# Fluid Statics: Pressure and Buoyancy

Physics I · Principles of Waves, Fluids and Thermodynamics · https://tryals.app/learn/physics-i/fluid-statics-pressure-and-buoyancy

## Hydrostatic Pressure

Water does not care what is above it: pressure at depth depends only on depth, not the container's shape.

**Pressure** is force per unit area: $P = F/A$ in pascals ($Pa$).

**Hydrostatic pressure** at depth $h$ is:

$$P = P_0 + \rho g h$$

where $P_0$ is atmospheric pressure and $\rho$ is density.

| Instrument | Principle |
| --- | --- |
| Manometer | Hydrostatic pressure |
| Barometer | Atmospheric pressure |
| Hydraulic press | Pascal's principle |
| Hydrometer | Buoyancy |

**Pascal's principle**: Confined fluid pressure transmits equally. Thus $\frac{F_1}{A_1} = \frac{F_2}{A_2}$ runs hydraulics.

## Buoyancy & Archimedes

**Archimedes' principle**: The buoyant force equals the weight of displaced fluid:

$$F_b = \rho_{\text{fluid}}\,g\,V_{\text{displaced}}$$

**Floating condition**: An object floats when $\rho_{\text{object}} < \rho_{\text{fluid}}$. The submerged fraction is:

$$\frac{V_{\text{sub}}}{V_{\text{total}}} = \frac{\rho_{\text{object}}}{\rho_{\text{fluid}}}$$

> **Common pitfall:** Buoyancy depends on the **displaced fluid's** weight, not the object's. A steel ship floats because its hollow shape displaces a huge volume of water; solid steel sinks.

## Practice questions

4 of this lesson's 11 practice questions, with answers. The full set is in the app.

### 1. Which of the following are consequences of Pascal's principle?

A. A heavy object always sinks regardless of shape
B. Pressure in a fluid is the same at equal depths
C. Hydraulic lift can multiply applied force
D. A small piston force can move a large piston

**Answer:** B. Pressure in a fluid is the same at equal depths; C. Hydraulic lift can multiply applied force; D. A small piston force can move a large piston

**Why:** Pascal's principle underlies hydraulic machines; buoyancy depends on displaced volume, not just mass.

Page: https://tryals.app/practice/physics-i/fluid-statics-pressure-and-buoyancy/which-of-the-following-are-consequences-of-pascals-principle

### 2. Sort each object into Floats in water or Sinks in water (density of water $= 1000$ kg/m$^{3}$).

**Answer:**

- Floats: Oak wood ($\rho$ $\approx 700$ $kg/m^{3}$), Ice ($\rho$ $\approx 917$ $kg/m^{3}$), Balsa wood ($\rho$ $\approx 120$ $kg/m^{3}$)
- Sinks: Aluminium ($\rho$ $\approx 2700$ $kg/m^{3}$), Lead ($\rho$ $\approx 11 340$ $kg/m^{3}$), Granite ($\rho$ $\approx 2700$ $kg/m^{3}$)

**Why:** Objects with density less than 1000 $kg/m^{3}$ float; those with greater density sink.

Page: https://tryals.app/practice/physics-i/fluid-statics-pressure-and-buoyancy/sort-each-object-into-floats-in-water-or-sinks-in-water-density-of

### 3. You float in a boat on a small pond, holding a heavy anchor. You **throw the anchor overboard** and it sinks. What happens to the pond’s water level?

A. It stays exactly the same
B. It rises only if the anchor is denser than water
C. It rises slightly
D. It falls slightly

**Answer:** D. It falls slightly

**Why:** Aboard, the anchor forces the boat to displace water equal to the anchor’s weight, a large volume, since water is less dense. Sunk, it displaces just its own smaller volume. Displacement shrinks, so the pond level drops. Archimedes beats intuition here.

Page: https://tryals.app/practice/physics-i/fluid-statics-pressure-and-buoyancy/you-float-in-a-boat-on-a-small-pond-holding-a-heavy-anchor-you

### 4. Pressure in a fluid depends on depth but not on the shape or volume of the container. Why does a narrow tube exert the same pressure as a wide tank at equal depth?

A. Because pressure depends on volume, which is equal at equal depth
B. Because a narrow tube contains less fluid and so weighs less
C. Because pressure depends only on the height of the column
D. Because the shape affects pressure only for compressible fluids

**Answer:** C. Because pressure depends only on the height of the column

**Why:** Only the column height enters $P = \rho g h$. This is why a thin tube of water can burst a barrel, and why hydraulic systems multiply force the way they do.

Page: https://tryals.app/practice/physics-i/fluid-statics-pressure-and-buoyancy/pressure-in-a-fluid-depends-on-depth-but-not-on-the-shape-or-volume