Lec.6 Deriving Bernoulli’s Equation

To derive Bernoulli’s equation, we apply the work–energy theorem to the fluid in a section of a flow tube. In we consider the element of fluid that at some initial time lies between the two cross sections a and c.
Bernoulli’s equation it states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the changes in kinetic and potential energies per unit volume that occur during the flow. We may also interpret Eq. (4) in terms of pressures. The first term on the right is the pressure difference associated with the change of speed of the fluid. The second term on the right is the additional pressure difference caused by the weight of the fluid and the difference in elevation of the two ends. The work dW is due to forces other than the conservative force of gravity, so it equals the change in the total mechanical energy (kinetic energy plus gravitational potential energy) associated with the fluid element. The mechanical energy for the fluid between sections b and c does not change.