An ideal fl uid fl ows through a horizontal pipe having a diameter that varies along its length. Does the sum of the pressure and kinetic energy per unit volume at different sections of the pipe

The sum of kinetic and pressure energy Increases as the pipe diameter increases.

Explanation:

An everyday occurrence and practical of this question have to do with you holding a water hose.A reduction in the size of the outlet cause the an increase in pressure and  a gain in kinetic energy.Little wonder how gardeners are able to properly water flowers at far distances.

This can be backed with Bernoulli’s theorem about total energy.

If the pipe is not of constant cross section, then the velocity of the water flowing will be inversely proportional to the pipe’s cross-sectional area.

The kinetic energy of the water is proportional to the square of the flow velocity.This energy will be highest where the cross-section is least.

So where the Kinetic energy is maximum, the pressure energy is minimum,thereby favoring an increase in the sum of pressure and kinetic energy per unit volume.

this could be newton#'s law of cooling. the cooling curve is exponential