Phil. U., M Eng Dep., Measurements, Chap#7 flow measurements is very important as it covers wide ranges of applications. The flow rate measurement devices frequently require accurate pressure and temperature measurements in order to calculate the output of the instrument. In fact, the accuracy of these flow- measurement instrumentations is governed primarily by the accuracy of the related temperature and pressure devices. Flow Measurements

Phil. U., M Eng Dep., Measurements, Chap#7 The flow rate is expressed in both volume and mass units per time. Some used terms are: - gallon per minute (gpm) = 231 cubic inch per minute = cubic centimeter per minute - 1 standard cubic foot per minute of air at 20  C, 1 atm = gram per second Flow Measurements

Phil. U., M Eng Dep., Measurements, Chap#7 (1) Direct weighing technique: - frequently employed for liquid flowmeters calibration. - suitable for steady-flow conditions. (2) Positive displacement flowmeters: - generally used for applications where consistently high accuracy is desired under steady-flow conditions. - Many types: Positive Displacement Measurements

Phil. U., M Eng Dep., Measurements, Chap#7 (a) nutating-disk meter (figure 7.1): water enters the left side of the meter and strikes the disk. The disk nutates about the vertical axis since its bottom and top remain in contact with the mounting chamber. As a result, the fluid moves through the meter. The nutating of the disk gives direct indication of the volume of the fluid which has passed through the meter. Positive Displacement Measurements

Phil. U., M Eng Dep., Measurements, Chap#7 Positive Displacement Measurements

Phil. U., M Eng Dep., Measurements, Chap#7 (b) rotary-vane flowmeter (figure 7.2): the vanes are spring-loaded so that they continuously maintain contact with the casing of the meter. A fixed quantity of fluid is tapped in each section as the drum rotates, and this fluid eventually finds its way to the exit. An appropriate register is connected to the drum-shaft to record the volume of the displaced fluid. Positive Displacement Measurements

Phil. U., M Eng Dep., Measurements, Chap#7 (c) lobed-impeller flowmeter (figure 7.3): the incoming fluid is trapped between the two rotors and is conveyed to the outlet as a result of their rotation. The number of revolutions of the rotor is an indication of the volumetric flow rate. (a) and (b) are used for liquid only while (c) can be used for both liquid and air. Positive Displacement Measurements

Phil. U., M Eng Dep., Measurements, Chap#7 Such devices are sometimes called head meters or differential pressures meters, because a head-loss or pressure drop measurements is taken as an indication of the flow rate. All obstruction meters follow general relations as follows: - Consider figure 7.4. the continuity equation for this situation is: m =  1 A 1 u 1 =  2 A 2 u 2 where u is the velocity Flow Obstruction Methods.

Phil. U., M Eng Dep., Measurements, Chap#7 - If the flow is adiabatic and frictionless, and the fluid is incompressible, Bernoulli equation may be written as: P 1 /  1 + u 1 /2 = P 2 /  2 + u 2 /2 Now, since  1 =  2, solving the above two equation simultaneously gives the pressure drop: Flow Obstruction Methods 22

Phil. U., M Eng Dep., Measurements, Chap#7 Flow Obstruction Methods Thus, a channel as in figure 7.4 could be used for a flow measurements by simply measure the pressure drop and calculating the flow from the above equation.

Phil. U., M Eng Dep., Measurements, Chap#7 Yet, no such channel is frictionless, and some losses are always present in the flow. Therefore, the calculated Q from the above equation, called Q ideal, is usually related to the actual flow rate by an empirical discharge coefficient, C, as: Q actual = CQ ideal C is not constant and may depend strongly on the flow Reynolds number and the channel geometry. Flow Obstruction Methods

Phil. U., M Eng Dep., Measurements, Chap#7 - For compressible fluids, the mass flow rate through the channel can be written as: Equations 7.8 to 7.10 Flow Obstruction Methods

Phil. U., M Eng Dep., Measurements, Chap#7 Three typical obstruction meters are frequently used, Venturi, flow nozzle, and orifice; as shown in figure 7.5. Each of the three meters has its discharge coefficient. These empirical values are usually given in figures as in figures 7.9 to Flow Obstruction Methods

Phil. U., M Eng Dep., Measurements, Chap#7 To summarize, the following semiempirical equations are used: Equations 7.17 – 7.20 Flow Obstruction Methods

Phil. U., M Eng Dep., Measurements, Chap#7 The rotameter is a very commonly used flow- measurement device and it is shown schematically in figure The flow enters the bottom of the tapered vertical tube and causes the bob (float) to rise upward until a point where the drag effect is just balanced by the weight and bouncy forces. The bob position is taken as an indication of the flow rate. Flow Measurements by Drag Effects; Rotameter

Phil. U., M Eng Dep., Measurements, Chap#7 Flow Measurements by Drag Effects; Rotameter

Phil. U., M Eng Dep., Measurements, Chap#7 The force balance on the bob gives: F d +  f V b g =  b V b g where: F d : the drag force = 0.5C d A b  f u m C d : a drag coefficient A b : the frontal area of the bob u m : the mean flow velocity of the annular area between the bob and the tube  f,  b : the densities of the fluid and the bob V b : volume of the bob Flow Measurements by Drag Effects; Rotameter 2 Flow Buoyancy Gravity

Phil. U., M Eng Dep., Measurements, Chap#7 Combining the F d equation with the force balance equation gives: Flow Measurements by Drag Effects; Rotameter

Phil. U., M Eng Dep., Measurements, Chap#7 The turbine meter is a popular flow-measurement device as shown in figure As the fluid moves through the meter, it causes a rotation of the small turbine wheel. In the turbine wheel body a permanent magnet is enclosed so that it rotates with the wheel. A reluctance pickup attached to the top of the meter detects a pulse for each revolution of the turbine wheel. Since the volumetric flow is proportional to the number of wheel revolutions, the total pulse output may be taken as an indication of total flow Flow Measurements by Drag Effects; Turbine meter

Phil. U., M Eng Dep., Measurements, Chap#7 Flow Measurements by Drag Effects; Turbine meter

Phil. U., M Eng Dep., Measurements, Chap#7 Next, we can define a flow coefficient K for the turbine meter such that: Q = f/K where: f is the pulse frequency K is dependent on the flow rate and the kinematic viscosity (  ) of the fluid. Flow Measurements by Drag Effects; Turbine meter

Phil. U., M Eng Dep., Measurements, Chap#7 The hot-wire anemometer is a device that is often used in research applications to study rapidly flow conditions. A wire is heated and placed in the flow stream. It can be shown that the heat transfer rate for this wire is: q = (a + bu )(T w - T  ) where: T w : wire temperature T  : fluid stream temperature u: fluid velocity a, b: constants obtained from the device calibration Hot Wire Anemometer 0.5

Phil. U., M Eng Dep., Measurements, Chap#7 Also, the heat transfer rate is equal to: q = i R w = i R o (1 +  (T w – T o )) where: i: electrical current R o : resistance of the wire at T o  : temperature coefficient of the resistance For measuring proposes, the wire is connected to a bridge circuit. R w and i are found from the bridge. Hot Wire Anemometer 22

Phil. U., M Eng Dep., Measurements, Chap#7 This device mainly is used for gaseous mass flow rate measurements. Consider figure The temperature difference (T 2 – T 1 ) is proportional to the mass flow of the gas such that: q = m.c p.(T 2 - T 1 ), where: q: the heater heat capacity c p : the gas specific heat Thus, the mass flow rate can be found as… Thermal Mass Flowmeters.

Phil. U., M Eng Dep., Measurements, Chap#7 Consider figure Since the fluid represents a conductor moving in the field, there will be an induced voltage according to: E = BLu x 10 V where: B: the magnetic flux density u: velocity of the conductor (flow velocity) L: the conductor length Magnetic Flowmeters -8

Phil. U., M Eng Dep., Measurements, Chap#7 The length of the conductor is proportional to the tube diameter, and the velocity is proportional to the mean flow velocity. Then, the induced voltage, E, is taken as an indication of flow velocity. There are two commercial types of this instrument; one is used for low-conductivity fluids and another for high- conductivity fluids. Magnetic Flowmeters

Phil. U., M Eng Dep., Measurements, Chap#7 The previous flow rate devices ignore the local variations of velocity and pressure in the flow channel and permit an indication of only the total flow through a particular cross section. In applications involving external flow situations, such aircraft or wind-tunnel tests, an entirely different type of measurement is required. In these instances, probes must be inserted in the flow to measure the local static and stagnation pressure. From these measurements the local flow velocity may be calculated. Pressure Probes

Phil. U., M Eng Dep., Measurements, Chap#7 Pressure Probes

Phil. U., M Eng Dep., Measurements, Chap#7 Pressure Probes