Problem 9.85

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Problem 9.85 [Difficulty: 3]
Given: Racing shell for crew approximated by half-cylinder:
L 7.32 m D 457 mm V 6.71
m
s

Find: (a) Location of transition on hull
(b) Thickness of turbulent BL at the rear of the hull
(c) Skin friction drag on hull
Solution:
Basic
equations:
FD CD
1
2
 ρ V
2
 A (Drag)
Transition occurs at Ret 5 10
5
 so the location of transition would be: xt
Ret ν
V
 xt 0.0745 m
For the turbulent boundary layer
δ
x
0.382
Rex
0.2
 Therefore δ
0.382 L
ReL
0.2

The Reynolds number at x = L is: ReL
V L
ν
4.91 10
7
 so the BL thickness is: δ
0.382 L
ReL
0.2
 δ 0.0810 m
The wetted area of the hull is: A
π D
2
L 5.2547 m
2
 For this Reynolds number: CD
0.455
log ReL  2.58
2.36 10
3

So the drag force is: FD CD
1
2
 ρ V
2
 A FD 278 N
Note that the rowers must produce an average power of P FD V 1.868 kW to move the shell at this speed.