I need your help on this fluid mechanics problem.
Problem Statement:
An open tank has a vertical partition and contains gasoline (ρ=700 kg/m3 ) to the right at a depth of 4m as sketched. The partition contains a rectangular gate that is 4m high and 2m wide and is hinged at the bottom with a stop at the top against outflow of gasoline. Water is slowly added to the left side of the tank that was originally empty. At what depth h will the gate start to open?
Diagram:
FBD:
So my friend already worked out this analysis for me:
FRg = γghcgAg
where g refers to gasoline..
FRg = (700 kg/m^3)(9.81 m/s^2)(2m)(4m * 2 m)
= 110*10^3 N
= 110 kN
FRw = γwhcwAw
where w refers to water...
FRw = (9.80*103 N/m^3)(h/2)(2m * h)
where h is depth of the water...
FRw = (9.80*103)h^2
For Equilibrium,
ΣMH = 0
so that,
FRw*lw = FRg*lg
with lw = h/3 and lg = 4/3 m
Thus,
(9.80*10^3)(h^2)(h/3) = (110*10^3 N)(4/3 m)
= h = 3.55 m
This all makes sense to me except one part. Where does "with lw = h/3 and lg = 4/3m" come from? How are these moment arms derived?
Thanks to anyone who can help.
Problem Statement:
An open tank has a vertical partition and contains gasoline (ρ=700 kg/m3 ) to the right at a depth of 4m as sketched. The partition contains a rectangular gate that is 4m high and 2m wide and is hinged at the bottom with a stop at the top against outflow of gasoline. Water is slowly added to the left side of the tank that was originally empty. At what depth h will the gate start to open?
Diagram:
FBD:
So my friend already worked out this analysis for me:
FRg = γghcgAg
where g refers to gasoline..
FRg = (700 kg/m^3)(9.81 m/s^2)(2m)(4m * 2 m)
= 110*10^3 N
= 110 kN
FRw = γwhcwAw
where w refers to water...
FRw = (9.80*103 N/m^3)(h/2)(2m * h)
where h is depth of the water...
FRw = (9.80*103)h^2
For Equilibrium,
ΣMH = 0
so that,
FRw*lw = FRg*lg
with lw = h/3 and lg = 4/3 m
Thus,
(9.80*10^3)(h^2)(h/3) = (110*10^3 N)(4/3 m)
= h = 3.55 m
This all makes sense to me except one part. Where does "with lw = h/3 and lg = 4/3m" come from? How are these moment arms derived?
Thanks to anyone who can help.
Last edited: