11.14: PROBLEM DEFINITION Situation: Wind is blowing on a 55

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11.14: PROBLEM DEFINITION

Situation:

Wind is blowing on a 55 gallon drum.

m = 48 lbm = 21 .

8 kg .

H

D

= 34 .

5 in = 0 .

876 m .

= 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.

16

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