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

在污水处理系统中安装了文丘里流量计以测量污水的流量。如果已知流量且黏性效应可忽略不计，则连接到流量计的压力表所显示的压力差是多少？
首先，根据管道和喉部各自的直径，计算它们的横截面积。
然后，利用连续性方程，根据给定的流量确定两个截面处的流速。
由于面积与流速成反比，废水从大直径管道进入较小的喉管时流速会加快。
接下来，应用伯努利方程，该方程将流动中两点之间的压强差与速度变化关联起来。
该方程表明，当水流从较粗管道进入较细喉管时，随着流速增加，将产生相应的压力下降。
最后，将速度代入伯努利方程，计算管道与喉部之间的压力差。
连接到流量计上的压力表将显示最终的压力差。

伯努利方程问题求解

文丘里流量计对于测量管道中的流体流速至关重要。它利用了伯努利方程描述的流体速度和压力之间的关系。当安装在污水系统中时，文丘里流量计通过测量压力差来准确确定废水流速。 第一步是计算管道和文丘里喉管的横截面积，以分析压力表指示的压力差。接下来，应用连续性方程，该方程表明，对于不可压缩流体，体积流速 (Q) 沿管道保持不变： <img alt="Equation 1" src="/files/ftp_upload/18035/18035_Equation_1.svg" style="text-align: center; height: 12px;"> A1 和 A2 是管道和喉管的横截面积，V1 和 V2 是这些部分的流体速度。通过重新排列方程，喉管处的速度可以表示为： <img alt="Equation 2" src="/files/ftp_upload/18035/18035_Equation_2.svg" style="text-align: center; height: 30px;"> 因此，可以根据给定的流速计算速度 V1 和 V2。 伯努利方程联系的是理想流体中的压力和速度，如下所示： <img alt="Equation 3" src="/files/ftp_upload/18035/18035_Equation_3.svg" style="text-align: center; height: 27px;"> 其中，P1 和 P2 是管道和喉管中的压力，⍴ 是流体的密度。压力差 (P1 - P2) 可以通过将速度 V1 和 V2 代入该方程来计算。压力表指示的压降 (ΔP) 反映了废水流过较窄喉管时速度的增加，这与能量守恒一致。

在污水处理系统中安装了文丘里流量计以测量废水流量。如果已知流量且黏性效应可忽略不计，则……

Education

教育

JoVE Core

Civil Engineering

土木工程

Unit 1

第一单元

Fluid Dynamics

流体力学

KEY TERMS AND CONCEPTS

关键术语与概念

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

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