An open tank has a vertical partition and on one side contains gasolin

quiquenobi2v6 2021-12-15 Answered

An open tank has a vertical partition and on one side contains gasoline with a density p=700kgm3 at a depth of 4m. Arectangular gate that is 4 m high and 2 m wide and hinged at one end is located in the partition. Water is slowly added to the empty side of the tank. At what depth, h, will the gate start to open?

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Expert Answer

esfloravaou
Answered 2021-12-16 Author has 43 answers
The depth of water possible that will cause for the gate to open can be solved by summing up the forces acting on the wall to the hinge.
The forces acting on the wall are the weight and the hydrostatic forces cause by the water and the gasoline.
Use γ for water which is equal to 9.80kNm3 trom Table 1.5.
The specific weight of the gasoline can be solved by multiplying its density by the acceleration due to gravity which is equal to 9.81ms2
γgas=p{gas}×g
=700kgm3×9.81ms2
=6867Nm3
=6.87kNm3
The hydrostatic force on the gate can be solved using the formula FR=γhcA where γ is the specific weight of liquid, hc is the centroid of the gate with liquid and A is the area of the gate with liquid.
Solve for the hydrostatic force exerted by the gasoline.
FR1=γgashcA
=6.87kNm3(4m2)(4m×2m)
=109.92kN
Solve for the hydrostatic force exerted by the water.
FR2=γwaterhcA
=9.80kNm3(h2)(h×2m)
Sum up the moment of the two hydrostatic forces.
Note that the location of the hydrostatic force for rectangular plane surfaces can be found 13 of the height of the liquid from the base.
FR1×134m=FR2×13h
=109.92kN×134m=9.80h2kNm2×13h
146.56kNm=3.27h3kNm2
146.56kNm3.27kNm2
44.87m3=h3
3{44.87m3}=3{h3}
3.55m=h
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intacte87
Answered 2021-12-17 Author has 42 answers
FRg=γghCgAg
where g refers to gasoline..
FRg=(700kgm3)(9.81ms2)(2m)(4m2m)
=110103N
=110kN
FRw=γwhcwAw
where w refers to water...
FRw=(9.80103Nm3)(h2)(2mh)
where h is depth of the water...
FRw=(9.80103)h2
For Equilibrium,
MH=0
so that,
FRwIw=FRgIg
with lw=h3 and Ip=43m
Thus,
(9.80103)(h2)(h3)=(110103N)(43m)
=h=3.55m
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