Question

a tank with a flat bottom of area a and vertical sides is filled to a depth h withwater. the top of the water is at atmospheric pressure. what is the absolute pressure at thebottom of the tank?

Answer 1

The absolute pressure at the bottom of the tank is determined by Pascal's Law, accounting for the atmospheric pressure at the water's surface and the weight of the water column.

The absolute pressure at the bottom of the tank can be determined by considering the pressure variation with depth in a fluid. The pressure at any depth in a fluid is given by Pascal's Law and is influenced by the weight of the fluid above that point.

The pressure at a certain depth (h) is expressed as:

`\[ P = P_0 + \rho \cdot g \cdot h \]`

where:

- (P) is the pressure at depth,

-
`\(P_0\)`is the atmospheric pressure at the top of the fluid,

-
`\(\rho\)` is the density of the fluid,

- (g) is the acceleration due to gravity, and

- (h) is the depth.

For the tank with a flat bottom, the depth (h) corresponds to the distance from the water's surface to the bottom of the tank.

As the water's surface is at atmospheric pressure,
`\(P_0\)` is the atmospheric pressure, and since the water is open to the atmosphere, the pressure at the water's surface is also atmospheric pressure.

Now, substitute these values into the pressure formula:

`\[ P_{\text{bottom}} = P_0 + \rho \cdot g \cdot h \]`

At the bottom of the tank, (h) is the total depth of the water. The density
`(\(\rho\))` of water and the acceleration due to gravity (g) are constants.

This equation provides the absolute pressure at the bottom of the tank, accounting for the weight of the water above that point.