Solução de Mecflu
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Transcript of Solução de Mecflu
8/12/2019 Solução de Mecflu
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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