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One of the most commonly used fluid flow measurement technology is by reading the pressure loss across a pipe restriction. This pressure drop can be achieved by a wide variety of flow sensors with different geometric shapes. These different flow sensors have their various strengths and weaknesses. These flow

The volumetric flow through a restriction in a pipe is given by:
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meters are also called ‘’head’’ meters. Examples of flow sensors using differential pressure technology as basis for flow measurement include:

(a) Orifice plate

(b) Flow nozzle

(c) Venturi tube

(d) Rotameters

(e) Pitot tubes

As a fluid passes through a restriction in a pipe, it accelerates, and the energy for this acceleration is obtained from the fluid’s static pressure. Consequently, the line pressure drops at the point of constriction. Part of the pressure drop is recovered as the flow returns to the unrestricted pipe.

The volumetric flow through a restriction in a pipe is given by:

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**Q = KA√ (∆P/ρ)**

Where :

Q = volumetric flow

K = discharge coefficient

A = cross sectional area of pipe’s opening

ΔP = differential pressure across flow element

ρ = density of flowing fluid

The discharge coefficient of flow elements are usually determined by laboratory tests. The discharge coefficient is influenced by the Reynolds number and by the beta ratio. The beta ratio is the ratio of the bore diameter of the flow restriction and the internal diameter of the pipe.

K = discharge coefficient

A = cross sectional area of pipe’s opening

ΔP = differential pressure across flow element

ρ = density of flowing fluid

The discharge coefficient of flow elements are usually determined by laboratory tests. The discharge coefficient is influenced by the Reynolds number and by the beta ratio. The beta ratio is the ratio of the bore diameter of the flow restriction and the internal diameter of the pipe.

Typically, to measure the flow rate using a differential pressure flow meter, a d/p cell commonly in the form of an integrated flow transmitter is used to measure the differential pressure across the pipe restriction. Because of the fact that the relationship between flow and differential pressure is not linear, most flow transmitters come with a square root extractor which effectively makes the relationship between flow and differential pressure to become linear. The d/p cell is usually connected between the upstream and downstream sides of the given flow sensor or pipe restriction as shown in the case for an orifice plate shown below:

The performance of a differential pressure flow meter installation is a function of the precision of the flow element and the accuracy of the d/p cell. Flow element precision is typically reported in percentage of actual reading, while in a d/p cell, accuracy is a percentage of calibrated span. Owing to the fact that the relationship between the flow and differential pressure is not linear, the error in flow measurements at low flow increases dramatically, limiting the range that differential pressure flow meters can be comfortably used without incurring serious measurement errors. In practice, differential pressure producing flow meters are limited to use in the range 3:1 or 4:1