In a nozzle how does velocity increase with the expense of pressure?

Question

In a nozzle the velocity is incresed with the expense of pressure.

Answer 1

The narrowing of the nozzle forces the flow to increase.
This is 'Bernoulli's Principle' which states that, 'An increase in velocity causes a decrease in pressure at the point of restriction'.
The 'Differential Pressure' (DP), between the inlet to the nozzle and the pressure across the restriction can be measured and translated into flow rate.

Answer 2

In a De Laval nozzle, the flow is compressed as it travels at subsonic speeds into the narrow, restricted part of the nozzle. At the throat (the narrowest part), the flow is moving at the speed of sound. If there is enough pressure at the throat, the flow will then go supersonic as the nozzle widens (according to the velocity-area relation). Up to a certain point, the wider the nozzle gets, the faster the flow will go. This enables rocket engines to achieve gas flow at several times the speed of sound, giving a large amount of thrust.

As the gas speeds up through the expanding part of the nozzle, its density, temperature, and pressure all drop. Perhaps that is what you were referring to.

Answer 3

If you consider the flow rate to be constant (such as gallons per second out of a fire hydrant) then in order to maintain the flow rate through a constricted aperture, you need to increase the velocity.

BTW: I'm not exactly sure what you mean by "expense of pressure."
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