# I Hydrostatic force on bottom

Tags:
1. Jun 30, 2016

### jzwillows

Is the force from a liquid against the horizontal bottom of a container a function of depth and cross sectional area at the bottom only, i.e., computed by the formula Force=unit weight of water x depth x cross sectional area? If so the force could be greater than the weight of water and that defies logic.

2. Jun 30, 2016

### Staff: Mentor

If the fluid is in equilibrium then $F=mg=\rho h A g$

3. Jun 30, 2016

An interesting question. What you are basically asking is if we take a funnel shaped container that is wider at the bottom than at the top, can we have more force on the bottom face than the total weight of water? And the answer is yes. The total forces on the water must be zero though. The bottom pushes up with more force than the weight (downward gravitational force), but the sides of the funnel container press partly downward on the water as the water presses (from water pressure) against this surface. Thereby the downward forces from the slanted walls plus gravity will equal (in magnitude) the upward force from the bottom face on the water so that the water is in equilibrium with zero net forces. The force that the bottom face presses upward is the same for a funnel shape as it is for a cylinder shape of the same height that is filled with water. The pressure at the bottom (force per unit area) simply depends on the depth of the water, plus any atmospheric pressure...editing... a follow-on: I believe a hydraulic brake works by a similar arrangement. You apply force (and pressure) at the narrow funnel opening. The pressure balances everywhere, but the bottom face has much larger area, thereby more total force on the brake pad than the force you apply with your foot. Instead of a funnel shape, you could have a somewhat narrow cylinder containing the water, with a wider bottom section, and it requires very little (weight of the) water in the cylinder to cause considerable force on the bottom face.

Last edited: Jun 30, 2016
4. Jun 30, 2016

### jzwillows

Thanks very much Charles.
.

5. Jul 1, 2016

6. Jul 1, 2016

### Staff: Mentor

Oh, I misunderstood the question. I thought he was talking about a cylinder.

7. Jul 2, 2016