Fluid Mechanics I
ENGR 2097
Winter 2015
ASSIGNEMNT 8
*** Please refer to the course outline on D2L for assignment policies ***
Question
Q1
Q2
Q3
Q4
Q5
Q6
Marks
15
15
20
15
20
(
Note for Q3
: You can start your calculation by
assuming the flow is laminar, but you need to
confirm your assumption with your calculated
Reynolds numbers.)
Q5
: The flow rate through the piping system shown
in the figure is 0.16 m
3
/s. Determine the power that
the pump adds to the water. The difference in
elevation of the two ponds is 61 m. Use
ρ
= 999.1
kg/m3 and
μ
= 1.138
×
10-3 kg/m
⋅
s for water.
Total
15
100

ENGR 2097 Assignment #8
Solutions
Q1
Solution
Oil is being discharged by a horizontal pipe from a storage tank open to
the atmosphere. The flow rate of oil through the pipe is
to be determined.
Assumptions
1
The flow is steady and incompressible.
2
The entrance effects are
negligible, and thus the flow is fully developed.
3
The entrance and exit loses are
negligible.
4
The flow is laminar (to be verified).
5
The pipe involves no components
such as bends, valves, and connectors.
6
The piping section involves no work devices
such as pumps and turbines.
Properties
The density and kinematic viscosity of oil are given to be
ρ
= 850 kg/m
3
and
ν
= 0.00062 m
2
/s, respectively. The dynamic viscosity is calculated to be
s
kg/m
527
.
0
)
/
m
00062
.
0
)(
kg/m
850
(
2
3
⋅
=
=
=
s
ρν
μ
Analysis
The pressure at the bottom of the tank is
2
2
2
3
gage
,
1
kN/m
35
.
33
m/s
kg
1000
kN
1
)
m
4
)(
m/s
81
.
9
)(
kg/m
850
(
=
Ο
Ο
Π
Ξ
Μ
Μ
Ν
Λ
⋅
=
=
gh
P
ρ
Disregarding inlet and outlet losses, the pressure drop across the pipe is
kPa
35
.
33
kN/m
35
.
33
2
gage
,
1
atm
1
2
1
=
=
=
−
=
−
=
Δ
P
P
P
P
P
P
Assume the flow is laminar
, then the flow rate through a horizontal pipe is determined
from
s
m
kN
s
m
kg
m
s
m
kg
m
m
kN
L
D
P
V
/
10
03
.
5
1
/
1000
)
40
)(
/
527
.
0
(
128
)
006
.
0
)(
14
.
3
)(
/
35
.
33
(
128
3
8
2
2
2
4
−
×
=
Ο
Ο
Π
Ξ
Μ
Μ
Ν
Λ
⋅
⋅
=
Δ
=
μ
π
!
The average fluid velocity and the Reynolds number in this case are
0172
.
0
s
kg/m
527
.
0
m)
m/s)(0.006
10
78
.
1
)(
kg/m
850
(
Re
m/s
10
78
.
1
4
/
m)
(0.006
/s
m
10
03
.
5
4
/
3
3
3
2
3
8
2
=
⋅
×
=
=
×
=
×
=
=
=
−
−
−
μ
ρ
π
π
VD
D
A
V
c
V
V
!
!
which is less than the critical Reynolds number 2300. Therefore,
the flow is laminar and
the analysis above is valid.
Discussion
The flow rate will be even less when the inlet and outlet losses are
considered, especially when the inlet is not well-rounded.
Q2
Solution
The flow rate through a specified water pipe is given. The pressure drop,
the head loss, and the pumping power requirements are to be determined.
Assumptions
1
The flow is steady and incompressible.
2
The entrance effects are
negligible, and thus the flow is fully developed.
3
The pipe involves no components such
Oil
tank
4 m
6 mm

as bends, valves, and connectors.
4
The piping section involves no work devices such as
pumps and turbines.
Properties
The density and dynamic viscosity of water are given to be
ρ
= 999.1 kg/m
3
and
μ
= 1.138
×
10
-3
kg/m
⋅
s, respectively. The roughness of stainless steel is 0.002 mm.