Augmented Bernoulli Equation
There were a number of assumptions used in deriving the Bernoulli equation. One of these was that the flow had no viscous losses. An augmented Bernoulli equation is frequently used to include various head loss or head creation terms. A pump is a device that creates head, while friction losses decrease head.
The “head” form of Bernoulli’s equation is
Recall that Bernoulli’s equation was derived using the assumption that there were no viscous shear stresses (ie. the flow is inviscid). The Bernoulli equation is generally modified to include viscous losses after the fact. One such modification is friction losses in pipe flow. The Darcy friction factor states that the head loss is equal to
Where the friction factor, f, can be computed using a Moody diagram. The augmented Bernoulli equation that accounts for the frictional head loss is
Note that the friction loss term appears on the right hand side of the equation (the outlet side).
How friction losses are incorporated into the Bernoulli equation.