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The hydrostatic force on the floor is $$F= \gamma \cdot h \cdot Area$$ for both the pipe and funnel. But, for the funnel there is so much more water. So, we expect the force to be higher for the funnel. But it is the same for both. Where does the other part of the force go for the funnel?

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  • $\begingroup$ Is the floor the only part of the pipe or tunnel that has a component of the wall in the vertical direction that water presses on? $\endgroup$ – tpg2114 Oct 9 at 3:26
  • $\begingroup$ Yes, I think so $\endgroup$ – Screenwriter James Oct 9 at 3:29
  • $\begingroup$ Okay -- well, revisit your drawings. Gravity points straight down. What is the normal vector for each wall surface you drew? And the floor? Once you draw your normal vectors for each wall section, are there any components of it that are not perpendicular to the gravity force? $\endgroup$ – tpg2114 Oct 9 at 3:31
  • $\begingroup$ Please find the link below.This may help-physics.usask.ca/~chang/course/ep324/lecture/lecture8.pdf $\endgroup$ – Nemu Rozario Oct 9 at 3:59
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Where does the other part of the force go for the funnel?

It's supported by the horizontal component of the sloping walls of the funnel, not the bottom of the cylindrical portion of the funnel.

See figures below. The bottom of the cylinder to the left supports the entire weight of the fluid above it. The weight of the fluid outside the cylindrical part of the funnel of the figure in the middle is not supported by the floor of the cylinder but by the horizontal component of the sloping walls of the funnel. This might be easier to visual with a different shape as shown in the figure to the right below.

Hope this helps.

enter image description here

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It presses on the funnel.

Imagine that the lower cylinder of the funnel extended all the way to the top. So you had water in the central cylinder pressing on the floor, and you had a separate conical area with the center cut out, full of water. You could drain the center cylinder and the rest of the water would still be there, pressing down on the funnel. But while the water level is the same for the outer cone and the inner cylinder, you can have them separate or not and it won't affect the pressure.

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