nozzle contraction is that of the quadrant of an ellipse, with the major axis
aligned with the flow axis,
as shown in Figure 10.9. The nozzle is typically installed inline, but can also
be used at the inlet to
and the outlet from a plenum or reservoir or
The sonic nozzle provides a very convenient method to meter and regulate a
gas flow. The
judicious selection of throat diameter can establish any desired fluid flow
rate provided that the flow
is sonic at the throat. This capability makes the sonic nozzle
The analysis can work in one of two ways. In the first approach, the analyzer
performs the fast
Fourier transform (FFT) continuously on small blocks of data from which the
Doppler frequency is
directly determined. In the second mode, the correlation mode,
The absolute capacitance. Oscillator and bridge circuits are
commonly used to operate the circuit
and to measure the small capacitance change providing an output
voltage E0.
Example 9.5
Estimate the theoretical capacitance of a sensor similar to that of
F
This predicted value as an estimate of the uncertainty resulting from this
effect, or we can use
the predicted value to correct the indicated value and assign a smaller
uncertainty based on the
uncertainty in the correction.
Equation 8.31 and Equation 8.3
The pressure drop across a valve through which air flows is
expected to be 10 kPa. If this
differential were applied to the two legs of a U-tube manometer
filled with mercury, estimate the
manometer deflection. What is the deflection if a 30-degree
inclin
the correlation R12(Dx*), where
R12Dx*
Z
A
Z
I1Dx*I2x* Dx*dx* 9:54
so identifying the common particle and allowing the estimate of the particle
displacement Dx*. By
repeating the cross-correlation between images for each interrogation area,
a velocity ve
Pump induced oscillations impose a trend on the
individual pressure measurements. This is confirmed by the high correlation
coefficient (see
Chapter 4) between p1 and p2. Notably, the pressure differential signal is
unaffected by this
periodicity because
Pressure and Velocity Measurements
9.1 INTRODUCTION
This chapter introduces methods to measure the pressure and the velocity
within fluids. Instruments
and procedures for establishing known values of pressure for calibration
purposes, as well as various
t
Pressure fluctuations occur as the flow fluctuates around the car. Statistical
variations from
average values give the stated randomuncertainty, uDp 0.10 cm H2O
(95%), which we assign large
degrees of freedom.
If we look at the rear deck of the car and us
Standard uncertainty of the data acquisition and reduction
procedure:
sp
hspi
ffiffiffiffiffiffiffiffi
MK
p where hspi
ffiXffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffiffiffiffiffiffiffiffiffiffiffi
or, rearranging,
pv
pt
_ px
1
2
rU2
x
9:36
Again pv, the difference between the total and static pressures at any point
in the flow, is the dynamic
pressure. Hence, measuring the dynamic pressure of a moving fluid at a
point provides a method for
estimat
The meter is installed between two flanges intended for this
purpose. Pressure taps are
located just ahead of the upstream contraction and at the throat.
Equation 10.12 is used with values
for both A and b based on the throat diameter, d0.
The quality of
The total system compliance could be measured using Equation 9.20 by
closing the pressure
tap, increasing the fluid volume in the tubing by a small known amount, such
as by syringe, and
measuring the corresponding pressure change.
Liquids
Liquids are rela
A three-digit display rounds E0 to 6.38 V. The difference between the input
and output values is
attributed to quantization error.With a clock speed of 100 kHz, each ramp
step requires 10 ms/step,
and conversion time 653 steps _ 10 ms/step 6530 ms.
COMMEN
Temperature and capillary effects in the manometer and gravity error in the
specific weights of the fluids are negligible. The degrees of freedom in the
stated uncertainties are
large.
FIND ud
SOLUTION The relation between pressure and manometer deflectio
natural frequency (t
_1)
z altitude (l )
C capacitance (F)
E voltage (V)
Em bulk modulus of elasticity (m
_1lt
_2)
Gr Grashof number
H manometer deflection height (l )
K static sensitivity
Kq charge sensitivity (m
_1lt
_2)
KE voltage sensitivity (Vm
_1t
_
Reciprocating piston within a cylinder can generate a sinusoidal variation in
pressure for
frequency-response calibration. The piston can be driven by a variable speed
motor and its displacement
measured by a fast-responding transducer, such as an LVDT (s
Thermal Anemometry
The rate at which energy, _Q, is transferred between a warm body at Ts and
a cooler moving fluid at Tf
is proportional both to the temperature difference between them and to the
thermal conductance of
the heat transfer path, hA. This th
Then, the mean flow rate along each line of traverse is
Q1
0:252 m3/s Q2
0:252 m3/s Q3
0:254 m3/s
The average pipe flow rate Q is the pooled mean of the individual flow rates
Q hQi 1
3
X3
j1
Qj
0:253 m3/s
Example 10.2
Referring to Example 10.1, determ
This chapter approaches uncertainty analysis as an evolution of information
from test design
through final data analysis.While the structure of the analysis remains the
sameat each step, the number
of errors identified and their uncertainty values may cha
The early Romans developed elaborate water systems to supply public baths
and private homes. In
fact, Sextus Frontinius (A.D. 40103), commissioner of water works for Rome,
authored a treatise on
design methods for urban water distribution systems. Evidenc
The capillary occupied by the gas. With g as the specific weight of the
mercury, the difference in
pressures is related by p2 _ p1 gy such that the unknown gas pressure is
just a function of y:
p1
gAy2=81 _ Ay 9:4
In practice, a commercial McLeod gauge h
Pressure can also be described in terms of the pressure exerted on a surface
that is submerged in
a column of fluid at depth h, as depicted in Figure 9.2. From hydrostatics, the
pressure at any depth
within a fluid of specific weight g can be written as
p
Pressure acts normal to the crystal axis and changes the crystal thickness t
by a small amount Dt. This sets up a charge, q KqpA, where p is the
pressure acting over the
electrode area A and Kq is the crystal charge sensitivity, a material property.
A cha
Static Pressure Measurement
The local value of static pressure in a moving stream is measured
by sensing the pressure in the
direction that is normal to the flow streamline.Within ducted
flows, static pressure is sensed by wall
taps, which are small, burr
Over its operating range. When this is a consideration, a voltage follower
(see Chapter 6) can be
inserted at the output of the transducer to isolate transducer load.
Bourdon Tube
The Bourdon tube is a curved metal tube having an elliptical cross section
This system is lightly damped. The magnitude frequency response,
M(v), is shown in Figure 9.23.
The transmission line effects control the transducer response. In effect, the
transmission line acts as
a mechanical low-pass filter for the transducer.
Heavil
The idea of using a nozzle as a flow meter was first proposed in
1891 by John Ripley
Freeman (18551932), an inspector and engineer employed by a
fire insurance firm. His work
required tedious tests to quantify pressure losses in pipes, hoses,
and fittings