Q.State Bernoulli's theorem for the steady flow of an ideal (incompressible and non-viscous) fluid, writing it as an equation, and briefly explain the physical meaning of each of the three terms in it. State one assumption on which Bernoulli's theorem depends.

Bernoulli's theorem states that for the steady flow of an ideal (incompressible, non-viscous) fluid along a single streamline:

where $P$ is the fluid's pressure at a point, $\rho$ is its (constant) density, $v$ is its flow speed at that point, $g$ is the acceleration due to gravity, and $h$ is the point's height above a chosen reference level.

Meaning of each term (each is a form of energy per unit volume of the fluid):

• $P$: the pressure energy per unit volume.
• $\tfrac12\rho v^2$: the kinetic energy per unit volume, directly analogous to $\tfrac12mv^2$ but written per unit volume.
• $\rho g h$: the gravitational potential energy per unit volume, directly analogous to $mgh$ but written per unit volume. …

State the equation, identify each of its three terms with the corresponding familiar form of mechanical energy (written per unit volume rather than per unit m …

• Forgetting that the constant in Bernoulli's theorem applies along a single streamline, not necessarily the same constant everywhere in the fluid, unless the flow is also irrotational. …