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# Flow Measurement – Devices, Instruments, Types of Flow Meters

By BYJU'S Exam Prep

Updated on: September 25th, 2023

**Flow measurement** is nothing but quantification of bulk fluid movement. A variety of ways can be used to measure a flow. Positive displacement flow meters collect a certain fixed volume of fluid and then count the number of times the volume is filled for flow measurement. Fluid is the substance that deforms continuously under the action of shear forces. Flow measurement is also called the study of velocity and discharge of fluid flow.

To measure the fluid’s mass flow rate or volume flow rate, we need to use some flow measurement devices, namely mechanical flow meters, variable area meters, and differential pressure head meters. Here we will focus mainly on the pitot tube, venturi meter, inclined venturi meter, and orifice meter. In this article, the procedure to apply continuity and Bernoulli equations to determine flow measurement is explained in detail.

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**What is Flow Measurement?**

Measurement of mass flow rate or volume flow rate of fluid flow is defined as Flow Measurement. Flow measurement applications in the water industry range from small dosing and treatment flow in pipes of a few millimeters in diameter to the flow of treated or wastewater in trunk mains and aqueducts of 2m in diameter and above. Large interceptor sewers are frequently utilized in larger cities to collect enormous amounts of effluent and spent water and transport it to wastewater treatment facilities for processing.

Some interceptors have a diameter of several meters, may have a unique shape, and typically run partially full. Due to their widespread and varied application, flow meters are essential to the industry’s complete water cycle. Metering has an indirect or direct impact on resource management, process control, planning for new construction, distribution management, leak detection, financial control, and environmental challenges. The volume flow measurement is done in terms of m^{3}/s. This article aims to build an expression for volume flow rate in the case of the pitot tube, venturi meter, and orifice meter by applying continuity and Bernoulli equations.

- Continuity Equation: Mass balance

m_{in}=m_{out}

ρ_{1}A_{1}V_{1}= ρ_{2}A_{2}V_{2}

- Bernoulli’s Equation:

P/ρg+V^{2}/2g+Z = Constant

P_{1}/ρg+V_{1}^{2}/2g+Z_{1}= P_{2}/ρg+V_{2}^{2}/2g+Z_{2}

- Pitot tube
- Venturi meter
- Orifice meter

**Pitot Tube Flow Measurement**

Stagnation pressure P_{stag} is defined as the sum of static pressure P_{static} and dynamic pressure P_{dyn}. The stagnation point is the point where the total velocity of fluid becomes zero; here, the total kinetic energy of the fluid is converted into pressure energy.

Take two sections 1 and 2, as shown in Fig.

Apply Bernoulli’s equation between 1 and 2

P_{1}/ρg+V_{1}^{2}/2g+Z_{1}=P_{2}/ρg+V_{2}^{2}/2g+Z_{2}

Here, Z_{1}=Z_{2} and V_{2}=0

P_{1}/ρg+V_{1}^{2}/2g=P_{2}/ρg

P_{1}+1/2ρV_{1}^{2}= P_{2}

Stagnation pressure P_{2}

P_{2}=P_{1}+1/2ρV_{1}^{2}

P_{1}= Static pressure and Dynamic pressure =1/2ρV_{1}^{2}

Dynamic pressure head (h)

h=P_{dyn}/ρg=1/2ρV_{1}^{2}/ρg= V_{1}^{2}/2g

The velocity of fluid flow V_{1}

V_{1}=√(2gh)

**Venturi Meter Flow Measurement**

The flow measurement using the Venturi meter is used to measure the mass flow rate or volume flow rate of fluid flow. Venturi meter consists of convergent portion, throat, and divergent portion and takes two sections 1 and 2 as shown in Fig. Apply Bernoulli’s equation between 1 and 2.

P_{1}/ρg+V_{1}^{2}/2g+Z_{1}=P_{2}/ρg+V_{2}^{2}/2g+Z_{2}

Here, Z_{1}=Z_{2}

P_{1}/ρg-P_{2}/ρg=V_{1}^{2}/2g-V_{2}^{2}/2g

(P_{1}-P_{2})/ρg= (V_{1}^{2}-V_{2}^{2})/2g

Continuity equation

A_{1}V_{1}=A_{2}V_{2}

V_{2}=A_{1}V_{1}/A_{2}

The difference in pressure head (h) b/w two sections 1 and 2

h=(P_{1}-P_{2})/ρg= V_{2}^{2}/2g-V_{1}^{2}/2g

h=(P_{1}-P_{2})/ρg= (V_{2}^{2}-V_{1}^{2})/2g=[(A_{1}V_{1}/A_{2})^{2}-V_{1}^{2}]/2g=V_{1}^{2}/2g[(A_{1}/A_{2})^{2}-1]

The velocity of fluid flow V_{1} at sections 1-1

V_{1}=√2gh/√[(A_{1}V_{1}/A_{2})^{2}-1]=A_{2}√2gh/√(A_{1}^{2}– A_{2}^{2})

The volume flow rate or Discharge of fluid flow

Q=A_{1}V_{1}

Q=A_{1}A_{2}√2gh/√(A_{1}^{2}– A_{2}^{2})

Coefficient of discharge C_{d} is defined as the ratio of actual flow rate Q_{actual} and theoretical flow rate Q.

C_{d}=Q_{actual}/Q

Q_{actual}=C_{d}Q

Q_{actual}=C_{d}A_{1}A_{2}√2gh/√(A_{1}^{2}– A_{2}^{2})

**Orifice Meter Flow Measurement**

The flow measurement using an orifice meter measures the mass flow rate or volume flow rate of fluid flow. Take two sections 1 and 2, as shown in Fig. Apply Bernoulli’s equation between 1 and 2.

P_{1}/ρg+V_{1}^{2}/2g+Z_{1}=P_{2}/ρg+V_{2}^{2}/2g+Z_{2}

Here, Z_{1}=Z_{2}

P_{1}/ρg-P_{2}/ρg=V_{1}^{2}/2g-V_{2}^{2}/2g

(P_{1}-P_{2})/ρg= (V_{1}^{2}-V_{2}^{2})/2g

The coefficient of contraction is defined as the ratio between the area of the jet at the vena contract and the area of the orifice. C_{c}= Area at vena contracta/Area of orifice.

C_{c}=A_{2}/A_{0}

A_{2}=C_{c}A_{0}

Continuity equation

A_{1}V_{1}=A_{2}V_{2}

V_{1}=C_{c}A_{0}V_{2}/A_{1}

h=(P_{1}-P_{2})/ρg= (V_{2}^{2}-V_{1}^{2})/2g=[V_{2}^{2}-(C_{c}A_{0}V_{2}/A_{1})^{2}]/2g=V_{2}^{2}/2g[1-C_{c}A_{0}/A_{1}]^{2}

The velocity of fluid flow V_{2} at sections 2-2

V_{2}=√2gh/√(C_{c}A_{0}/A_{1})^{2}=A_{1}√2gh/√(C_{c}A_{0})^{2}

The volume flow rate or Discharge of fluid flow

Q=A_{2}V_{2}=C_{c}A_{0}V_{2}

Q=C_{c}A_{0}√2gh/√[1-(C_{c}A_{0}/A_{1})^{2}]

The relationship between the coefficient of discharge of orifice meter C_{d}*and coefficient of contraction C_{c}

C_{d}*=C_{c}×√[1-(A_{0}/A_{1})^{2}]/√[1-(C_{c}A_{0}/A_{1})^{2}]

C_{c}/√[1-(C_{c}A_{0}/A_{1})^{2}]=C_{d}*/√[1-(A_{0}/A_{1})^{2}]

The volume flow rate or Discharge of fluid flow

Here,

- A
_{1}= Area of a cross-section of a pipe - A
_{0}= Area of a cross-section of orifice meter - C
_{d}*= Coefficient of discharge of orifice meter