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182  Solutions Manual   Fluid Mechanics, Fifth Edition

 

C2.7  Venice, Italy is slowly sinking,

so now, especially in winter,

 plazas and walkways are flooded.

The proposed solution is the floating

levee of Fig. P2.7. When filled with air,

it rises to block off the sea. The levee is

30 m high and 5 m wide. Assume a uniform

Storm – filledwith air to float

g. .

Hinge

Levee filled with water – no storm

Venice

Lagoon –

24 m deep

Adriatic Sea -25 m deep in

a strong storm

density of 300 kg/m3 when

floating. For the 1-meter

Sea-Lagoon difference shown, estimate the angle at which the levee floats.

Solution: The writer thinks this problem is

FAS

FVL

B

W

rather laborious. Assume  seawater  = 1025 kg/m3.

There are 4 forces: the hydrostatic force FAS on the

Adriatic side, the hydrostatic force F on the lagoonVL

side, the weight W of the levee, and the buoyancy B

of the submerged part of the levee. On the Adriatic

side, 25/cos   meters are submerged. On the lagoon side,

24/cos  meters are submerged. For buoyancy, average the two depths, (25+24)/2 = 24.5 m.

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Chapter 2   Pressure Distribution in a Fluid 183

For weight, the whole length of 30 m is used. Compute the four forces per unit width

into the paper (since this width b will cancel out of all moments):

m N  E gL B

m N gLW 

 E  LghF 

 E  LghF 

averagesub

levee

submerged VLVL

submerged  AS  AS 

/6232.1)5)(5.24)(81.9)(1025()widthlevee(

/441500)5)(30)(81.9)(300()widthlevee(

cos/6896.2)cos/24)(2/24)(81.9)(1025(

cos/6142.3)cos/25)(2/25)(81.9)(1025(

  

  

    

    

The hydrostatic forces have CP two-thirds of the way down the levee surfaces. The

weight CG is in the center of the levee (15 m above the hinge). The buoyancy center is

halfway down from the surface, or about (24.5)/2 m. The moments about the hinge are

where the forces are listed above and are not retyped here. Everything is known except

the listing angle    (measured from the vertical). Some iteration is required, say, on

Excel, or, for a good initial guess (about  = 15-30), EES converges nicely to    Ans.  

 ________________________________________________________________________  

C2.8  What is the uncertainty is using pressure measurement as an altimeter? A gage

on the side of an airplane measures a local pressure of 54 kPa, with an uncertainty of 3

kPa. The estimated lapse rate that day is 0.0070 K/m, with an uncertainty of 0.001 K/m.

Effective sea-level temperature is 10C, with an uncertainty of 4C. Effective sea-level

 pressure is 100 kPa, with an uncertainty of 3 kPa. Estimate the airplane’s altitude and its

uncertainty.

0sin)2

5.24()

3

cos/24(sin)15()

3

cos/25(      

     m BmF mW mF  M  VL AS hinge