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

[email protected]

http://lcgui.net

Lecture 15. Flow rate measurement

2

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 3

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 4

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 5

Flow rate measurement

Vortex-shedding flow meters

- 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 = 𝜋𝐷 2 ℎ𝑓 4𝑆

Drag (target) flow meters

- bluff object immersed in flow - drag force F D measured - flow velocity determined by - flow rate given as

k

– constant depending on the structure 6

Flow rate measurement

Turbine 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 7

Flow rate measurement

Ultrasonic 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:

f t

– transmitted frequency

f r

– 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) 8

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

E B

– electric potential

k

– numerical coeficient – magnetic flux density

D

– pipe diameter

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

r t

– radius of the tube

K S

– constant 9

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

C p

– 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

10

Flow rate measurement

Selection of flow meters

11

Homework

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

12