Venturi Meter: 

Fluid enters a venturi meter through a converging cone (angle of

15o   to  20o).  It  then  passes through the  throat which has  the  minimum cross- sectional area, maximum velocity, and minimum pressure in the meter. The fluid then slows down through a diverging cone (angle 5o to 7o) for the transition back to the full pipe diameter.  Figure 1 shows the shape of a typical venturi meter and the parameters defined above as applied to this type of meter.  D2 is the diameter of the throat and P2 is the pressure at the throat.  D1 and P1 are the diameter and pressure, respectively, in the pipe before entering the converging portion of the meter.

Figure 1. Venturi Meter Parameters

Due to the smooth transition to the throat and gradual transition back to full pipe diameter, the head loss through a venturi meter is quite low and the discharge coefficient is quite high.  For a venturi meter the discharge coefficient is typically called the venturi coefficient, Cv, resulting in the following equation:da

The value of the venturi coefficient, Cv, will typically range from 0.95 to nearly one.  In ISO 5167 (ISO 5167-1:2003 – see Reference #2 at the end of this course), Cv is given as 0.995 for cast iron or machined venturi meters and 0.985 for welded sheet metal venturi meters meeting ISO specifications, all for Reynold’s Number between 2 x 105  and 106.  Information on the venturi coefficient will typically be provided by the venturi meter manufacturers.

Example #1:   Water at 50 oF is flowing through a venturi meter with a 2 inch throat diameter in a 4 inch diameter pipe.  Per manufacturer’s information, Cv =

0.99 for this meter under these flow conditions.  What is the flow rate through the meter if the pressure difference, P1 – P2, is measured as 8 inches of Hg.

Solution:  The density of water in the temperature range from 32oF to 70oF is 1.94 slugs/ft3.   A2   =  πD22/4 =  π(2/12)2/4  = 0.02182 ft2.  β  =  2/4 = 0.5.  Converting the pressure difference to lb/ft2:  P1 – P2   =  (8 in Hg)(70.73 lb/ft2/in Hg)  =  565.8 lb/ft2. Substituting all of these values into equation (3):