The following points highlight the five main types of devices for measuring of flow in pipes. The devices are: 1. The Venturimeter 2. The Pitot Tube 3. Orifice Plate or Orifice Meter 4. The Flow Nozzle 5. Free Jets.

#### Flow MeasuringDevice # 1. The Venturimeter:

A Venturimeter is a device meant for measuring the quantity of a liquid flowing through a pipe. In its simplest form, the device consists of a short converging section leading to a throat and followed by a diverging section. The entrance and the exit diameters will be the same as that of the pipe line to which it is fitted.

Tubes are provided which enter the pipe at the entrance section (also called the enlarged end) and at the throat. These tubes are meant for measurement of pressure. Pressure can be measured by piezometer tubes. Alternatively, the tubes may be connected to a U-tube containing a heavy liquid like mercury.

As the liquid flows through the venturimeter, the velocity at the throat section is increased due to the decrease in the area of flow. This increase in velocity is accompanied by a consequent reduction of pressure.

The venturimeter is an application of Bernoulli’s theorem. Consider sections 1-1 and 2-2 corresponding to the entrance and throat sections respectively.

The discharge equation in the above form will be found convenient.

Note:

It must be noted that the converging cone must be of shorter length than that of the diverging cone. The diverging cone acts as a diffuser decelerating the flow so as to regain the pressure. A decelerating flow is not stable. Only if the increase in area is made gradual the flow can be stable, otherwise the flow is likely to separate from the wall resulting in cavitation and energy losses. Generally an included angle of 5° to 15° is provided for the diverging cone.

An included angle of 20° to 30° is provided for the converging cone. In order discharge determinations are accurate it is very necessary that eddies should not be present in the approaching flow, and the flow must have a symmetrical velocity distribution. To satisfy this condition the venturimeter must be preceded with a straight pipe for a distance of about 10 pipe diameters. Fig. 7.60 shows the recommended dimensions for a venturimeter.

#### Flow Measuring Device # 2. The Pitot Tube:

A pitot tube is a simple device meant for measuring the velocity of a liquid at any point. In its simple form the pitot tube consists of a glass tube whose lower end is bent at right angles (Fig. 7.72). The device is placed in a moving liquid with the lower opening directed in the upstream direction.

The liquid level in the pitot tube will depend on the velocity of the stream. The pitot tube in the form shown in the figure is meant for measuring the velocity at any point in a stream of liquid whose surface is open to the atmosphere.

Let the inlet of the pitot tube be at depth H below the liquid surface. Consider the two points A and B. The point B is just at the inlet to the pitot tube while the point A is at the same level as that of B but at some distance from B.

If the pitot tube is to be used to measure the velocity of a liquid in a pipe, then we must adopt some method to know the static pressure head H. For instance, we may use a pitot tube and a vertical piezometer tube and measure the difference of the liquid levels in the two tubes. See Fig.7.73. Another method is to connect the pitot tube and the piezometer tube and note the difference of liquid levels in the two tubes. See Fig.7.74.

In another arrangement the pitot tube and vertical tube connected to the pipe may be connected to a U-tube containing a heavy liquid like mercury. See Fig. 7.83. If the difference of level of the heavy liquid in the U-tube is y.

In the arrangements described above two openings are needed in the pipe wall. Moreover, the static pressure tap does not sense the pressure at the point where the stagnation pressure is measured. To overcome these difficulties the pitot-static tube (Fig. 7.76) is devised.

In this arrangement the static pressure tapping and the impact tapping are combined into a single pitot-static tube. This tube is actually a double tube. The inner tube measures the impact pressure while the outer tube which has several holes, is meant for measuring the static pressure. The inner and the outer tubes may be connected to a U-tube differential manometer. If y is the difference of the levels of the manometer liquid,

then h = (S – 1)y

where S is the specific gravity of the manometer liquid relative to the liquid flowing through the pipe.

#### Flow Measuring Device # 3. Orifice Plate or Orifice Meter:

An orifice meter is another device to gauge the flow of a liquid through a pipe. It consists of a flat plate containing a circular orifice provided concentrically with the pipe across the flow as shown in Fig. 7.81. It is fitted to the pipe by flanged joint. This device works on the same principle as that of the venturimeter.

As the flow passes through the orifice the moving stream converges passing through a somewhat stagnant fluid and later spreads to fill the pipe. Generally the diameter of the orifice is about half of the pipe.

Pressure gauges are fitted one on either side of the orifice plate. The pressure tapping on the downstream side is provided close to the orifice plate at the section of minimum area of the stream (vena contracta) and is usually at a distance of 0.5 times the diameter of the orifice. The pressure tapping on the upstream side is provided at a section 1-1 at a sufficient distance from the orifice plate beyond the region of convergence (see Fig. 7.81.).

This distance may be about 1.5 times the diameter of the pipe to ensure that the pressure tapping is made at a section where the pipe runs full. Since a sudden enlargement of the flow section takes place beyond the vena contracta section, a loss of energy head takes place.

(Note, such sudden enlargement of the flow section is prevented in the venturimeter). Accordingly the value of Cd for the orifice meter is correspondingly lower.

A comparison between the venturimeter and the orifice meter is given below:

Venturimeter:

1. Accuracy is high for all diameter ratios.

2. This has high efficiency. Recovery pressure is greater than any other gauging device.

3. Due to smooth boundary this resists wear effectively.

4. Dirt and sediments are not collected.

5. This is a costly device.

6. Due to its large size and weight it is inconvenient to install.

7. There is no scope to change the throat pipe area ratio.

8. Coefficient of discharge is 0.95 to 1.

Orifice Meter:

1. Accuracy is low particularly for high orifice pipe.

2. This has low efficiency. There is considerable pressure loss.

3. This is subject to wear. The sharpness of the orifice gets affected leading to inaccuracy.

4. Due to obstruction, dirt and sediments are collected.

5. This is a cheap device and can be easily made in any workship.

6. The device is very simple and can be easily installed.

7. The orifice size can be changed by replacing different orifice plates.

8. Coefficient of discharge is 0.60 to 0.64.

#### Flow Measuring Device # 4. The Flow Nozzle:

This is another device for the measurement of flow in pipes. The design features of this device are intermediate to the venturimeter and the orifice meter. It is similar to the venturimeter with a smooth converging approach but without any diverging zone. The discharge equation is the same as that of the venturimeter.

#### Flow Measuring Device # 5. Free Jets:

A jet of water exposed to the atmosphere is called a free jet. Ignoring atmospheric resistance, when a jet is issued from a source it will describe a parabola.

Let a jet of water be discharged from a nozzle at a point A at an angle α with the horizontal at a velocity u. Let P be any point on the centre line of the jet. Let the coordinates of P be (x,y) with respect to the point of projection of the jet A.

Let a liquid particle take t seconds to reach P. This displacement of the particle from A to P consists of a horizontal displacement x and a vertical displacement y. The motion corresponding to the horizontal displacement is a uniform motion.

The horizontal component of the velocity is constant and equal to u cos α. The motion corresponding to vertical displacement is an accelerated motion affected by gravity. Hence the horizontal and vertical displacements in time t are given by,