11.14: PROBLEM DEFINITION
Situation:
Wind is blowing on a 55 gallon drum.
m = 48 lbm = 21 .
8 kg .
H = 34 .
5 in = 0 .
876 m .
D = 22 .
5 in = 0 .
571 m .
Find: Wind speed (m/s) that will cause the drum to tip over.
Assumptions:
The drum will tip over before it slips.
Air temperature is 20 ◦ C .
C
D is the same as that of a rectangular plate. Thus, C
D
≈ 1 .
20 from Table 11.1.
Properties: Air ( 20 ◦ C ), Table A.3, ρ = 1 .
2 kg / m 3 , ν = 15 .
1 × 10 − 6 m 2 / s .
PLAN
1. Relate the drag force to wind speed using the drag force equation.
2. To determine when the drum will tip, sum moments about point O.
Drag Force
Weight
Point “O”
3. Find the wind speed by combining results from steps 1 and 2.
SOLUTION
1. Drag force:
F
D
= C
D
A
Ref
ρV
2
2
2. Moment equilibrium (about 0).
= C
D
HD
ρV
2
2
F
D
H
2
= mg
D
2
15
(1)
(2)

3. Combine Eqs. (1) and (2):
C
D
HD
ρV
2
2
= mg
D
H
Solve for the wind speed
V =
= s mg
D
H s
ρC
D
2
HD
= r
H
2
2 mg
ρC
2 (21 .
8 kg) (9 .
81 m / s 2 )
D
(0 .
876 m)
2
(1 .
2 kg / m 3 ) (1 .
2)
V = 19 .
7 m / s
REVIEW
This wind speed is about 44 mph.
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