Name: venturi meter flow rate from pressure
Uploaded: 2026-01-30T03:08:31.000Z
Duration: 1 min 16 s
Channel: JoVE

Ein Venturi-Messgerät wird in einem Abwassersystem installiert, um die Abwasserdurchflussrate zu messen. Wenn die Durchflussrate bekannt ist und viskose Effekte vernachlässigbar sind, wie groß ist die Druckdifferenz, die von dem am Durchflussmesser angebrachten Manometer angezeigt wird?
Berechnen Sie zunächst die Querschnittsflächen sowohl des Rohres als auch des Halses anhand ihrer jeweiligen Durchmesser.
Bestimmen Sie dann mit Hilfe der Kontinuitätsgleichung die Geschwindigkeiten in beiden Abschnitten basierend auf der gegebenen Durchflussrate.
Da Fläche und Geschwindigkeit umgekehrt proportional sind, beschleunigt sich das Abwasser, wenn es von dem Rohr mit größerem Durchmesser in den kleineren Hals fließt.
Wenden Sie als Nächstes die Bernoulli-Gleichung an, die die Druckdifferenz zwischen zwei Punkten in der Strömung mit der Geschwindigkeitsänderung in Beziehung setzt.
Diese Gleichung zeigt, dass mit zunehmender Geschwindigkeit, wenn sich das Wasser aus dem größeren Rohr in den kleineren Hals bewegt, ein entsprechender Druckabfall auftritt.
Berechnen Sie schließlich die Druckdifferenz zwischen dem Rohr und dem Hals, indem Sie die Geschwindigkeiten in die Bernoulli-Gleichung einsetzen.
Das am Durchflussmesser angebrachte Manometer zeigt die endgültige Druckdifferenz an.

bernoulli-gleichung – problemlösung

Ein Venturi-Messgerät ist für die Messung von Flüssigkeitsdurchflussraten in Rohrleitungen unerlässlich. Es nutzt die Beziehung zwischen Flüssigkeitsgeschwindigkeit und Druck, die durch die Bernoulli-Gleichung beschrieben wird. Wenn es in einem Abwassersystem installiert ist, bestimmt das Venturi-Messgerät die Abwasserdurchflussrate genau, indem es Druckunterschiede misst.

Der erste Schritt besteht darin, die Querschnittsflächen des Rohrs und der Venturi-Kehle zu berechnen, um den vom Druckmesser angezeigten Druckunterschied zu analysieren. Als Nächstes wird die Kontinuitätsgleichung angewendet, die besagt, dass die Volumenstromrate (Q) entlang der Rohrleitung für eine inkompressible Flüssigkeit konstant bleibt:

<img alt="Equation 1" src="/files/ftp_upload/18035/18035_Equation_1.svg" style="text-align: center; height: 12px;">

A_1 und A_2 sind die Querschnittsflächen von Rohr und Kehle und V_1 und V_2 sind die Flüssigkeitsgeschwindigkeiten in diesen Abschnitten. Durch Umstellen der Gleichung kann die Geschwindigkeit an der Verengung wie folgt ausgedrückt werden:

<img alt="Equation 2" src="/files/ftp_upload/18035/18035_Equation_2.svg" style="text-align: center; height: 30px;">

Somit können die Geschwindigkeiten V_1 und V_2 für eine gegebene Durchflussrate berechnet werden.

Die Bernoulli-Gleichung setzt Druck und Geschwindigkeit in einer idealen Flüssigkeit in Beziehung, gegeben durch:

<img alt="Equation 3" src="/files/ftp_upload/18035/18035_Equation_3.svg" style="text-align: center; height: 27px;">

Hier sind P_1 und P_2 die Drücke im Rohr und in der Verengung und ⍴ die Dichte der Flüssigkeit. Die Druckdifferenz (P_1 - P_2) kann berechnet werden, indem die Geschwindigkeiten V_1 und V_2 in diese Gleichung eingesetzt werden. Dieser Druckabfall (ΔP), der durch das Druckmessgerät angezeigt wird, spiegelt die Geschwindigkeitszunahme wider, wenn das Abwasser durch die engere Verengung fließt, was mit der Energieeinsparung vereinbar ist.

Bernoulli-Gleichung – Problemlösung

Ein Venturi-Messgerät wird in einem Abwassersystem installiert, um die Abwasserdurchflussrate zu messen. Wenn die Durchflussrate bekannt ist und viskose Effekte vernachlässigbar sind, was ist dann ...

Education

Lehre

JoVE Core

Civil Engineering

Bauingenieurwesen

Unit 1

Einheit 1

Fluid Dynamics

Strömungsmechanik

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

Bernoulli's Equation: Problem Solving

venturi meter flow rate from pressure

A Venturi meter measures fluid flow rate in a pipeline by using pressure changes and Bernoulli's equation. In a sewage system, it can be used to determine wastewater flow rate by reading the pressure difference across the meter. The narrowed throat makes the fluid speed up, and that change in speed is linked to pressure drop.

The first step is to find the cross-sectional areas of the pipe and the Venturi throat. These areas are needed to interpret the pressure difference shown on the pressure gauge. Next, the continuity equation is applied. For an incompressible fluid, the volumetric flow rate Q stays constant, and the pipe and throat areas are written as A1 and A2 with velocities V1 and V2.

From the continuity equation, the throat velocity can be rearranged and calculated from the flow rate. Once V1 and V2 are known, Bernoulli's equation is used to relate pressure and velocity in an ideal fluid. With the fluid density included, the pressures P1 and P2 in the pipe and throat can be compared to find the pressure difference.

Substituting the velocities into Bernoulli's equation gives the pressure drop, ΔP. That pressure drop is the value indicated by the pressure gauge. It reflects the increase in fluid speed as wastewater moves through the narrower throat, which follows energy conservation.

Venturi Meter Flow Rate from Pressure

bernoulli's equation for flow along a streamline

bernoulli-s-equation-for-flow-along-a-streamline

Pressure and Speed in Bernoulli's Equation

Bernoulli's equation links pressure, speed, and height in a moving fluid along a streamline. It is used for incompressible, inviscid fluids under steady flow. The idea comes from applying Newton's second law to a small fluid element. That element feels forces from pressure differences, gravity, and changes in velocity. The resulting equation shows how fluid energy is shared. In the equation, P is pressure, ρ is fluid density, v is velocity, g is the acceleration due to gravity, and h is...

bernoulli's equation for flow normal to a streamline

bernoulli-s-equation-for-flow-normal-to-a-streamline

Pressure Changes Across Curved Streamlines

Bernoulli's equation for flow normal to a streamline describes how pressure changes across curved streamlines. When a fluid follows a curved path, the outer side of the curve experiences centrifugal force, which pushes the fluid outward. The pressure is therefore higher on the inner side, near the center of curvature, and lower farther out. The size of this pressure difference depends on the fluid's velocity and the radius of curvature. In flows with nearly straight streamlines, the pressure...

bernoulli's equation: problem solving

A Venturi meter measures fluid flow rate in a pipeline by using pressure changes and Bernoulli's equation. In a sewage system, it can be used to determine wastewater flow rate by reading the pressure difference across the meter. The narrowed throat makes the fluid speed up, and that change in speed is linked to pressure drop. The first step is to find the cross-sectional areas of the pipe and the Venturi throat. These areas are needed to interpret the pressure difference shown on the pressure...

static, stagnation, dynamic and total pressure

static-stagnation-dynamic-and-total-pressure

Pitot-Static Measurement in Bernoulli Flow

Static pressure, dynamic pressure, stagnation pressure, and total pressure are key ideas in fluid dynamics. They are often explained with Bernoulli's equation. In that equation, p is static pressure, 1/2ρV^2 is dynamic pressure, γz is hydrostatic pressure or potential energy pressure, and pT is total pressure. For incompressible flow, the total pressure stays constant along a streamline. Static pressure is the pressure a fluid exerts when it is at rest, or when flowing fluid is brought to rest...

free jet

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...

continuity equation

Fluid Flow and Area Changes

Fluid flow and area changes are linked by the continuity equation. For a steady flow of an incompressible fluid in a confined system, the mass flow rate stays constant. This idea is useful in nozzles, syringes, and pipes where the cross-sectional area changes. The mass flow rate is written as an equation that connects density, area, and velocity. For incompressible flow, the density stays the same, so the equation becomes simpler. When the area gets smaller, the fluid speed must increase. When...

energy line and hydraulic gradient line

Fluid Head Profiles in Pipes and Channels

Fluid head profiles in pipes and channels show how pressure, speed, and height change in a flowing fluid. These profiles come from Bernoulli's equation for steady, incompressible, inviscid flow. In that equation, total head includes pressure head, velocity head, and elevation head. The energy line (EL) shows the total head available in the flow. It sits above the datum and includes all three energy parts. Under ideal conditions, the EL stays horizontal because the total energy does not change...

design example: designing water slide

Water Slide Speed and Bernoulli's Principle

Water slide speed is controlled by Bernoulli's principle and the height of the slide. Engineers use these ideas to keep the ride exciting while making sure the water stays safe for riders. As water moves downhill, gravity makes it speed up. The water at the bottom depends on the height it starts from. A taller slide gives the water more potential energy at the top. That energy changes into kinetic energy as the water descends, so the flow becomes faster. Bernoulli's principle helps describe...

key terms and concepts

See how a Venturi meter uses continuity and Bernoulli's equation to turn pressure differences into wastewater flow rate in a sewage system.

Venturi Meter Flow Rate from Pressure | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Venturi Meter Flow Rate from Pressure

Description

Transcript

Tags