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)
• (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:

• ΔE = Borda-Carnot mechanical energy loss
• ε = empirical loss coefficient
• ρ = fluid density
• v₁ = mean flow velocity before expansion
• v₂ = 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:

       ρ = M/V

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)