Name: liquid speed from reservoir outlets
Uploaded: 2026-01-30T03:08:28.000Z
Duration: 1 min 14 s
Channel: JoVE

Free jets demonstrate fluid behavior described by Bernoulli's equation, as the fluid exits a nozzle and flows freely into the air.
The flow velocity at the nozzle is determined by the height of the fluid column above it, which converts potential energy into kinetic energy.
The jet's exit pressure matches the atmospheric pressure, and the velocity increases as the fluid flows from a large reservoir.
Due to fluid inertia, the jet narrows just outside the nozzle, forming the smallest cross-sectional area. This phenomenon is known as the vena contracta.
The ratio of the area of the jet at the vena contracta and the area of the nozzle gives the contraction coefficient.
Various nozzle shapes, such as knife-edge, well-rounded, sharp-edge, and re-entrant designs, impact the flow pattern and the contraction coefficient.
In designing systems such as spillways and weirs, the vena contracta effect is considered for accurate flow measurement.
Free jets are crucial in civil engineering applications for controlling fluid flow and minimizing structural impact.

free jet

Free jets describe the flow of liquid exiting a reservoir through an opening into the atmosphere without resistance. The velocity (v) of the liquid jet is derived using Bernoulli's principle and expressed as:
<img alt="Velocity formula \( v = \sqrt{2gh} \); static equilibrium; equations; educational resource." src="/files/ftp_upload/18037/18037_Equation_1.svg" style="text-align: center; height: 15px;" data-altupdatedat="1776744004000" data-alt="Equation 1">
Where h is the height of the liquid above the opening. This relationship assumes atmospheric pressure at both the reservoir surface and the jet exit. The fluid column's height governs the fluid's velocity at the nozzle in a reservoir, where the fluid's potential energy converts into kinetic energy during flow.
The phenomenon of vena contracta occurs when the liquid exits through a sharp-edged orifice, causing the jet diameter dj to be smaller than the nozzle diameter do. This occurs because the fluid streamlines cannot follow the abrupt edges, creating a contracted flow region. The contraction coefficient is the ratio of the jet's cross-sectional area at the vena contracta to the nozzle's cross-sectional area, quantifying the degree of jet contraction. This parameter is influenced by the nozzle's geometry, with various designs such as knife-edge, sharp-edge, well-rounded, and re-entrant nozzles producing distinct flow patterns and contraction characteristics. For a well-rounded nozzle, Cc = 1.0, while sharp or knife-edged orifices reduce Cc to approximately 0.61. Re-entrant nozzles exhibit even lower values.
These flow characteristics and contraction effects are critical in engineering applications involving liquid discharge, from reservoirs to industrial nozzles.

Free Jet

Free jets demonstrate fluid behavior described by Bernoulli's equation, as the fluid exits a nozzle and flows freely into the air.
The flow velocity ...

Education

JoVE Core

Civil Engineering

Unit 1

Fluid Dynamics

KEY TERMS AND CONCEPTS

liquid speed from reservoir outlets

Free jets show how liquid moves after leaving a reservoir through an opening and flowing into the air without resistance. The jet speed is found with Bernoulli’s principle, and it depends on the height of liquid above the opening. This relationship assumes atmospheric pressure at both the reservoir surface and the jet exit.

The liquid column’s height controls the speed at the nozzle because the fluid’s potential energy changes into kinetic energy during flow. As the liquid leaves the reservoir, its motion reflects this energy conversion. This is why a deeper liquid level can produce a faster jet.

A sharp-edged orifice can also cause vena contracta, which is the narrowed region where the jet becomes smaller than the nozzle opening. This happens because the streamlines cannot follow the abrupt edge smoothly. The contraction coefficient measures this narrowing by comparing the jet area at vena contracta with the nozzle area.

Nozzle shape changes the flow pattern and the amount of contraction. Knife-edge, sharp-edge, well-rounded, and re-entrant nozzles each produce different results. For a well-rounded nozzle, the contraction coefficient is 1.0, while sharp or knife-edged openings reduce it to about 0.61, and re-entrant nozzles produce even lower values. These effects matter in engineering systems that discharge liquid from reservoirs and industrial nozzles.

Liquid Speed from Reservoir Outlets

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Free jets show how liquid moves after leaving a reservoir through an opening and flowing into the air without resistance. The jet speed is found with Bernoulli’s principle, and it depends on the height of liquid above the opening. This relationship assumes atmospheric pressure at both the reservoir surface and the jet exit. The liquid column’s height controls the speed at the nozzle because the fluid’s potential energy changes into kinetic energy during flow. As the liquid leaves the...

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key terms and concepts

Learn how liquid speed from a reservoir depends on height, Bernoulli’s principle, and nozzle shape, including vena contracta and contraction coefficient.

Liquid Speed from Reservoir Outlets | JoVE K12

JoVE Core Civil Engineering offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Liquid Speed from Reservoir Outlets

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