Question

A stream of water goes through a garden hose into a nozzle. As the water speeds up, what happens to the water pressure? (13.3)

   A stream of water goes through a garden hose into a nozzle. As the water speeds up, what happens to the water pressure? (13.3)

Physics Principle and Problems

Physics Principle and Problems

Paul W. Zitzewitz,… 1st Edition

Chapter 13, Problem 62

Instant Answer

Solved by Expert Dading Chen

05/25/2020

Step 1

Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. This principle is written mathematically as: \[P + \frac{1}{2}ρv^2 + ρgh = Show more…

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A stream of water goes through a garden hose into a nozzle. As the water speeds up, what happens to the water pressure? (13.3)

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Key Concepts

Continuity Equation

The Continuity Equation is a principle derived from the conservation of mass in fluid dynamics, which asserts that for an incompressible fluid, the product of the cross-sectional area and the fluid velocity must remain constant along a flow path. This concept explains why, when the cross-sectional area of a flow is reduced (as in the case of a nozzle), the velocity of the fluid increases, which in turn, based on Bernoulli's Principle, leads to a decrease in fluid pressure.

Bernoulli's Principle

Bernoulli's Principle is a fundamental concept in fluid dynamics which states that in a streamline flow of an incompressible, non-viscous fluid, the sum of the static pressure, dynamic pressure (related to velocity), and hydrostatic pressure remains constant along the flow. This principle explains how an increase in the fluid's velocity leads to a corresponding decrease in its pressure, and is key to understanding phenomena like the pressure drop observed when water flows through a nozzle.

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