Variable-Area Flow Meter

In the obstruction flow meters, the flow is allowed to pass through a reduced cross-sectional area and the corresponding pressure difference is measured by using any differential pressure measuring device. The expression for volume flow rate is given by,

(7.3.1)

where, are the smaller and larger diameters for the flow, respectively, is the discharge coefficient and ρ is the density of the fluid. It may be noted from Eq. (7.3.1) that the pressure drop varies as square of the flow rate. In other words, if these devices are to be used for wide range of flow rate measurements, then the pressure measuring equipment should have capability of handling lager pressure range. By incorporating larger pressure ranges, the accuracy of the device will be poor for low flow rates i.e. the small pressure readings in that range will be limited by the pressure transducer resolution. This is the major drawback of the obstruction flow devices.

One of the solutions is to use two pressure measuring systems, one for low flow rates and the other for high flow rates. A simple, reliable and inexpensive device used for measuring flow rates for wide ranges of liquids and gases. This device is easy to install with no electrical connections and gives a direct reading of flow rate. It is known as variable area flow meter and also called as rotameter/floatmeter . It consists of a vertical tapered conical transparent tube made of glass/plastic with a float / bob inside the tube as shown in Fig. 7.3.1. The bob is free to move inside the tube and is heavier than the fluid it displaces. At any point of time, the float experiences three fundamental forces; drag, buoyancy and its own weight. With increase in flow velocity, the drag force increases and the flow velocity reduces with increase in cross-sectional area in the tapered tube. At certain velocity, the float settles at a location where enough drag is generated to balance the weight of the bob and buoyancy force . In other words, the net force acting on the bob is zero and thus it is in equilibrium for a given flow rate. The degree of tapering of the tube can be made such that the vertical rise changes linearly with the flow rate and a suitable scale outside the tube is fixed so that the flow rate can be determined by matching the position of float.

Fig. 7.3.1: Schematic diagram of a rotameter.