Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net

Lecture 15. Flow rate measurement

Flow rate measurement Averaging Pitot tubes - a tube spanning the cross section of the pipe - multiple frontal openings for averaged total pressure - second tube facing backwards to measure static pressure

Flow rate measurement Laminar flow elements - contain tube bundles or long honeycombs - create laminar flow with Re<2300 - linear response between flow rate and pressure drop

Flow rate measurement Rotameters (variable-area flow meters) - vertical tube with cross section increasing linearly upwards - a float at a position with drag, buoyancy and weight in balance - height of float proportional to flow rate

Flow rate measurement Vortex-shedding flow meters 𝑄= 𝜋 𝐷 2 ℎ𝑓 4𝑆 - a bluff object results in periodic shedding of vortices - vibration frequency (f) measured downstream - constant Strouhal number with Re>5000: h – front width of the bluff V – flow velocity - S=0.14-0.21, dependent on shape of the bluff body 𝑄= 𝜋 𝐷 2 ℎ𝑓 4𝑆 Drag (target) flow meters - bluff object immersed in flow - drag force FD measured - flow velocity determined by - flow rate given as k – constant depending on the structure

Flow rate measurement Turbine flow meters Paddle-wheel flow meters - an immersed rotor with vanes - angular velocity measured with pulse counter - flow rate proportional to angular velocity k – constant n – number of pulses per unit time Paddle-wheel flow meters - axis normal to flow direction

Flow rate measurement Ultrasonic flow meters Doppler flow meters - use sound waves to measure flow rate of fluid Doppler flow meters - 2 piezoelectric crystals: transmitter & receiver - solid particles or gas bubbles reflect ultrasound - frequency difference used to determine velocity - Doppler shift: ft – transmitted frequency fr – received frequency c – sound speed  – measurement angle Time-of-flight flow meters - Two pairs of transmitter & receiver - located upstream and downstream - sound pulse transported by flowing fluid - frequency change used to calculate flow velocity l – distance between transducers - independent of sound speed (temperature)

Flow rate measurement Electromagnetic (magnetic, induction) flow meters - conductive fluid passing across a controlled magnetic field - flow velocity obtained by measuring changes of induced voltage - flow rate determined accordingly k – numerical coeficient B – magnetic flux density D – pipe diameter E – electric potential Coriolis flow meters - flow guided into U-shaped tube - twist induced to the tube by Coriolis acceleration - time delay t between motions of two legs measured - mass flow rate related as rt – radius of the tube KS – constant

Flow rate measurement Thermal flow meters Heated-tube flow meters - flowing gas passed electrically heated tube - temperature measured up- and down stream - heat transfer rate related to mass flow rate Cp – specific heat under constant pressure Immersion-probe flow meters - two resistance temperature detectors (RTDs) - one RTD used to measure gas temperature - another heated with current to higher temperature - electric power related non-linearly to V

Flow rate measurement Selection of flow meters

Homework - Read textbook 9.5-9.15 on page 212 - 219 Questions and Problems: 2 on page 219 - Due on 09/30