Orifice Meter:  

The orifice meter is the simplest of the three differential pressure flow meters.  It consists of a circular plate with a hole in the middle, typically held in place between pipe flanges as shown in Figure 2.

For an orifice meter, the diameter of the orifice, d, is used for D2 (A2 = Ao), and the discharge coefficient is typically called an orifice coefficient, Co, resulting in the following equation for an orifice meter:

The preferred locations of the pressure taps for an orifice meter have undergone change  over  time.  Previously  the  downstream pressure  tap  was  preferentially located at the vena-contracta, the minimum jet area, which occurs downstream of the orifice plate as shown in Figure 2. For a vena-contracta tap, the tap location depended upon the orifice hole size.   This link between the tap location and the orifice size made it difficult to change orifice plates with different hole sizes in a given meter in order to alter the range of measurement.  In 1991, the ISO-5167 international standard came out, in which three types of differential measuring taps were identified for orifice meters as illustrated in Figure 3 below. In ISO-5167, the distance of the pressure taps from the orifice plate is specified as a fixed distance or as a function of the pipe diameter, rather than the orifice diameter as shown in Figure 3.

In ISO-5167, an equation for the orifice coefficient, Co, is given as a function of β, Reynolds Number, and L1 & L2, the respective distances of the pressure taps from the orifice plate as shown in Figures 2 and 3.  This equation (indicated below) can

be  used  for  an  orifice  meter  with  any  of  the  three  standard  pressure  tap configurations.

Figure 3. ISO standard orifice meter pressure tap locations

The ISO-5167 equation for Co  (see Reference #3 at the end of this course) is as follows:

Co   =  0.5959 +  0.0312 β2.1   - 0.1840 β8   +  0.0029 β2.5(106/Re)0.75

+ 0.0900(L1/D)[β4/(1 - β4)]  - 0.0337 (L2/D) β3                     (5)

Where:     Co   =  orifice coefficient, as defined in equation (4), dimensionless

L1   =  pressure tap distance from upstream face of the plate, inches

L2   =  pressure tap distance from downstream face of the plate, inches

D =  pipe diameter, inches

β  =  ratio of orifice diameter to pipe diameter  =  d/D, dimensionless

Re  =  Reynolds number =  DV/ν  =  DVρ/µ,  dimensionless (D in ft) V =  average velocity of fluid in pipe =  Q/(πD2/4),  ft/sec (D in ft)

ν  =  kinematic viscosity of the flowing fluid, ft2/sec

ρ  =  density of the flowing fluid, slugs/ft3

µ =  dynamic viscosity of the flowing fluid, lb-sec/ft2

As shown in Figure 3:  L1  = L2  = 0 for corner taps;  L1  = L2  = 1 inch for flange taps;  L1 =  D  and  L2 =  D/2 for D – D/2 taps.   Equation (5) is not intended for use with any other arbitrary values for L1 and L2.

There are minimum allowable values of Reynolds number for use in equation (5) as follows.  For flange taps and (D – D/2) taps, Reynolds number must be greater than 1260β2D.  For corner taps, Reynolds number must be greater than 10,000 if β is greater than 0.45, and Reynolds number must be greater than 5,000 if β is less than 0.45.

Fluid properties (ν or ρ and µ) are needed in order to use equation (5).  Tables or graphs with values of ν,  ρ,  and µ for water and other fluids over a range of temperatures are available in many handbooks or textbooks (such as fluid mechanics or thermodynamics) as for example in Reference #1 at the end of this course. Table 1 shows density and viscosity for water at temperatures from 32o F to

70o F.

Table 1. Density and Viscosity of Water

Example #2:  What is the Reynolds number for water at 50oF, flowing at 0.35 cfs through a 4 inch diameter pipe?

Solution:  Calculate V from V = Q/A = Q/(πD2/4) = 0.35/[π(4/12)2/4] = 4.01 ft/s. From Table 1:  ν  =  1.407 x 10-5 ft2/s.  From the problem statement:  D = 4/12 ft. Substituting into the expression for Re = (4/12)(4.01)/(1.407 x 10-5):

Re = 9.50 x 104