# Borda-Carnot equation

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DeltaE =
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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)
• (v1) This is the fluid velocity before the sudden expansion.
• (v2) This is the fluid velocity after the sudden expansion.

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•(v1-v2)2

where:

### 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.