CHAPTER
4 MEASUREMENT OF VELOCITY IN A FLUID
in which subscript 1 refers to conditions at the entrance to the tube and subscript 2 refers to conditions at the top of the column of fluid which rises in the tube. Now, Z_{2} = Z + Z' 
taking the datum level at the mouth of the tube and letting Z' be the height of the upper liquid surface in the pipe above the datum, and Z be the additional height of the fluid level in the tube above the upper liquid surface in the pipe; Z' may be neglected if P_{1} is measured at the upper surface of the liquid in the pipe, or if Z' is small compared with Z. v_{2} = 0 as there is no flow in the tube. P_{2} = 0 if atmospheric pressure is taken as datum and if the top of the tube is open to the atmosphere. Z_{1} = 0 because the datum level is at the mouth of the tube. The equation then simplifies to
This analysis shows that the differential head on the manometer measures the sum of the velocity head and the pressure head in the flowing liquid. The
Pitot tube can be combined with a piezometer tube, and connected across
a common manometer as shown in Fig. 4.1(d).
The differential head across the manometer is the velocity head plus the
static head of the Pitot tube, less the static head of the piezometer
tube. In other words, the differential head measures directly the velocity
head of the flowing liquid or gas. This differential arrangement is known
as a Pitotstatic tube and it is extensively used in
the measurement of flow velocities.
where Z is the differential head measured in terms of the flowing fluid.
From eqn. (4.2) we have
In
working with Pitotstatic tubes, it is convenient to convert pressure
heads into equivalent heads of the flowing fluid, in this case air, using
the relationship:
= 12.16 m^{2}s2^{}^{} Therefore v_{1} = 3.5 m s^{1}
A gradual constriction has been interposed in a pipe decreasing the area of flow from A_{1} to A_{2}. If the fluid is assumed to be incompressible and the respective velocities and static pressures are v_{1} and v_{2}, and P_{1} and P_{2}, then we can write Bernouilli's equation (eqn.3.7) for the section of horizontal pipe:
Furthermore, from the mass balance, eqn. (3.5)
also, as it is the same fluid
so that we have
By joining the two sections of a pipe to a Umanometer, as shown in Fig.
4.2, the differential head
and so Z = (P_{2} _{}P_{1})/r_{m} g If A_{1} and A_{2} are measured, the velocity in the pipe, v_{1}, can be calculated. This device is called a Venturi meter. In actual practice, energy losses do occur in the pipe between the two measuring points and a coefficient C is introduced to allow for this:
In a properly designed Venturi meter, C lies between 0.95 and 1.0. The orifice meter operates on the same principle as the Venturi meter, constricting the flow and measuring the corresponding static pressure drop. Instead of a tapered tube, a plate with a hole in the centre is inserted in the pipe to cause the pressure difference. The same equations hold as for the Venturi meter; but in the case of the orifice meter the coefficient, called the orifice discharge coefficient, is smaller. Values are obtained from standard tables, for example British Standard Specification 1042. Orifices have much greater pressure losses than Venturi meters, but they are easier to construct and to insert in pipes. Various other types
of meters are used: Back to the top 
