MECHANICS of FLUIDS LABORATORY - Mechanical Engineering

EXPERIMENT 16
MEASUREMENT OF VELOCITY
AND
CALIBRATION OF A METER FOR COMPRESSIBLE FLOW
The objective of this experiment is to
determine a calibration curve for a meter placed
in a pipe that is conveying air. The meters of
interest are an orifice meter and a venturi meter.
These meters are calibrated in this experiment by
using a pitot-static tube to measure the velocity,
from which the flow rate is calculated.
Pitot Static Tube
When a fluid flows through a pipe, it exerts
pressure that is made up of static and dynamic
components. The static pressure is indicated by a
measuring device moving with the flow or that
causes no velocity change in the flow. Usually, to
measure static pressure, a small hole
perpendicular to the flow is drilled through the
container wall and connected to a manometer (or
pressure gage) as indicated in Figure 16.1.
The dynamic pressure is due to the movement
of the fluid. The dynamic pressure and the static
pressure together make up the total or stagnation
pressure. The stagnation pressure can be measured
in the flow with a pitot tube. The pitot tube is an
open ended tube facing the flow directly. Figure
16.1 gives a sketch of the measurement of
stagnation pressure.
flow
stagnation pressure
measurement
static pressure
measurement
pitot tube
h
FIGURE 16.1. Measurement of static and
stagnation pressures.
The pitot-static tube combines the effects of
static and stagnation pressure measurement into
one device. Figure 16.2 is a schematic of the pitotstatic
tube. It consists of a tube within a tube
which is placed in the duct facing upstream. The
pressure tap that faces the flow directly gives a
measurement of the stagnation pressure, while
h
the tap that is perpendicular to the flow gives
the static pressure.
When the pitot-static tube is immersed in the
flow of a fluid, the pressure difference
(stagnation minus static) can be read directly
using a manometer and connecting the pressure
taps to each leg. Applying the Bernoulli equation
between the two pressure taps yields:
four to eight holes
equally spaced
flow direction
section A-A
enlarged
A
A
manometer
connections
FIGURE 16.2. Schematic of a pitot-static tube.
p 1
ρg + V 1 2
2g + z 1 = p 2
ρg + V 2 2
2g + z 2
where state “1” as the stagnation state (which
will be changed to subscript “t”), and state “2” as
the static state (no subscript). Elevation
differences are negligible, and at the point where
stagnation pressure is measured, the velocity is
zero. The Bernoulli equation thus reduces to:
p t
ρg = p ρg + V2
2g
Next, we rearrange the preceding equation and
solve for velocity
V =
√⎺⎺⎺
2(p t - p)
ρ
A manometer connected to the pitot-static tube
would provide head loss readings ∆h given by
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