Subsurface Ventilation and Environmental Engineering

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Hence the level in the reservoir remains unchanged. The addition of a micrometer scale gives this instrument both a good range and high accuracy.

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One of the problems in some water manometers is a misformed meniscus, particularly if the inclination of the tube is less than 5 degrees from the horizontal. This difficulty may be overcome by employing a light oil, or other liquid that has good wetting properties on glass. Alternatively, the two limbs may be made large enough in diameter to give horizontal liquid surfaces whose position can be sensed electronically or by touch probes adjusted through micrometers.

U tube manometers, or water gauges as they are commonly known, may feature as part of the permanent instrumentation of main and booster fans. Provided that the connections are kept firm and clean, there is little that can go wrong with these devices.

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Compact and portable inclined gauges are available for rapid readings of pressure differences across doors and stoppings in underground ventilation systems. However, in modern pressure surveying Chapter 6 manometers have been replaced by the diaphragm gauge. This instrument consists essentially of a flexible diaphragm, across which is applied the differential pressure. The strain induced in the diaphragm is sensed electrically, mechanically or by magnetic means and transmitted to a visual indicator or recorder. In addition to its portability and rapid reaction, the diaphragm gauge has many advantages for the subsurface ventilation engineer.

Secondly, it reacts relatively quickly to changes in temperature and does not require precise levelling. Thirdly, diaphragm gauges can be manufactured over a wide variety of ranges. A ventilation survey team may typically carry gauges ranging from 0 - Pa to 0 5 kPa or to encompass the value of the highest fan pressure in the system. One disadvantage of the diaphragm gauge is that its calibration may change with time and usage. Re-calibration against a laboratory precision manometer is recommended prior to an important survey.

Other appliances are used occasionally for differential pressures in subsurface pressure surveys. Piezoelectric instruments are likely to increase in popularity. The aerostat principle eliminates the need for tubing between the two measurement points and leads to a type of differential barometer. In this instrument, a closed and rigid air vessel is maintained at a constant temperature and is connected to the outside atmospheres via a manometer or diaphragm gauge. As the inside of the vessel remains at near constant pressure, any variations in atmospheric pressure cause a reaction on the manometer or gauge.

Instruments based on this principle require independent calibration as slight movements of the diaphragm or liquid in the manometer result in the inside pressure not remaining truly constant. Bernoulli's equation for ideal fluids As a fluid stream passes through a pipe, duct or other continuous opening, there will, in general, be changes in its velocity, elevation and pressure. In order to follow such changes it is useful to identify the differing forms of energy contained within a given mass of the fluid.

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For the time being, we will consider that the fluid is ideal; that is, it has no viscosity and proceeds along the pipe with no shear forces and no frictional losses. Secondly, we will ignore any thermal effects and consider mechanical energy only. Suppose we have a mass, m, of fluid moving at velocity, u, at an elevation, Z, and a barometric pressure P. There are three forms of mechanical energy that we need to consider.

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In each case, we shall quantify the relevant term by assessing how much work we would have to do in order to raise that energy quantity from zero to its actual value in the pipe, duct or airway. Potential energy Any base elevation may be used as the datum for potential energy. In most circumstances of underground ventilation engineering, it is differences in elevation that are important.

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If our mass m is located on the base datum then it will have a potential energy of zero relative to that datum. We then exert an upward force, F, sufficient to counteract the effect of gravity. This gives the potential energy of the mass at elevation Z. Flow work Suppose we have a horizontal pipe, open at both ends and of cross sectional area A as shown in Figure 2.

We wish to insert a plug of fluid, volume v and mass m into the pipe. However, even in the absence of friction, there is a resistance due to the pressure of the fluid, P, that already exists in the pipe. Hence, we must exert a force, F, on the plug of fluid to overcome that resisting pressure. Our intent is to find the work done on the plug of fluid in order to move it a distance s into the pipe. Figure 2.


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As fluid continues to be inserted into the pipe to produce a continuous flow, then each individual plug must have this amount of work done on it. That energy is retained within the fluid stream and is known as the flow work. The appearance of pressure, P, within the expression for flow work has resulted in the term sometimes being labelled "pressure energy". This is very misleading as flow work is entirely different to the "elastic energy" stored when a closed vessel of fluid is compressed.

Some authorities also object to the term "flow work" and have suggested "convected energy" or, simply, the "Pv work". Note that in Figure 2. Hence the pressure, P, inside the pipe does not change with time the fluid is not compressed when plugs of fluid continue to be inserted in a frictionless manner.

When the fluid exits the system, it will carry kinetic and potential energy, and the corresponding flow work with it.


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Now we are in a position to quantify the total mechanical energy of our mass of fluid, m. From expressions 2.

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If no mechanical energy is added to or subtracted from the fluid during its traverse through the pipe, duct or airway, and in the absence of frictional effects, the total mechanical energy must remain constant throughout the airway. Then equation 2. Another way of expressing this equation is to consider two stations, 1 and 2 along the pipe, duct or airway. Now as we are still considering the fluid to be incompressible constant density , giving. Furthermore, if we multiplied throughout by then each term would take the units of pressure.

Bernoulli's equation has, traditionally, been expressed in this form for incompressible flow. It was first derived by Daniel Bernoulli , a Swiss mathematician, and is known throughout the world by his name. As fluid flows along any closed system, Bernoulli's equation allows us to track the inter-relationships between the variables. Velocity u, elevation Z, and pressure P may all vary, but their combination as expressed in Bernoulli's equation remains true. It must be remembered, however, that it has been derived here on the assumptions of ideal frictionless conditions, constant density and steady-state flow.

We shall see later how the equation must be amended for the real flow of compressible fluids. Consider the level duct shown on Figure 2.

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Three gauge pressures are measured. To facilitate visualization, the pressures are indicated as liquid heads on U tube manometers. Any drilling burrs on the inside have been smoothed out so that the pressure indicated is not influenced by the local kinetic energy of the air.

The other limb of the manometer is open to the ambient atmosphere. The gauge pressure indicated is known as the static pressure, ps. In position b the left tube has been extended into the duct and its open end turned so that it faces directly into the fluid stream. As the fluid impacts against the open end of the tube, it is brought to rest and the loss of its kinetic energy results in a local increase in pressure.

The pressure within the tube then reflects the sum of the static pressure and the kinetic effect.

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