given) = 50 m
iii. Pump Head, h shaft/pump = Sum of Head Loss + Gain of Elevation
= 86.75 + 50
=136.75 m
iv. Pump Efficiency, ɳ = 0.8
v.
Pump Power = 
= 
=1,338,834 watt = 1339 KWatt
In HP = 1339 * 1.341 = 1796 HP
VII. Reference
1. Fluid mechanics FM White Book.
2. https://www.engineeringtoolbox.com/mechanical-energy-equation-d_614.html
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