Velocity and Flow Rate Measuring Instruments used in Pipes - Essay Example

Velo and Flow Rate Measuring Instruments used in Pipes Introduction: Many important fluids are transported through pipes. Some examples are transportation of water from reservoirs to end user households and industries, transportation of crude oil from exploration wells to refineries, transportation of different chemicals within and / or different industrial complexes. It is important to know the flow rate and velocity of the liquid being transported through the pipes for various regions including safety, process control, commercial accounting, leak and / or theft detection etc. The measurements of fluid velocity and flow rate are done by different instruments like Pitot tube, Stagnation tube, Venturi meter, Rotameter etc. These instruments work on some common fluid mechanics principles and therefore it is useful to discuss some relevant fluid mechanics principles that form the basic principle of flow velocity and flow rate measuring instruments. Some relevant fluid mechanics principles are briefly discussed below. Fluid Mechanic Principles: Some relevant principles of fluid mechanics that are underlying principles of various flow velocity and flow rate measuring equipments are – “Pascal’s Law”, “Equation of Continuity” and Bernoullli’s Equation”. These are briefly discussed below. Pascal’s Law The law states that pressure applied to any region of a liquid is transmitted to the entire liquid without any drop in the magnitude. This is the underlying principle for pressure measurement using manometer. This law has several interesting applications like hydraulic lift and other hydraulic devices. This law can be mathematically stated as P2 = P1 + gh …………. (1) Where P1 and P2 are pressures at points 1 and 2 respectively, ‘’ is density of the liquid, ‘g’ is the acceleration due to gravity and ‘h’ is the elevation of point 2 with respect to point 1. Equation of Continuity This is essentially a statement of the law of conservation of matter as applied in fluid mechanics. This law states that for an incompressible fluid the flow rate remains the same at any cross-section along the flow direction. i.e. A1v1 = A2v2 = Q ……………... (2) where ‘A’ is area of cross-section, ‘v’ is fluid velocity and ‘Q’ is the flow rate. Bernoulli’s Equation This equation is essentially a statement of the law of conservation of energy as applied in fluid mechanics. This law states that for an incompressible and non-viscous fluid the total mechanical energy remains conserved along the flow line. This law can be mathematically expressed as ……………(3) Here ‘P’ is pressure, ‘h’ is elevation, ‘’ is density of the liquid, ‘g’ is the acceleration due to gravity and ‘v’ is velocity of the fluid. This equation forms the backbone of most of the flow velocity and flow rate measuring instruments. Some of the important instruments measuring flow rate and flow velocity in a pipe are briefly discussed in the subsequent sections. It must be noted that this equation is for non-viscous fluid only and therefore, should not be applied for a highly viscous liquid flow as in that case there will be conversion of mechanical energy into thermal energy, which is not considered in this equation. Different Measuring Equipments: There are many instruments which are used for measurement of flow velocity and flow rate in a pipe. What is essentially measured is the flow velocity (v) which is then converted into flow rate (Q) by the following equation: Flow rate Q = A*v Where ‘A’ is the area of cross-section at the point where fluid velocity is ‘v’ and from continuity equation, this remains the flow rate all along the pipe. Some important flow velocity and flow rate measuring instruments are – ‘Pitot Tube’, ‘Stagnation Tube’, ‘Venturi Meter’, ‘Orifice Meter’, “Rota Meter’, ‘Calorimetric Flow Meter’, ‘Turbine Flow Meter’, ‘Vortex Flow Meter’, ‘Electromagnetic Flow Meter’, ‘Ultrasonic Doppler Flow Meter’, ‘Positive Displacement Flow Meter’, ‘Thermal Flow Meter’ etc. to name a few (http://www.engineeringtoolbox.com/flow-meters-d_493.html). In subsequent sections the basic principles and equations pertaining to four different flow velocity and flow rate measuring instruments namely – ‘Pitot Tube’, ‘Stagnation Tube’, ‘Venturi Meter’ and ‘Orifice Meter’ will be discussed. 1. Stagnation Tube The schematic drawing showing the stagnation tube is shown in Fig. 1, below. This instrument works on the principle contained in ‘Bernoulli’s Equation”, which was discussed earlier and is presented below again. ……………(3) In case of ‘Stagnation Tube, this equation reduces into the following form Where ‘v’ is the velocity of the liquid, ‘’ is density of the liquid, ‘g’ is the acceleration due to gravity and ‘z’ is the rise in the stagnation column. It should not be used for highly viscous flow as Bernoulli’s Equation is not applicable for that situation. Fig. 1: Schematic Drawing of a Stagnation tube 2. Pitot Tube The schematic drawing showing the working of a ‘Pitot Tube’ is shown in Fig. 2, below (http://www.engineeringtoolbox.com/flow-meters-d_493.html). This underlying principle of operation of the equipment is Bernoulli’s Equation, which has been discussed in the preceding section in equation (3) and is typed below again. ……………(3) In case of ‘Pitot Tube”, h1 = h2 and v2 = 0; hence equation (3) reduces to the following form: Thus what is measured by the ‘Pitot Tube’ is differential pressure between stagnant liquid (v = 0) and the flowing liquid (v = fluid velocity). This velocity is then converted into flow rate by multiplying the flow velocity with the area of the cross-section where the flow velocity was measured. Here one must exercise caution as this cannot be used for highly viscous liquid. Fig. 2: Schematic Diagram Showing Working of Pitot Tube Comparision between Stagnation Tube and Pitot Tube Both Stagnation Tube and Pitot tube work on the same Bernoulli’s equation and therefore, the difference is only in terms of what is measured. In case of Stagnation tube the rise is the stagnation column due to the stagnation pressure is measured. On the other hand in case of Pitot Tube the stagnation pressure is measured directly as the pressure differential and not as height of the liquid. This is the only difference. 3. Venturi Meter A schematic diagram showing working of Venturi Meter is shown in Fig. 3, below (http://www.cee.mtu.edu/~dwatkins/ce3600_labs/venturi.pdf). This instrument also works on the same “Bernoulli’s Principle” which can be stated as This is a variable cross-section instrument. It has two cross-sections to alter the velocity of liquid in predetermined manner and the pressure change due to this predetermined velocity change is measured. In case of Venturi Meter, h1 = h2 Therefore, Bernoulli’s equation reduces in the following form …………. (4) Now, v1 and v2 are related to the area of cross-section and therefore to the diameter of the two sections by the continuity equation. Therefore, …………… (5) Using equation (5) in equation (4) and the measured values of P1 and P2 one can calculate v1 and / or v2 and hence the flow rate in the pipe. 4. Orifice Meter This instrument also works on the same Bernoulli’s equation. In this instrument a large plate (equal to the diameter of the pipe) with a small orifice is inserted into the flow path so as to force the entire liquid through the small orifice in the plate. As the liquid converges through the orifice, a minimum flow diameter is achieved at a point just after the orifice. This point is known as “Veena Contracta”. Due to the change in the diameter of the flow, there is corresponding change in the flow velocity (in accordance with the Continuity Equation) and therefore, in the pressure (according to Bernoulli’s Equation). The pressure difference between “Veena Contracta” and the main pipeline is measured. The procedure of solving the flow velocity remains the same as in cae of Venturi Meter discussed in the preceding section. Comparision between Venturi Meter and Orifice Meter While both the instruments work on the principle of Bernoulli’s equation and introduce in variation in the cross-sectional area of the flow path, there is small difference in the two instruments. Venturi meter is much more longer than an orifice plate, which is essentially a plate. Normally the reduction in cross-section is much larger in case of the orifice meter than that in case of Venturi Meter. Hence, measurements are more accurate in case of orifice plate than in case of venture meter. Conclusions: The basic principles of fluid mechanics relevant to flow velocity and flow rate measurements and four different instruments measuring flow velocity and flow rate in a pipe has been briefly discussed in this report. References: http://www.engineeringtoolbox.com/flow-meters-d_493.html http://www.cee.mtu.edu/~dwatkins/ce3600_labs/venturi.pdf Read More