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

ベンチュリーメーターは、廃水流量を測定するために下水道に設置されています。流量が分かっていて、粘性の影響が無視できる場合、流量計に取り付けられている圧力計が示す圧力差はどれくらいですか?
まず、パイプとスロートの両方の断面積をそれぞれの直径を使用して計算します。
次に、連続方程式を使用して、与えられた流量に基づいて両方のセクションの速度を決定します。
面積と速度は反比例するため、廃水は大口径のパイプから小さなスロートに移動するときに速度が上がります。
次に、流れの 2 点間の圧力差を速度の変化に関連付けるベルヌーイの方程式を適用します。
この方程式は、水が大きなパイプから小さなスロートに移動するときに速度が増加すると、対応する圧力降下が発生することを示しています。
最後に、速度をベルヌーイの方程式に代入して、パイプとスロートの間の圧力差を計算します。
流量計に取り付けられた圧力計は、最終的な圧力差を示します。

ベルヌーイの方程式 - 問題解決

ベンチュリメータは、パイプライン内の流体の流量を測定するために不可欠です。これは、ベルヌーイの方程式で説明される流体の速度と圧力の関係を利用します。下水システムに設置すると、ベンチュリメータは圧力差を測定することで廃水の流量を正確に決定します。

 最初のステップは、管とベンチュリスロートの断面積を計算して、圧力計で示される圧力差を分析することです。次に、連続方程式を適用します。この方程式は、非圧縮性流体の場合、体積流量 (Q) がパイプラインに沿って一定のままであることを示しています。

<img alt="Equation 1" src="/files/ftp_upload/18035/18035_Equation_1.svg" style="text-align: center; height: 12px;">

A_1 と A_2 は管とスロートの断面積であり、V_1 と V_2 はこれらの部分の流体速度です。方程式を整理すると、スロートでの速度は次のように表すことができます。

<img alt="Equation 2" src="/files/ftp_upload/18035/18035_Equation_2.svg" style="text-align: center; height: 30px;">

 したがって、速度 V_1 と V_2 は、特定の流量に対して計算できます。

 ベルヌーイの方程式は、理想的な流体の圧力と速度を次のように関連付けます。

<img alt="Equation 3" src="/files/ftp_upload/18035/18035_Equation_3.svg" style="text-align: center; height: 27px;">

 ここで、P_1 と P_2 は管とスロート内の圧力、⍴ は流体の密度です。圧力差 (P_1 - P_2) は、速度 V_1 と V_2 をこの方程式に代入することで計算できます。圧力計で示されるこの圧力低下 (ΔP) は、廃水が狭いスロートを流れる際の速度の増加を反映しており、エネルギー保存と一致しています。

ベンチュリーメーターは、廃水流量を測定するために下水道に設置されています。流量が既知で、粘性の影響が無視できる場合、何ですか...

Education

JoVE Core

Civil Engineering

土木工学

Unit 1

ユニット1

Fluid Dynamics

流体力学

KEY TERMS AND CONCEPTS

主要用語と概念

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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