Question

Assertion: Aeroplanes are made to run on the runway before take-off, so that they acquire the necessary lift. Reason: This is as per Bernoulli's theorem.

Suppose that an incompressible fluid is flowing through the pipe of varying cross-sectional area, in a steady flow. Its velocity must change as a consequence of equation of continuity. A force is required to produce this acceleration, which is caused by the fluid surrounding it, the pressure must be different in different regions. Bernoulli's equation is a general expression that relates the pressure difference between two points in a pipe to both velocity changes (kinetic energy change) and elevation (height) changes (potential energy change). The statement of Bernoulli's relation is: As we move along a streamline the sum of the pressure (P), the kinetic energy per unit volume and the potential energy per unit volume (ρgh) remains a constant. Note that in applying the energy conservation principle, there is an assumption that no energy is lost due to friction. In practice, it has a large number of useful applications and can help explain a wide variety of phenomena for low viscosity incompressible fluids.