1. 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

2. Lecture 15. Flow rate measurement

3. 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

4. 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

5. 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

6. 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= , 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

7. 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

8. 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)

9. 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

10. 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

11. Flow rate measurement
Selection of flow meters

12. Homework
- Read textbook on page
Questions and Problems: 2 on page 219
- Due on 09/30