26. Flow Measurement and Safety Devices CH EN 374: Fluid Mechanics

Pitot Tubes

Problem Find the average velocity v in the pipe in terms of 𝜌, 𝑃 1 , 𝑃 2

Pitot Tube Calculations 𝑣= 2( 𝑃 1 − 𝑃 2 ) 𝜌

Advantages: cheap and simple, no moving parts Disadvantages: easy to clog

Obstruction Flow Meters Basic idea: Obstruction induces pressure loss Measure pressure loss, relate to velocity Types: Orifice meter: most loss, least expensive Flow nozzle: medium loss, medium expensive Venturi meter: least loss, most expensive

Problem Find 𝑉 in terms of 𝜌,𝑃 1 , 𝑃 2 ,𝑑,𝐷, and 𝐴 𝑑 , the area of the orifice.

Obstruction Flow Meter Calculations 𝑉 = 𝐴 𝑑 𝐶 𝐷 2( 𝑃 1 − 𝑃 2 ) 𝜌(1− 𝛽 4 ) 𝛽= 𝑑 𝐷

Discharge Coefficient CD 𝑅𝑒~<30,000 Orifice meters: 𝐶 𝐷 =0.5959+0.0312 𝛽 2.1 −0.814 𝛽 8 91.78 𝛽 2.5 𝑅 𝑒 0.75 Nozzle meters: 𝐶 𝐷 =0.9975− 6.53 𝛽 0.5 𝑅 𝑒 0.5 𝑅𝑒~>30,000 Orifice meters: 𝐶 𝐷 =0.61 Nozzle meters: 𝐶 𝐷 =0.96 𝑉𝑒𝑛𝑡𝑢𝑟𝑖 𝑚𝑒𝑡𝑒𝑟𝑠: 0.95> 𝐶 𝐷 >0.99 Unless told otherwise, assume 𝐶 𝐷 =0.98

Problem The flow rate of methanol at 20°𝐶 (𝜌=788.4 𝑘𝑔 𝑚 3 , 𝜇=5.857𝑥 10 −4 𝑘𝑔/𝑚∙𝑠) through a 3-cm diameter pipe is to be measured with a 1.5-cm diameter flow nozzle equipped with a differential pressure gage. If the pressure gauge reads a difference of 3 kPa, determine the flow rate of methanol through the pipe and the average flow velocity.

Pressure Relief Valves Safety Devices Pressure Relief Valves Rupture Discs Burst at a certain pressure and must be replaced Usually used in combination with valve Designed to open at a certain pressure, releasing fluid and equalizing pressure