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.

I dont think that makes a helluva a lot of sense. i would think the answer would be: (9.80*103)(h3) = 4(110*103 N) I haven't taken an engineering class in 4 years so take that with a grain of salt.

That's what I thought too but I didn't think he would make that simple of a mistake. It gets the right answer, I just thought perhaps I was missing something.

That's not Little Big League, is it? And to quote another awesome character in response to that problem.... "Seriously.... da fuck???"

You need to calculate the center of pressure for the moment arms, you can't just use h and 4. Cp = (I / (Yc*A)) + Yc where I is interia, Yc is the distance to center of mass, and A is area Cp for water = ((1/12) * 2 * h^3)/((h/2) * (h*2)) + h/2 = 2h/3 Cp for gas = ((1/12) * 2 * 4^3)/((4/2)*(4*2)) + (4/2) = 8/3 Multiply by a factor of 1/2 and you get h/3 and 4/3. Even though you can get the same answer using 4 and h, technically thats not the correct way to do it and I guess its just a coincidence they're the same.