Applications: Flow Measurement

1
TOPIC 5

• Applications
• Fluid flow measurement

5.8
2
Applications Flow Measurement

• The Bernoulli equation (5.3 or 5.4) can be
  applied to several commonly occurring situations
  in which useful relations involving pressures,
  velocities and elevations may be obtained.
• A very important application in engineering is
  fluid flow measurement
• Measurement of velocity Pitot-static tube
• Measurement of flow rate Venturi meter
• Orifice meter

5.9
3
The Pitot-Static Tube

• P1 is a Static pressure It is measured by a
  device (static tube) that causes no velocity
  change to the flow. This is usually accomplished
  by drilling a small hole normal to a wall along
  which the fluid is flowing.
• P2 is a Stagnation pressure It is the pressure
  measured by an open-ended tube facing the flow
  direction. Such a device is called a Pitot tube.

1
2
P2
P1,V1
Stagnation Point V20
5.10
4
Pitot-Static tube
Bernoulli equation (5.3) between 1 and 2

• Stagnation Pressure is higher than Static Pressure

(Recall that position 2 is a stagnation point
V2 0)
(5.5)
We can measure pressures P1 and P2 using
hydrostatics P1Patm rgh1, P2Patm rgh2 or
using a Pressure Gauge
5.11
5
Pitot-static tube
The static and Pitot tube are often combined into
the one-piece Pitot-static tube.
5.12
6
Example Measurement of Velocity

• An airplane flies at an elevation of 10,000 ft
  in standard atmosphere. The pressure difference
  indicated by the Pitot-static probe attached to
  the fuselage is 0.1313 psi. What is the velocity
  of the airplane? (The density of air at this
  altitude is 0.056 lbm/ft3)

5.13
7
Orifice, Nozzle and Venturi meters
Basic principle Increase in velocity causes a
decrease in pressure.

• Fluid is accelerated by forcing it to flow
  through a constriction, thereby increasing
  kinetic energy and decreasing pressure energy.
  The flow rate is determined by measuring the
  pressure difference between the meter inlet and a
  point of reduced pressure.
• Desirable characteristics of flow meters
• Reliable, repeatable calibration
• Introduction of small energy loss into the system
• Inexpensive
• Minimum space requirements

5.14
8
Generalized flow obstruction in a pipe
1
2
V1
P1
P2
Continuity equation between 1 and 2
Bernoulli equation between 1 and 2
(5.6)
5.15
9
Generalized flow obstruction in a pipe

• In eq. (5.6) frictional losses have not been
  taken into account
• To account for frictional losses we use a
  discharge coefficient, Cu

(5.7)

• The volumetric flow rate can be easily calculated

10
Orifice Meter
This type of meter consists of a thin flat plate
with a circular hole drilled in its center. It is
very simple, inexpensive and easy to install, but
it can cause significant pressure drops.
1
2
V1
Front view of orifice plate
P1
P2
Where the discharge coefficient, Cu f(Re,
D2/D1), can be found in Figure 5.14, textbook
(5.12 2nd edition)
5.16
11
Nozzle Meter
The nozzle meter uses a contoured nozzle. The
resulting flow pattern for the nozzle meter is
closer to ideal.
Where the nozzle discharge coefficient, Cu f(Re,
D2/D1), can be found in textbooks and is higher
than the orifice discharge coefficient.
5.17
12
Venturi Meter
This device consists of a conical contraction, a
short cylindrical throat and a conical expansion.
The fluid is accelerated by being passed through
the converging cone. The velocity at the throat
is assumed to be constant and an average velocity
is used. The venturi tube is a reliable flow
measuring device that causes little pressure
drop. It is used widely particularly for large
liquid and gas flows.
P2
P1
Where the discharge coefficient, Cu f(Re), can
be found in Figure 5.11, textbook (5.9 2nd
edition)
5.18
13
Example 1 Flow through an orifice meter
A lubricating oil flows through a 5 Schedule 40
steel pipe (which corresponds to 5.047in ID) at
300 gal/min. A sharp-edged orifice is inserted
into this pipe and attached to a mercury
manometer. At the flow temperature the oil has a
specific gravity of 0.87 and a viscosity of 15cp.
What manometer reading is expected if the
manometer is positioned vertically and the
orifice diameter is 3.5 in?
5.19
14
Example 1
Cu
15
Example 2 Flow through an orifice meter
An orifice meter like that shown in the previous
page is used to monitor the water flow rate in a
10 cm diameter pipe. Determine the volumetric
flow rate if the orifice has a diameter of 2 cm
and the manometer shows a 30 cm difference in
mercury.
5.20
16
Summary

• The mechanical energy equation (or generalized
  Bernoulli equation) is an expression of the
  energy balance equation for steady flow and
  constant-density fluids.
• The mechanical energy equation can be applied
  with negligible error to almost all steady flows
  of liquids and for steady flows of gases at low
  velocities.
• A special case of the mechanical energy equation,
  the Bernoulli equation, can be derived if we
  assume frictionless flow and absence of shaft
  work.
• A large number of devices for the measurement of
  fluid velocity and flow rate are based on the
  conservation of energy. The Bernoulli equation
  can be conveniently used to make the appropriate
  calculations.