All fluids-assignments

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ALL-Fluids-Assignments
Fluid Mechanics (University of Newcastle (Australia))
StuDocu is not sponsored or endorsed by any college or university
ALL-Fluids-Assignments
Fluid Mechanics (University of Newcastle (Australia))
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lOMoARcPSD|4710873

CIVL 2310 Fluid Mechanics
Assignment 1 2003
Due Date: 14th
August 2003
Question 1:
Assuming hydrostatic pressure distributions, uniform velocity profiles, and negligible
viscous effects, find the horizontal force needed to hold the gate in the position shown in
Figure 1.
Figure 1
Solution
lOMoARcPSD|4710873

Question 2:
For the system shown in Figure 2 estimate:
a) the pressure and velocity at the exit if p1=60000 N/m2
and V1=20 m/s. Neglect losses
and consider that the pressure at the expansion is p1
b) calculate the loss coefficient K using V1 in the head loss term.
Figure 2
Solution
a)
Continuity 2211 AVAV =
smV
V
/
..
5
030015020
2
2
2
2
=∴
××=×× ππ
Momentum )( 12112211 VVAVApAp −=− ρ
2
2
22
2
2
90000
2052001501000030015060000
mNp
p
/
)(...
=∴
−×××=××−×× πππ
b)
Energy Lhz
g
Vp
z
g
Vp
+++=++ 2
2
22
1
2
11
22 γγ
790
8192
0
8192
5
9810
90000
0
8192
20
9810
60000
2
1
22
.
...
=∴
×
++
×
+=+
×
+
K
V
K
lOMoARcPSD|4710873

Assignment 1 2004
Due Date: 11th
August 2004
Question 1:
Neglect viscous effects, assume uniform velocity profiles, and find the horizontal force component
acting on the obstruction shown below.
Figure 1
lOMoARcPSD|4710873

Question 2:
Find the x and y force components on the horizontal T-section shown in the figure. Neglect head
losses.
Figure 2
lOMoARcPSD|4710873

Assignment 1 2005
Due Date: 10th
August 2005
Question 1:
Assuming hydrostatic pressure distributions, uniform velocity profiles, and negligible
viscous effects, find the horizontal force needed to hold the gate in the position shown in
Figure 1.
Figure 1
Solution
a)
b) continuity V2=60V1
applying energy V2=10.76, V1=0.18 m/s
applying momentum F=660587 N
lOMoARcPSD|4710873

Question 2:
a) Find the x and y force components on the bend shown in Figure 2 neglecting head
losses.
b) Repeat part a) incorporating the effects of head losses. Compute the head loss for the
bend using K=1.1 and V1 and the head loss for the contraction using K=0.02 and V2.
Figure 2
a)
b)
V2=19.7, V1=4.9 m/s
Fx=1126 N
Fy=488 N
p1=200 kPa
+K1 +K2
lOMoARcPSD|4710873

Assignment 1 2006 Solution
Question 1:
Assuming uniform velocity profiles, find F needed to hold the plug in the pipe shown in the next
figure. DO NOT NEGLECT HEAD LOSSES. Compute the head loss for the plug using K=5 and
the velocity at the plug.
Continuity
2211 VAVA =
2
222
)02.0025.0(4025.0 V−=×× ππ
smV /11.112 =
Energy
g
kV
g
Vp
g
Vp
22
2
22211
++=+
γγ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×
−×+
=
81.92
411.11511.11
9810
222
1p
3622961 =p
Momentum
)411.11(4025.01000025.0362296
)(
22
12
.
11
−×××−××=
−=−
ππF
VVmFAp
NF 655=
0
lOMoARcPSD|4710873

Question 2:
Neglect viscous effects, assume uniform velocity profiles, and find the horizontal force component
acting on the obstruction shown below.
Figure 1
lOMoARcPSD|4710873

Assignment 1 2007
Due Date: 15th
March 2007
Question 1:
Neglecting losses, determine the x and y components of the force needed to hold the Y fitting in
place, Fx and Fy. The plane of the fitting is horizontal, so you can neglect the weight of the water
and consider that all pipes have the same z coordinate.
45o
60o
Q2=0.2 m3
/s Q3=0.3 m3
/s
P1=73.7 kPa 0.5 m
diameter
0.35 m
diameter
0.18 m
diameter
Fy
Fx
lOMoARcPSD|4710873

lOMoARcPSD|4710873

Assignment 1 2008
Due Date: 20th
March 2008
Question 1:
a) Assuming hydrostatic pressure distributions, uniform velocity profiles, and negligible viscous
effects, find the horizontal force needed to hold the gate in the position shown in Figure 1.
Figure 1
b) Repeat part a) with the gate lowered so that the downstream depth is 10 cm. Compare with a)
and discuss implications for the design of the gate.
Solution
a)
lOMoARcPSD|4710873

Question 2:
Determine the x and y components of the force needed to hold the horizontal T-section in place,
Fx and Fy. The plane of the fitting is horizontal, so you can neglect the weight of the water and
consider that all pipes have the same z coordinate. DO NOT NEGLECT HEAD LOSSES.
Compute head losses between section 1 and 3 using K=0.3 and V1 and between section 1 and 2
using K=0.2 and V1.
50
lOMoARcPSD|4710873

Assignment 1 2009
Due Date: 26th
March 2009
Question 1:
Figure 1
Solution
a)
lOMoARcPSD|4710873

Head losses in ass1 Q2:
Fittings (valves, elbows, contractions, expansions) produce head losses in pipes. We
usually account for that in the hL term of the Energy equation in the form:
g
V
K
2
2
where K is a coefficient that corresponds to the particular fitting and V is a velocity
associated with the fitting. You will learn how to choose those values later on. For now
just use the K and V values given in the problem announcement. If there are several
fittings in the pipe under analysis, then the total hL would be (for example for two fittings
as in the example):
g
V
K
g
V
KhL
22
2
2
2
2
1
1 +=
where K1 and V1 correspond to fitting 1 and K2 and V2 correspond to fitting 2.
lOMoARcPSD|4710873

Assignment 1 2011
Due Date: 28th
March
Question 1:
Figure 1
Solution
a)
lOMoARcPSD|4710873

Assignment 2 2003
Due Date: 9th
September 2003
Question 1:
The drag force FD on the smooth sphere of Figure 1 falling in a liquid depends on the constant
sphere speed V, the density of the sphere s, the liquid density and viscosity µ, the sphere
diameter D, and gravity g. Find an expression for the dimensionless force FD/( V2
D2
) using the
M-L-T system.
Figure 1
Solution
lOMoARcPSD|4710873

Question 2:
A 1:60 scale model of a ship is used in a water tank to simulate a ship speed of 10 m/s. What
should be the model speed? If a towing force of 10 N is measured on the model, what force is
expected on the prototype? Neglect viscous effects.
Solution
lOMoARcPSD|4710873

Assignment 2 2003
Due Date: 9th
September 2003
Question 1:
The drag force FD on the smooth sphere of Figure 1 falling in a liquid depends on the constant
sphere speed V, the density of the sphere ρs, the liquid density ρ and viscosity µ, the sphere
diameter D, and gravity g. Find an expression for the dimensionless force FD/( ρV2
D2
) using the
M-L-T system.
Figure 1
Solution
lOMoARcPSD|4710873

Assignment 2 2004
Due Date: 8th
September 2004
Question 1:
Under certain conditions, the drag force FD on the airfoil of Figure 1 depends on the fluid velocity
V, the liquid density ρ and viscosity µ, the cord length c, the angle of attack α and the length of
the wing w. Find an expression for the dimensionless force FD/( ρV2
c2
) using the M-L-T system.
Figure 1
),,,,,( αµρ wcVfFD =
Repeating variables V, c, ρ. The π terms are:
αππ
µ
ρ
π
ρ
π ==== 432221 ,,,
w
ccV
cV
FD






= α
µ
ρ
ρ
,,
w
ccV
f
cV
FD
122
FD
lOMoARcPSD|4710873

Question 2:
A 1:30 reduced scale model study of a submarine is carried on to investigate a shape
modification.
a) The real submarine (prototype) is 2 m in diameter and it is designed to travel at 15 m/s
when totally submerged. The 1:30 model submarine is towed totally submerged in a water
tank at 2 m/s and a drag force of 2.15 N is measured. Predict the drag force in the prototype
(hint: assume high-Reynolds-number conditions).
b) Would your previous results apply if the submarine emerges and travels on the water
surface? Briefly explain why or why not.
DpDm CC =
pp
Dp
mm
Dm
AV
F
AV
F
22
2
1
2
1
ρρ
=
KN
A
A
V
V
FF
m
p
m
p
DmDp 109302556152 2
2
2
=== *.*.
b) No, wave drag becomes important and Froude similarity must be used. This is not possible
since
ppm
m
m
yygy
V
F
53
30819
2 .
/*.
===
ppp
p
p
yygy
V
F
84
819
15 .
*.
===
IN BOTH QUESTIONS, SHOW ALL WORKING.
lOMoARcPSD|4710873

Assignment 2 2005
Due Date: 31st
August 2005
Question 1:
The drag force FD on the smooth sphere of Figure 1 falling in a liquid depends on the liquid
density ρ and viscosity µ, the submerged density of the sphere (ρs- ρ), the constant sphere speed
V, the sphere diameter D, and gravity g. Find an expression for the dimensionless force FD/(
ρV2
D2
Figure 1
Solution
-ρ
-ρ
[ρs-ρ]
ρs-ρ
,ρs-ρ
lOMoARcPSD|4710873

Question 2:
A weir is placed on a water channel. The flow rate over the weir is 2 m3
/s. A 1:10 model of the
weir is tested in a laboratory water channel.
a) What flow rate should be used in the model?
b) If a force of 12 N is measured in the model weir, what force would be expected in the
prototype?
c) Downstream of the weir, the channel is piped and goes underground. If we want to study the
friction on the pipe, can we extend the model and include the pipe? Briefly explain why or why
not.
Solution
lOMoARcPSD|4710873

Assignment 2 2004
Due Date: 8th
September 2004
Question 1:
c2
Figure 1
αππ
µ
ρ
π
ρ
π ==== 432221 ,,,
w
ccV
cV
FD
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
= α
µ
ρ
ρ
,,
w
ccV
f
cV
FD
122
FD
lOMoARcPSD|4710873

Question 2:
A 1:10 model study is to be carried out on a low speed airfoil that is to fly at a prototype velocity of
50 m/s.
a) If a wind tunnel is used for the model, what velocity should be used in the model? Is such a
test advisable?
b) If a water channel is used, what would be the velocity in the model and the drag force ratio
between model and prototype?
lOMoARcPSD|4710873

Question 1:
The drag force FD on the smooth sphere of Figure 1 falling in a liquid depends on the liquid
density ρ and viscosity µ, the submerged density of the sphere (ρs- ρ), the constant sphere speed
V, the sphere diameter D, and gravity g. Find an expression for the dimensionless force FD/(
ρV2
D2
Figure 1
Solution
Question 2:
It is desired to study the motion of water waves in an open channel by using a 1:20 scale model.
You must:
a) Determine the scale ratios (prototype-to-model) for
velocity
force
acceleration
b) Determine the time it takes for a wave in the model channel to travel a certain distance if it
takes 30 seconds to travel the corresponding distance in the prototype.
-ρ
-ρ
[ρs-ρ]
ρs-ρ
,ρs-ρ
lOMoARcPSD|4710873

Assignment 2 2008
Due Date: 10th
April 2008
Question 1:
c2
Figure 1
αππ
µ
ρ
π
ρ
π ==== 432221 ,,,
w
ccV
cV
FD
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
= α
µ
ρ
ρ
,,
w
ccV
f
cV
FD
122
Question 2:
A 1/50 reduced scale model of a submarine is carried out to investigate a shape modification.
You are asked to:
a) Neglecting viscous effects, predict the velocity and drag force in the prototype when the
model submarine is travelling on the water surface at 2 m/s and a drag of 30 N is
measured.
b) Briefly explain if your results still apply when the submarine travels totally submerged.
FD
lOMoARcPSD|4710873

Assignment 2 2009
Due Date: 23 April 2009
Question 1:
c2
Figure 1
αππ
µ
ρ
π
ρ
π ==== 432221 ,,,
w
ccV
cV
FD
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
= α
µ
ρ
ρ
,,
w
ccV
f
cV
FD
122
Question 2:
A 1:20 scale model of a weir is used to determine the forces on the structure under different flow
conditions. The model weir is placed on a laboratory water channel and the flow rate over the
weir is 2 m3
/s. Please answer the following:
b) If a force of 1.2 N is measured in the model weir, what force would be expected in the
prototype?
not.
FD
lOMoARcPSD|4710873

Assignment 2 2011
Due Date: 15th
April
Question 1:
V, the liquid density ρ and viscosity μ, the cord length c, the angle of attack α and the length of
the wing w. Find an expression for the dimensionless force FD/( ρV
2
c
2
Figure 1
αππ
µ
ρ
π
ρ
π ==== 432221 ,,,
w
ccV
cV
FD






= α
µ
ρ
ρ
,,
w
ccV
f
cV
FD
122
Question 2:
A 1:20 scale model of a weir is used to determine the forces on the structure under different flow
conditions. The model weir is placed on a laboratory water channel and the flow rate over the
weir is 2 m
3
/s. Please answer the following:
b) If a force of 1.2 N is measured in the model weir, what force would be expected in the
prototype?
not.
FD
lOMoARcPSD|4710873

Assignment 3 2003
Due Date: 25th
September 2003
Question 1:
A stream function is given by:
x
y
y 1
1010 −
+= tanψ
a) show that it is a possible ideal flow
b) assuming water to be flowing, find the pressure along the x-axis if p=100kPa far away (x=∞)
c) locate any stagnation points (v=0) along the x-axis
Solution
lOMoARcPSD|4710873

Question 2:
Flow past a cylinder is given by a combination of uniform flow and a doublet. The corresponding
streamfunctions are:
Uy=ψ uniform flow
22
yx
y
+
−=
µ
ψ doublet
For a uniform flow of 10 m/s and a doublet strength of 40 m3
/s you are asked to:
a) compute the velocity at points A, B, C and D
b) compute the pressure at A and C assuming p=0 far away (x=∞)
c) (optional) sketch the streamlines using the Potential Flow Builder and verify your previous
results noting that the program gives the velocity components (u, v) and 2
50 U
p
Cp
ρ.
=
A
(2;0)
B
(4;0)
C
(0;2)
D
(0;4)
lOMoARcPSD|4710873

Solution:
lOMoARcPSD|4710873

Assignment 3 2004
Due Date: 22nd
September 2004
Question 1:
2222
4020 yxyx +=+= ln)ln(ψ
b) assuming water to be flowing, find the pressure at (0, 2m) if p=20kPa far away
c) sketch the streamlines
Solution
lOMoARcPSD|4710873

Question 2:
Flow past a cylinder is given by a combination of uniform water flow of 4 m/s and a doublet of
strength 4 m3
/s. The corresponding streamfunctions are:
Uy−=ψ uniform flow
22
yx
y
+
=
µ
ψ doublet
a) Compute the velocity at points A, B, and C
b) Compute the pressure at A, B and C assuming p=50 kPa far away (x=∞)
c) (optional) Sketch the streamlines using the Potential Flow Builder and verify your previous
50 U
p
Cp
ρ.
=
IN BOTH QUESTIONS, SHOW ALL WORKING.
A
(rc;0)
C
(0;rc) B (0.707rc; 0.707rc)
U∞
lOMoARcPSD|4710873

Assignment 3 2005
Due Date: 21st
September 2005
Question 1:
x
y
y 1
1010 −
+= tanψ
b) assuming water to be flowing, find the pressure along the x-axis if p=100kPa far away (x=-∞)
lOMoARcPSD|4710873

Question 2:
Consider the frictionless flow past a cylinder shown in the next figure. The cylinder radius is 2m.
a) compute the velocity at points A and B.
b) compute the pressure at A and B assuming p=0 far away (x=-∞)
c) (optional) sketch the streamlines using the Potential Flow Builder and verify your previous
50 U
p
Cp
ρ.
=
A
(-0.707rc;
-0.707rc)
B (0; 1.5rc)
lOMoARcPSD|4710873

Assignment 3 2006
Due Date:
Question 1:
2222
c) sketch the streamlines and name the flow pattern
Solution
lOMoARcPSD|4710873

Question 2:
strength 6 m3
A
(rc;0)
C
(0;rc) B (0.707rc; 0.707rc)
U∞
lOMoARcPSD|4710873

Question 1:
x
y
y 1
1010 −
+= tanψ
b) assuming water to be flowing, find the pressure along the x-axis if p=100kPa far away (x=-∞)
lOMoARcPSD|4710873

Question 2:
A circular cylinder of 0.5 m diameter is immersed in a uniform water flow (20o
C) of velocity 5 m/s.
For potential, steady, incompressible flow around the cylinder you are asked to:
a) Write the corresponding stream function
b) Determine the maximum and minimum values of velocity and pressure on the cylinder surface.
Pressure far from the cylinder is 100 kPa.
2.
lOMoARcPSD|4710873

Assignment 3 2008
Due Date:
Question 1:
2222
c) sketch the streamlines and name the flow pattern
Solution
lOMoARcPSD|4710873

Question 2:
Combination of a flow to the right of 30 m/s and a source of strength 50 π m2
/s at the origin
results in the flow pattern of the next figure. You are asked to:
Locate any stagnation points.
a) Find velocity and pressure at points A and C if the fluid is water and the pressure far away
(x = -∞) is 100 kPa.
b) Find the y intercept yB of the body (hint: use the value of the streamline that goes through A).
U∞ = 30 m/s A
B
C
(-2,0) (0,0)
lOMoARcPSD|4710873

Assignment 3 2009
Due Date: 7th
May 2009
Question 1:
2222
Solution
lOMoARcPSD|4710873

Question 2:
strength 4 m3
22
yx
y
+
=
µ
ψ doublet
A
(rc;0)
C
(0;rc) B (0.707rc; 0.707rc)
U∞
lOMoARcPSD|4710873

Assignment 3 2011
Due Date: 13th
May
Question 1:
2222
Solution
lOMoARcPSD|4710873

Question 2:
strength 4 m
3
22
yx
y
+
=
µ
ψ doublet
A
(rc;0)
C
(0;rc) B (0.707rc; 0.707rc)
U∞
lOMoARcPSD|4710873

Assignment 4 2003
Due Date: 17th
October 2003
Question 1 (30%):
A flagpole is composed of three sections: a 5-cm-diameter top section that is 10 m long, a 7.5-
cm-diameter middle section 15 m long and a 10-cm-diameter bottom section 20 m long. Calculate
the total force acting on the flag pole for a 25-m/s windspeed. Make the calculations for:
a) A winter day at -300
C.
b) A summer day at 350
C.
Question 2 (70%):
The pump of the next figure has a characteristic curve shown below.
a) Estimate the flow rate.
b) Sketch the EGL and the HGL.
lOMoARcPSD|4710873

Solution
ηp (%)
lOMoARcPSD|4710873

Assignment 4 2004
Due Date: 18th
October 2004
Question 1:
A 2-m-diamater smokestack stands 60 m high. It is designed to resist a 40-m/s wind. At this
speed, what total force would be expected and what moment would the base be required to
resist? Make the calculations for:
C.
C.
Solution
a)
mNM
NF
FigfromC
VD
D
D
..
.)(.
)..(..
.
Re
6
2
6
5
1076330400105
2801259060240451
2
1
98901047
10081
240
×=×=
=×××××=∴
=∴×=
×
×
= −
ν
b)
mNM
NF
FigfromC
VD
D
D
..
.)(.
)..(..
.
Re
6
2
6
5
1003330400105
0881019060240171
2
1
98901084
10651
240
×=×=
=×××××=∴
=∴×=
×
×
= −
ν
lOMoARcPSD|4710873

Question 2:
The system shown in the figure has a pump with a characteristic curve shown below.
a) Estimate the flow rate and the power required by the pump. Account for all entrance/exit and
frictional loses.
b) Draw the EGL (energy grade line) and the HGL (hydraulic grade line).
Solution
200 m 100 m
ηp (%)
lOMoARcPSD|4710873

Assignment 4 2005
Due Date: 19th
October 2005
Question 1:
the total force acting on the flag pole and the resisting moment for a 25-m/s windspeed. Make the
calculations for:
C.
C.
Question 2 :
The system of the figure has a turbine with a characteristic curve HT=8Q, where Ht is the head
used by the turbine in m and Q is the discharge in m3
/s. Turbine efficiency ηT=0.88.
a) Estimate the flow rate and the power generated by the turbine. Account for all
entrance/exit and frictional loses.
lOMoARcPSD|4710873

20 m
lOMoARcPSD|4710873

Assignment 4 2006
Due Date: 23rd
May 2006
Question 1:
calculations for:
C.
C.
lOMoARcPSD|4710873

Question 2:
The system shown in the figure has a pump with a characteristic curve shown below. The system
starts pumping when the right reservoir water level is 20 m below the left reservoir and stops
when the right reservoir level is 20 m above the left reservoir.
a) Estimate the flow rate and the power required by the pump for the two situations of the figure.
Account for all entrance/exit and frictional loses.
b) Sketch the EGL (energy grade line) and the HGL (hydraulic grade line) for both situations.
ηp (%)
20 m
lOMoARcPSD|4710873

Assignment 4 2007
Due Date: 21st
May 2007
Question 1:
A 2-m-diamater smokestack stands 60 m high. It is designed to resist a 40-m/s wind. At this
speed, what total force would be expected and what moment would the base be required to
resist? Make the calculations for:
C.
C.
Solution
a)
mNM
NF
FigfromC
VD
D
D
..
.)(.
)..(..
.
Re
6
2
6
5
1076330400105
2801259060240451
2
1
98901047
10081
240
×=×=
=×××××=∴
=∴×=
×
×
= −
ν
b)
mNM
NF
FigfromC
VD
D
D
..
.)(.
)..(..
.
Re
6
2
6
5
1003330400105
0881019060240171
2
1
98901084
10651
240
×=×=
=×××××=∴
=∴×=
×
×
= −
ν
125 280
101 088 2.97
1.15
lOMoARcPSD|4710873

Question 2:
The pump of the next figure has a characteristic curve shown below.
a) Estimate the flow rate and pump power requirements.
b) Sketch the EGL and the HGL of the system.
ηp (%)
lOMoARcPSD|4710873

Assignment 4 2008
Due Date: 15th May 2008
Question 1:
calculations for:
C.
C.
lOMoARcPSD|4710873

Question 2:
An oil (γ =8044 N/m3
, µ = 0.2 Ns/m2
) is pumped between two storage tanks in a pipe with L=2440 m,
D=200 mm and e (roughness)= 0.2 mm. The pipe has two valves with head loss coefficients K=5.5, placed
as shown in the figure. Using the pump curve provided below you must:
a) Estimate the oil discharge and pump power requirements.
0
10
20
30
40
50
60
0 0.02 0.04 0.06 0.08 0.1 0.12
Q (m3
/s)
Hp(m)
0
10
20
30
40
50
60
70
80
ηp(%)
32 m
P
L/4 L/4L/4L/4
flow
lOMoARcPSD|4710873

Assignment 4 2009
Due Date: 21st
May 2009
Question 1:
calculations for:
C.
C.
lOMoARcPSD|4710873

Assignment 4 2011
Due Date: 26th May
Question 1:
calculations for:
0
C.
0
C.
lOMoARcPSD|4710873

Assignment 5 2003
Due Date: 31st
October 2003
Question 1:
In the piping system shown in the next figure:
a) determine the r values for the pipes using the data of the table, assuming high
Reynolds number flow.
b) determine the water flow distribution using the Hardy-Cross method. Starting with the
Qinitial values in the table and the flow directions of the figure, perform two iterations.
Use n=2.
Pipe L (m) D (m) e (m) Qinitial (m
3
/s)
1 500 0.3 0.00015 0.15
2 600 0.25 0.00015 0.075
3 126 0.15 0.00015 0.05
4 229 0.25 0.00015 0.1
5 236 0.3 0.00015 0.025
Solution
0.075 m3
/s
C
D
E
lOMoARcPSD|4710873

Assignment 5 2004
Due Date: 1st
November 2004
Question 1:
Consider the pipe network in the figure. The reservoir provides all the water required by the
demand. Determine the flow distribution using the Hardy Cross method after two iterations.
Assume initial flow directions as given in the figure and initial discharges Q1=Q3. Use n=2.
Reservoir
Q1
Q2
Q3
r1=3 s2
/m5
r3=2 s2
/m5
r2=5 s2
/m5
∆Q
lOMoARcPSD|4710873

Assignment 5 2005
Due Date: 28th
October 2005
Question 1:
1) Determine the flow distribution in the following water system using the Hardy Cross method.
Assume initial flow directions as given in the figure and initial discharges Q1=Q3=3.5 m3
/s
and Q2=0. Use r1=r2=r3=2 s2
/m5
.
Loop Pipe Qi ±riQi
2
riQi Qi ±riQi
2
riQi Qi
m
m
m
1st
iteration 2nd
iteration
lOMoARcPSD|4710873

Assignment 5 2006
Question 1:
/s
/m5
.
Loop Pipe Qi ±riQi
2
riQi Qi ±riQi
2
riQi Qi
m
m
m
1st
iteration 2nd
iteration
lOMoARcPSD|4710873

Due Date: June 1 2007
Question 1:
Consider the pipe network in the figure. The reservoir provides all the water required by
the demand. Determine the flow distribution using the Hardy Cross method after two
iterations. Assume initial flow directions as given in the figure and initial discharges Q1=Q3.
Use n=2.
Reservoir
Q
Q1
Q2
Q3
r1=2 s2
/m5
r3=3 s2
/m5
r2=5 s2
/m5
∆Q
0.035 m3
/s
0.015 m3
/s
lOMoARcPSD|4710873

Assignment 5 2008
Due Date: May 30 2007
Question 1:
Consider the pipe network in the figure. Determine the flow distribution using the Hardy Cross method after one
iteration. Assume initial flow discharges and directions as given in the figure. Use n =2.
0.2 m3
/s 0.05 m3
/s
0.2 m3
/s 0.45 m3
/s
r1=51s2
/m5
Q1=0.3 m3
/s
r3=1636 s2
/m5
Q3=0.02 m3
/s
r2=280 s2
/m5
Q2=0.15 m3
/s
r4=310 s2
/m5
Q4=0.23 m3
/s
r5=14875 s2
/m5
Q5=0.03 m3
/s
lOMoARcPSD|4710873

Assignment 5 2009
Due Date: 4th
June 2009
Question 1:
/s
/m5
.
Loop Pipe Qi ±riQi
2
riQi Qi ±riQi
2
riQi Qi
m
m
m
1st
iteration 2nd
iteration
lOMoARcPSD|4710873

Assignment 5 2011
Due Date: 2nd
June
Question 1:
Assume initial flow directions as given in the figure and initial discharges Q1=Q3=3.5 m
3
/s
and Q2=0. Use r1=r2=r3=2 s
2
/m
5
.
Loop Pipe Qi ±riQi
2
riQi Qi ±riQi
2
riQi Qi
m
m
m
1st
iteration 2nd
iteration
lOMoARcPSD|4710873

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