Page 65 - ebook fluid mechanics_finalize

FLUID MECHANICS

Example 3.6

Consider a barge filled with rock. The barge is 7 m wide, 17 m long, and 2.5 m deep. If the

barge and rock weigh 2 MN, determine the depth of submergence of the barge in water
as shown in the figure below.

Rock

Barge

2.5 m
d
17 m

Submergence Depth

3
3
The specific weight of water is 9,810 N/m (or 9.81 kN/m ). From the buoyancy concept,
the volume of displaced fluid (water) must balance the weight of the barge. Thus,

Wbarge= ρwater X gX Vbarge

Substituting volume, Vbarge= B x l x d we have:

W barg e =  water  g B l D

Wbarge= (1000 x 9.81)(7 m)(17 m) d Or

W
d = b arg e
(9810 N / m 3 )( m 177 )( m )

Substituting the weight of the barge gives:

2 MN
d = = . 1 71 m
( 8.9 x10 3 N / m 3 )( m 177 )( m )

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