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# Borda-Carnot equation

EmilyB.Borda-Carnot equation

The **Borda-Carnot Equation** calculator computes the mechanical energy loss of a fluid due to sudden expansion.

**INSTRUCTIONS:** Choose the preferred units and enter the following:

- (
**ε**) This the the empirical loss coefficient - (
**ρ**) This is the density of the fluid (see common mean densities below) - (
**v**) This is the fluid velocity before the sudden expansion._{1} - (
**v**) This is the fluid velocity after the sudden expansion._{2}

**Mechanical Energy Loss:** The calculator returns the mechanical energy loss as a change in pressure in units of Pascals (Pa). However, this can be automatically converted to other pressure units via the pull-down menu.

### The Science

The **Borda-Carnot equation** in fluid dynamics is an empirical description of the mechanical energy losses of the fluid due to a (sudden) flow expansion. It describes how the total head reduces due to the losses. This in contrast with Bernoulli's principle for dissipationless flow (without irreversible losses), where the total head is a constant along a streamline. The Borda-Carnot equation is used for open channel flow as well as in pipe flows:

**ΔE = ε•½•ρ•(v _{1}-v_{2})^{2}**

where:

- ΔE = Borda-Carnot mechanical energy loss
- ε = empirical loss coefficient
- ρ = fluid density
- v
_{1}= mean flow velocity before expansion - v
_{2}= mean flow velocity after expansion

### Common Mean Densities

vCalc has a large library of mean densities for different substances. To look up the mean density of a substance including many fluids, CLICK HERE.

Density is computed as follows:

where:

- (M) is mass of the object
- (V) is the volume.

To compute density with the formula above, CLICK HERE.

## References

Wikipedia (https://en.wikipedia.org/wiki/Borda%E2%80%93Carnot_equation)