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 12. Pressure-measuring instrumentation

3. What exactly is pressure?
Stress tensor
Normal stresses: 11 , 22 , 33
Shear stress: 12 , 13 , 21 , 23 , 31 , 32
(12 = 21 , 13 = 31 , 23 = 32)
External forces: F1 , F2 ,, Fn
Pressure
- average normal stress (mechanical definition)
- positive when compressive, negative when tensile
- absolute pressure
Hydrostatic pressure difference between two locations A and B
 – fluid density
g – gravitational acceleration
z – vertical upwards direction

4. What exactly is pressure?
Reference pressure in surrounding environment, e.g. atmospheric pressure patm
Gauge pressure: pg = p - patm
Total (stagnation) pressure P0:
p – pressure
 – fluid density
V – fluid velocity
Incompressible flow
- Static pressure: p
- Dynamic pressure: V2/2
Compressible flow
 – ratio of specific speeds
M – Mach number
Pressure changes across a normal shock wave
- Upstream of the shock wave: p, p0
- Downstream of the shock wave: p’, p0’

5. Pressure-measuring instrumentation
Liquid-in-glass manometers
e.g. a liquid-filled, U-shaped manometer
– three different fluids with densities 1, 2, and 3
– fluid 2 must be a liquid
– pressure difference between position A and B:
– if both fluid 1 and 3 are gases:
Static sensitivity of U-tube manometer
k = 1/(2g)
(fluid 1 and 3 are gases)
Inclined manometer
– static sensitivity increased w. decreasing density of fluid 2
k = 1/(2gcos)
– static sensitivity increased with >0

6. Pressure-measuring instrumentation
Liquid-in-glass manometers
Error sources of liquid-filled manometer
– variations of fluid densities
– non-vertical positioning
– capillarity
– meniscus-reading errors
Prandtl-type micromanometer
– to reduce capillarity and meniscus-reading errors

7. Pressure-measuring instrumentation
Deadweight gauges
- Highly accurate device
- Cumbersome in use
- Standards for calibration of other pressuregauges
Elastic-element gauges
- Widely used, general-purpose pressure gauges

8. Pressure-measuring instrumentation
Electrical pressure transducers
- provide electric output signal dependent on pressure
- based on electric property change (e.g. resistance, capacitance, or inductance)
- result from pressure-induced displacement or deformation
- require excitation power for operation
- require calibration
- susceptible to temperature and humidity effects
- superior frequency response (great advantage over liquid-in-gas and mechanical pressure gauges)
As pressure increases, the flexible conductive plates will move farther apart, changing the capacitance of the transducer. This change in capacitance is measurable and is proportional to the change in pressure.
Variable-capacitance transducers

9. Pressure-measuring instrumentation
Variable-resistance transducers
Variable-reluctance pressure transducer

10. Pressure-measuring instrumentation
Piezoelectric transducers
- may be a passive sensor
Strain-gauge transducers

11. Wall-pressure measurement
Linear variable differential transformer
When the core is centered, equal voltages are induced in two oppositely wound secondary windings and the output voltage is zero. A change of pressure moves the core, increasing the voltage induced in one secondary and decreasing the voltage induced in the other. The change in output (differential) voltage is thus a measure of the pressure.
Semiconductor pressure transducers
Semiconductor Distortion Gauge

12. Homework
- Read textbook on page
Questions and Problems: 1 on page 203
- Due on 09/23