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

2. Pitot Tubes

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

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

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

6. 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

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

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

11. Discharge Coefficient CD
𝑅𝑒~<30,000
Orifice meters: 𝐶 𝐷 = 𝛽 2.1 −0.814 𝛽 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

12. 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.

13. 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