Volume and Mass Flow Rate Measurement

Author: John M. Cimbala, Penn State University Latest revision: 09 December 2009

Introduction and notation • In many engineering applications, either mass flow rate or volume flow rate must be measured. • Notation used in this learning module: o Velocity V and volume V are distinguished either by adding a bar through the V to indicate volume ( V ) or by using a different font (V). o Mass flow rate m and volume flow rate V are indicated by adding an overdot on m or V respectively. o Some authors use Q for volume flow rate, but this gets confused with heat transfer – I prefer V . • If the density ρ of the fluid is known, mass flow rate and volume flow rate are related by m = ρV . • In all the examples used in this learning module, we consider only incompressible flow. Special care must be taken when the flow is compressible, such as the flow of air or natural gas through a pipeline. • Most of the instruments discussed here measure volume flow rate; other instruments measure mass flow rate. Mass flow rate measurements are more common in gases [gas density varies more than does liquid density]. • Instruments that measure volume flow rate are called flowmeters. • There are two broad categories of flowmeter: o An end-line flowmeter, also called a discharge flowmeter, is used at the outlet or discharge of the flow – at the end of the line. To measure volume flow rate, we measure how much time Δt it takes to fill up a container of known volume, and calculate V = V / Δt . A simple example of an end-line flowmeter is measurement of the volume flow rate through a garden hose using a bucket and stopwatch, as sketched to the right. There are some variations of the bucket and stop-watch approach – for example, we may weigh the fluid instead, and calculate the mass flow rate instead of the volume flow rate. End-line flow measurement is extremely accurate, and is often used to calibrate in-line flowmeters. • An in-line flowmeter is a device that is placed in line with the pipe or duct rather than at the outlet. o An in-line flowmeter is necessary when the outlet or discharge is not available or splits into many separate outlets. For example, the water company must measure the volume of water used in your home or apartment. Obviously, an end-line technique would not work here. o There are five main categories of in-line flowmeters: Obstruction flowmeters – measure the pressure drop across an obstruction placed in the flow. Positive displacement flowmeters – fill up a known volume and then pass it on down the line. Turbine flowmeters or paddlewheel flowmeters – spin a shaft and measure its rpm. Rotameters – raise an object due to aerodynamic drag, and measure its height. Miscellaneous flowmeters – use magnetic, optical, sonic, ultrasonic, vortex shedding, or various other means to measure volume flow rate. o We discuss each of these types of end-line flowmeters individually in the notes below. Obstruction flowmeters • The operating principle of an obstruction flowmeter is as follows: o A pressure drop is created in the pipe or duct by adding some kind of obstruction, as sketched below.

V

o o • • •

Obstruction

D

V

The pressure drop associated with the obstruction is measured. The volume flow rate is calibrated as a function of measured pressure drop. All obstruction flowmeters cause a pressure drop (irreversible head loss) in the piping system – this pressure drop is called a minor loss. There are three main types of obstruction flowmeter – orifice, flow nozzle, and Venturi. All work on the same principle, but have different performance characteristics. We develop the equations for the orifice flowmeter – the equations for the flow nozzle and Venturi flowmeters are the same, but with a different discharge coefficient.

Volume and Mass Flow Rate Measurement, Page 2

Orifice flowmeter • The obstruction in an orifice flowmeter is...