Measurement of flowing fluids Variable head meters Variation of flow rate thro a constant area generates a variable pressure drop which is related to the flow rate Venturi meter Orifice meter Variable area meters Consists of devices in which the pressure drop is constant, or nearly so, and the area thro which the fluid flows varies with the flow rate. The area is related, thro proper calibration, to the flow rate Rotameter

Venturi meter

In this meter the fluid is accelerated by its passage through a converging cone of angle 15º-20º. The pressure difference between the upstream end if the cone and the throat is measured and provides the signal for the rate of flow. The fluid is then retarded in a cone of smaller angle (5º-7º) in which large proportion of kinetic energy is converted back to pressure energy. The attraction of this meter lies in its high energy recovery so that it may be used where only a small pressure head is available, though its construction is expensive.

Although venturi meters can be applied to the measurement of gas, they are most commonly used for liquids. The following treatment is limited to incompressible fluids. The basic equation for the venturi meter is obtained by writing the Bernoulli equation for incompressible fluids between the two sections a and b. Friction is neglected, the meter is assumed to be horizontal. If va and vb are the average upstream and downstream velocities, respectively, and r is the density of the fluid, vb2 - va2 = 2(pa - pb)/r ---1

The continuity equation can be written as, va = (Db/Da)2 vb = b2 vb --- 2 where Da = diameter of pipe Db = diameter of throat of meter b = diameter ratio, Db/Da If va is eliminated from equn.1 and 2, the result is (3)

Equn.3 applies strictly to the frictionless flow of non-compressible fluids. To account for the small friction loss between locations a and b, equn.3 is corrected by introducing an empirical factor Cv. The coefficient Cv is determined experimentally. It is called the venturi coefficient, For a well designed venturi, the constant Cv is about 0.98 for pipe diameters of 2 to 8 inch and about 0.99 for larger sizes.

Volumetric flow rate: The velocity through the venturi throat vb usually is not the quantity desired. The flow rates of practical interest are the mass and volumetric flow rates through the meter. Volumetric flow rate is calculated from, Q = Abvb and Mass flow rate = volumetric flow rate x density

Orifice Meter The venturi meter described earlier is a reliable flow measuring device. Furthermore, it causes little pressure loss. For these reasons it is widely used, particularly for large-volume liquid and gas flows. However this meter is relatively complex to construct and hence expensive. Especially for small pipelines, its cost seems prohibitive, so simpler devices such as orifice meters are used.

Orifice Meter

The orifice meter consists of a flat orifice plate with a circular hole drilled in it. There is a pressure tap upstream from the orifice plate and another just downstream. The principle of the orifice meter is identical with that of the venturi meter. Bernoulli's equation provides a basis for correlating the increase in velocity head with the decrease in pressure head.

Similar to venturi meter……… where…. b= (orifice dia / tank dia) Co = orifice coefficient (0.51-0.61)

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