# Physics Study Guide/Fluids

## Buoyancy

**Buoyancy** is the force due to pressure differences on the top and
bottom of an object under a fluid (gas or liquid).

Net force = buoyant force - force due to gravity on the object

## Bernoulli\'s Principle

Fluid flow is a complex phenomenon. An ideal fluid may be described as:

-   The fluid flow is **steady** i.e its velocity at each point is
    constant with time.
-   The fluid is **incompressible**. This condition applies well to
    liquids and in certain circumstances to gases.
-   The fluid flow is **non-viscous**. Internal friction is neglected.
    An object moving through this fluid does not experience a retarding
    force. We relax this condition in the discussion of **Stokes\'
    Law**.
-   The fluid flow is **irrotational**. There is no angular momentum of
    the fluid about any point. A very small wheel placed at an arbitrary
    point in the fluid does not rotate about its center. Note that if
    turbulence is present, the wheel would most likely rotate and its
    flow is then not irrotational.

As the fluid moves through a pipe of varying cross-section and
elevation, the pressure will change along the pipe. The Swiss physicist
Daniel Bernoulli
(1700-1782) first derived an
expression relating the pressure to fluid speed and height. This result
is a consequence of conservation of energy and applies to ideal fluids
as described above.

\'\'Consider an ideal fluid flowing in a pipe of varying cross-section.
A fluid in a section of length $\Delta x_1$ moves to the section of
length $\Delta x_2$ in time $\Delta t$ . The relation given by Bernoulli
is:

where:

$$P$$ is pressure at cross-section

$$h$$ is height of cross-section

$$\rho$$ is density

$$v$$ is velocity of fluid at cross-section

In words, the Bernoulli relation may be stated as: *As we move along a
streamline the sum of the pressure ($P$), the kinetic energy per unit
volume and the potential energy per unit volume remains a constant.*

------------------------------------------------------------------------

*(To be concluded)*
