Fluids Mechanics ll

1. © Dr. A.B.M. Toufique Hasan (BUET) 7
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (July 2021)
Drag Force cont…
The body streamlining is very important to reduce the drag.
For high performance vehicles and other moving bodies, the name of the game is drag reduction , for
which intense research continues for both aerodynamic and hydrodynamic applications.
Rectangular cylinder Cylinder with rounded nose
Cylinder with rounded nose and
streamlined sharp trailing edge
Circular cylinder with the same drag as case (c)

2. © Dr. A.B.M. Toufique Hasan (BUET) 8
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (July 2021)
Drag Force cont…
Fig. Drag coefficients of smooth two dimensional
(wide span) bodies at low Mach number
Creeping
flow

3. © Dr. A.B.M. Toufique Hasan (BUET) 9
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (July 2021)
Drag Force cont…

4. © Dr. A.B.M. Toufique Hasan (BUET) 10
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (July 2021)
Drag Force cont…

5. © Dr. A.B.M. Toufique Hasan (BUET) 11
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (Jan. 2020)

6. © Dr. A.B.M. Toufique Hasan (BUET) 12
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (Jan. 2020)
Automobile Aerodynamic Drag
Porsche Taycan (EV)
CD = 0.25
Tesla Model S (EV)
CD = 0.24
Volkswagen XL 1
(Diesel+PIH)
CD = 0.19
Audi A3
CD = 0.31

7. © Dr. A.B.M. Toufique Hasan (BUET) 13
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (Jan. 2020)
Drag Force cont…
Problem:
A square 15-cm piling is acted on by a water flow of 1.5 m/s that is 6 m deep as shown in fig. Estimate the maximum
bending moment exerted by the flow on the bottom of the piling.
15 cm
6 m
1.5 m/s
Solution:
The flow of water will introduce drag force on the square pile.
Reynolds number for this flow problem is:
4
5
6
10
10
25
.
2
10
1
)
15
.
0
)(
5
.
1
(
Re >
×
=
×
=
=
−
∞
ν
h
U
(ρ= 1000 kg/m3 and ν = 10-6 m2/s for water)*
Thus, CD data can be used from the Table and for square
cylinder, CD is 2.1. (Table 7.2)
N
4
.
2179
area
cted
area/proje
frontal
;
)
6
15
.
0
(
5
.
1
1000
2
1
)
1
.
2
(
2
1
Now,
2
2
=
⇒
=






×
×
×
×
=
⇒






= ∞
D
D
D
D
F
A
F
A
U
C
F ρ

8. © Dr. A.B.M. Toufique Hasan (BUET) 14
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (Jan. 2020)
15 cm
6 m
1.5 m/s
Since the upstream flow is uniform, the center of action of this
force should be at middle of the depth.
Therefore, the bending moment on the bottom of the piling will be
Nm
2
.
6532
)
2
6
)(
4
.
2179
(
2
=
=
×
=
L
F
M D
(ρ= 1000 kg/m3 and ν = 10-6 m2/s for water)*
FD
Further study:
Solve the above problem considering the section of the pile as
(i) Equilateral triangle
(ii) Half cylinder

9. © Dr. A.B.M. Toufique Hasan (BUET) 2
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (Jan. 2020)
Problem:
Electrical transmission towers are stationed at 500 m interval and a conducting cable 2 cm in diameter is strung
between them. If an 80 km/h wind is blowing transversely across the wires, calculate the total force each tower
carrying 20 such cables is subjected to. Assume there is no interference between the wires.
kN
56
.
3
)
500
02
.
0
(
60
60
1000
80
2
.
1
2
1
2
.
1
2
1
,
cable
single
for
Drag
2
2
=
⇒








×






×
×
×
×
=
⇒






= ∞
D
D
D
D
F
F
A
U
C
F ρ
4
5
10
3
10
8
.
1
02
.
0
60
60
1000
80
2
.
1
Re ×
≈
×
×






×
×
×
=
= −
∞
µ
ρ d
U
d
From the graph of drag coefficient: CD = 1.2
So, the total drag for 20 cables = 20x3.56 = 71.2 kN (Ans.)
Solution:

10. © Dr. A.B.M. Toufique Hasan (BUET) 3
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (Jan. 2020)
(Continuation) Problem:
Also establish whether the wires are likely to be subjected to self-induced vibrations and if so what the frequency
would be?
(Ans.)
Hz
220
=
f
Solution:
∞
=






−
=
U
fd
St
St
number,
Strouhal
where
Re
7
.
19
1
198
.
0

11. © Dr. A.B.M. Toufique Hasan (BUET) 4
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (Jan. 2020)
Problem:
A hot film probe is mounted on a cone-and-rod system in a sea level airstream of 45 m/s as shown in figure. Estimate
the maximum cone vertex angle allowable if the flow-induced bending moment at the root of the rod is not to
exceed 30 N.cm.
Solution:
(Ans.)
60°
≈
θ

12. © Dr. A.B.M. Toufique Hasan (BUET) 5
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (Jan. 2020)
Problem:
A pickup truck has a clean drag area CDA of 3.25m2. Estimate the horsepower required to drive the truck at 88 km/h
(a) clean and (b) with the 0.9-by 1.8-m sign as shown in figure installed if the rolling resistance is 667 N at sea level.
1.8 m
0.9 m
Solution:

13. © Dr. A.B.M. Toufique Hasan (BUET)
Problem:
A high speed car with m = 2000 kg, CD = 0.3, and A = 1m2 deploys a 2-m parachute to slow down from an
initial velocity of 100 m/s as shown in figure. Assuming constant CD, brakes free, an no rolling resistance,
calculate the distance and velocity of the car after 1, 10, 100, and 1000 s.
Assume sea-level condition, and neglect interference between the wake of the car and the parachute.
6
L-3 T-2, Dept. of ME ME 323: Fluid Mechanics-II (July 2021)