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So, I'm having trouble answering an assignment. I need to find the force in the spring just before the gate opens, and I know how to get exactly that (taking the moment at A). But, I'm having trouble finding Fv.

In my understanding, Fv is the weight of the fluid above the curved surface, at least that's what my textbook says so. But, in this problem, the fluid above the arc is different from the one below it. What then would be the hydrostatic force Fv of the water if the fluid above the curved surface is not water? Will there be two Fv? One from the hydrostatic force exerted by the water (upward) and one from the hydrostatic force exerted by liquid X (downward)? How do I find it?

I'm really having a hard time trying to imagine what the FBD looks like, so any help will be appreciated.

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  • $\begingroup$ Try not to start your work with forces , but with pressure and pressure differences which only depend on h and the density of the fluids. $\endgroup$
    – trula
    Sep 23 at 17:31
  • $\begingroup$ Welcome to Physics SE! It might be illuminating to draw a small portion of the gate in conjunction with the inside and outside pressures acting normal to its surface. The pressure is $\rho_i g h_i$ for fluid $i$, where $h$ is the depth below a free surface. If a free surface doesn’t exist, you need more information, or you might make an assumption (e.g., the density of a gas is negligible). Remember that positive pressures push on surfaces—they don’t suck on them. $\endgroup$ Sep 23 at 17:31
  • $\begingroup$ An example which may help using the idea of centre of pressure? $\endgroup$
    – Farcher
    Sep 24 at 9:56

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