Venturi Meters 2 Equations Codes Installation blog contains

- Venturimeter Equations
- Coefficient of Discharge of Venturimeter (Cd)
- Codes and Standards of Venturi meter
- Installation of a venturi meter
- Venturi meter Upstream and Downstream Pipe Straight Leg Requirement

### 1. Venturimeter Equations

Bernoulli’s principle states the relation between pressure (P), kinetic energy, and gravitational potential energy of a fluid inside a pipe.

The mathematical form of Bernoulli’s equation is given as:

Where,

p= pressure inside the pipe

ρ =density of the fluid

g =gravitational constant

v = velocity

z=elevation or head

a = cross-sectional area of the pipe

d= diameter of the pipe

Suffix 1 and 2 are used to denote two different areas; 1 denotes cylindrical inlet section and 2 denotes throat section.

Now as the pipe is horizontal; there is no difference in elevation of pipe center line; So, z1=z2. Re-arranging the above equation we get the following:

**(p1-p2)/ρg = (v22-v12)/2g**

(p1 – p2)/ ρg is the difference of pressure heads in sections 1 and 2 which is equal to h that can be measured in the differential manometer. So the above equation becomes

**h=(v22-v12)/2g……….eq.1**

Now applying continuity equations between the same sections 1 and 2, we get

**a1v1=a2v2 or v1=(a2v2)/a1**

Putting this value of v1 in eq.1 and solving we get,

So, the rate of flow through the throat (Q) can be calculated as Q=a2v2; Substituting the above value of v2 we get,This Q represents the theoretical discharge of Venturi Meter in ideal condition.

But in actual practice, there will be always be some frictional loss.

Hence, the actual discharge will always be less than the theoretical discharge.

So, to calculate the actual discharge, the above Q value is multiplied by Cd, called the Coefficient of discharge of venturimeter.

So the actual flow rate through the throat of the venturimeter will be given by the following equation.

### 2. Coefficient of Discharge of Venturimeter (Cd)

The coefficient of discharge for Venturimeter, Cd is defined as the ratio of the actual flow rate through the venturi meter tube to the theoretical flow rate. So the venturi meter discharge coefficient is given by:

**Cd=Qact/Q**

As Qactual will always be less than Qtheoretical due to frictional losses, the value of Cd is always less than 1.0.

The typical range of the discharge coefficient of a Venturi meter is 0.95-0.99 but this can be increased by proper machining of the convergent section.

The value of venturimeter discharge coefficient differs from one flowmeter to the other depending on the venturimeter geometry and the Reynolds number.

ISO-5167 code provides the values of venturimeter discharge coefficients. For accurate flow measurement, normally straight length requirement upstream and downstream of venturimeter is specified.

### 3. Codes and Standards of Venturi meter

The codes and standards that provide guidelines related to venturi meters are

- ISO 5167
- ISO 9300
- AWWA M33
- ISO TR 15377
- BS 1042
- ASME MFC-8M
- ASTM D2458
- AGA 9

### 4. Installation of a venturi meter

Proper installation of venturi meter is the key for ideal operation. So, the installation of venturi meters must be performed following manufacturer guidelines. Normally, the following guidelines to be followed while installing a venturi meter in a piping or pipeline system:

The flow direction arrow in the venturi meter should be checked and installed to agree with the direction of the flow.

Flanges at the venturi meter ends should be properly aligned with the piping flanges.

Pipe Support should not be placed on venturi meters.

Bolts should not be over-torqued.

Installation tolerances should be within industry standards.

Pressure taps should be oriented horizontally for liquid service applications

### 5. Venturi meter Upstream and Downstream Pipe Straight Leg Requirement

For proper functioning and accurate results, the flow through the venturi meters should stabilize. This calls for minimum straight pipe length requirements upstream and downstream of the venturi meter.

Depending on the type of fitting, type of venturi meter, and beta ratio (the throat diameter divided by the inlet diameter) the straight leg requirement varies.

The following image provides a sample table that provides typical strength leg requirements while installing a venturi meter in a piping system.