## Conservation of Energy

**conservation of energy principle**and states that the

**total energy**of an isolated system remains constant — it is said to be conserved over time. This is equivalent to the

**First Law of Thermodynamics**, which is used to develop the general energy equation in thermodynamics. This principle can be use in the analysis of

**flowing fluids**and this principle is expressed mathematically by following equation:

where h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and Φ is the viscous dissipation function.

## Bernoulli’s Theorem

**The Bernoulli’s theorem** can be considered to be a statement of the **conservation of energy principle** appropriate for flowing fluids. It is one of the most important/useful equations in **fluid mechanics**. It puts into a relation **pressure and velocity** in an **inviscid incompressible flow**. **Bernoulli’s equation** has some restrictions in its applicability, they summarized in following points:

- steady flow system,
- density is constant (which also means the fluid is incompressible),
- no work is done on or by the fluid,
- no heat is transferred to or from the fluid,
- no change occurs in the internal energy,
- the equation relates the states at two points along a single streamline (not conditions on two different streamlines)

Under these conditions, the general energy equation is simplified to:

This equation is the most famous equation in **fluid dynamics**. **The Bernoulli’s equation** describes the qualitative behavior flowing fluid that is usually labeled with the term **Bernoulli’s effect**. This effect causes the **lowering of fluid pressure** in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy. The dimensions of terms in the equation are kinetic energy per unit volume.

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