Pressure head flow measurement

The three most common obstmetion meters include the orifice, Venturi, and Tuy6re. The operating principle is based on reducing the cross-section of the pipe normal to the flow field and measuring the increase in pressure drop the velocity head (n /2) increases at the expense of the pressure head (P/p). The reduction in pressure head is measured at two points in the pipe—one immediately downstream and the other upstream— Figure 6.5. 

Variable-Area Flow Meters. In variable-head flow meters, the pressure differential varies with flow rate across a constant restriction. In variable-area meters, the differential is maintained constant and the restriction area allowed to change in proportion to the flow rate. A variable-area meter is thus essentially a form of variable orifice. In its most common form, a variable-area meter consists of a tapered tube mounted vertically and containing a float that is free to move in the tube. When flow is introduced into the small diameter bottom end, the float rises to a point of dynamic equiHbrium at which the pressure differential across the float balances the weight of the float less its buoyancy. The shape and weight of the float, the relative diameters of tube and float, and the variation of the tube diameter with elevation all determine the performance characteristics of the meter for a specific set of fluid conditions. A ball float in a conical constant-taper glass tube is the most common design it is widely used in the measurement of low flow rates at essentially constant viscosity. The flow rate is normally deterrnined visually by float position relative to an etched scale on the side of the tube. Such a meter is simple and inexpensive but, with care in manufacture and caHbration, can provide rea dings accurate to within several percent of full-scale flow for either Hquid or gas. 

Head-Area Meters. The Bernoulli principle, the basis of closed-pipe differential-pressure flow measurement, can also be appHed to open-channel Hquid flows. When an obstmction is placed in an open channel, the flowing Hquid backs up and, by means of the Bernoulli equation, the flow rate can be shown to be proportional to the head, the exact relationship being a function of the obstmction shape. 

The basic design is that of the Ostwald viscometer a U-tube with two reservoir bulbs separated by a capillary, as shown in Figure 24a. The Hquid is added to the viscometer, pulled into the upper reservoir by suction, and then allowed to drain by gravity back into the lower reservoir. The time that it takes for the Hquid to pass between two etched marks, one above and one below the upper reservoir, is a measure of the viscosity. In U-tube viscometers, the effective pressure head and therefore the flow time depend on the volume of Hquid in the instmment. Hence, the conditions must be the same for each measurement. 

Measurement versus Equipment Performance Pumps that are in reasonable condition typically operate within 5 percent of their pump curve. Consequently, pressures and flows that are inconsistent with the pump curve imply that the indicated flow and/or pressure are incorrecl . Figure 30-16 shows a single impeller curve plotted as head versus flow. The point shown is inconsistent with the pump operation. Therefore, that pair of flow and pressure measurements is not validated and should not be used in the subsequent steps. 

The measurement of the linear velocity as a function of shaft RPM can be done at room temperature and pressure in air. It is best to do this on the catalyst already charged for the test. Since u is proportional to the square of the head generated, the relationship will hold for any fluid at any MW, T, and P if the u is expressed at the operating conditions. The measurement can be done with the flow measuring attachment and flow meter as shown in Figure 3.5.1. 

A good method for a simple calibration facility is a system where a constant airflow is produced by using two water containers and an arrangement of a virtually constant pressure head, The constant water flow into the second container displaces an equal airflow out of the container (Fig. 12.21). With this arrangement the difficult measurement of a small airflow is changed into a much easier and accurate measurement of a small water flow. 

The relevance of methods in this section to the measurement of specific surface depends on certain relationships that are assumed to hold between the rate of fluid flow, the pressure head,... 

The flow of fluids is most commonly measured using head flowmeters. The operation of these flowmeters is based on the Bernoulli equation. A constriction in the flow path is used to increase the flow velocity. This is accompanied by a decrease in pressure head and since the resultant pressure drop is a function of the flow rate of fluid, the latter can be evaluated. The flowmeters for closed conduits can be used for both gases and liquids. The flowmeters for open conduits can only be used for liquids. Head flowmeters include orifice and venturi meters, flow nozzles, Pitot tubes and weirs. They consist of a primary element which causes the pressure or head loss and a secondary element which measures it. The primary element does not contain any moving parts. The most common secondary elements for closed conduit flowmeters are U-tube manometers and differential pressure transducers. 

Orifice meters, Venturi meters and flow nozzles measure volumetric flow rate Q or mean velocity u. In contrast the Pitot tube shown in a horizontal pipe in Figure 8.7 measures a point velocity v. Thus Pitot tubes can be used to obtain velocity profiles in either open or closed conduits. At point 2 in Figure 8.7 a small amount of fluid is brought to a standstill. Thus the combined head at point 2 is the pressure head P/( pg) plus the velocity head v2/(2g) if the potential head z at the centre of the horizontal pipe is arbitrarily taken to be zero. Since at point 3 fluid is not brought to a standstill, the head at point 3 is the pressure head only if points 2 and 3 are sufficiently close for them to be considered to have the same potential head... 

A number of instrument variables need to be set prior to making measurements. These include slit, wavelength, lamp current, lamp alignment, amplifier gain, aspiration rate, burner head position, acetylene pressure, air pressure, acetylene flow rate, and air flow rate. Some instruments are rather automated in the setup process, while others are not. Your instructor will provide detailed instructions for the particular instrument you are using. Be sure to turn on the fume hood above the flame. 

Differential Pressure Meters Differential pressure meters or head meters measure the change in pressure across a special flow element. The differential pressure increases with increasing flow rate. The pitot tubes described previously work on this principle. Other examples include orifices [see also Eqs. (6-111) and (8-102), and Fig. 10-14], nozzles (Fig. 10-19), targets, venturis (see also Sec. 8 and Fig. 10-17), and elbow meters. Averaging pitot tubes produce a pressure differential that is based on multiple measuring points across the flow path. 

Liquid Viscosity — The value (in centipoise) is a measure of the ability of a liquid to flow through a pipe or a hole higher values indicate that the liquid flows less readily under a fixed pressure head. For example, heavy oils have higher viscosities (i.e., are more viscous) than gasoline. Liquid viscosities decrease rapidly with an increase in temperature. A basic law of fluid mechanics states that the force per unit area needed to shear a fluid is proportional to the velocity gradient. The constant of proportionality is the viscosity. 

The typical pressure profile of the standpipe and the valve is shown in Fig. 8.18. As can be seen in the figure, the pressure head over the standpipe Aps, in the absolute sense, is equal to the sum of the overall pressure head, Apt, and the pressure drop over the valve, Ap0. From Eq. (8.92), the particle volume fraction in the standpipe can be estimated from the measured height of the bulk particles. Thus, given the particle mass flow rate, the leakage flow of gas in the standpipe can be estimated from Eq. (8.95). 

Head flow meters operate on the principle of placing a restriction in the line to cause a differential pressure head. The differential pressure, which is caused by the head, is measured and converted to a flow measurement. Industrial applications of head flow meters incorporate a pneumatic or electrical transmitting system for remote readout of flow rate. Generally, the indicating instrument extracts the square root of the differential pressure and displays the flow rate on a linear indicator. 

There are two elements in a head flow meter the primary element is the restriction in the line, and the secondary element is the differential pressure measuring device. Figure 1 shows the basic operating characteristics of a head flow meter. 

The head flow meter actually measures volume flow rate rather than mass flow rate. Mass flow rate is easily calculated or computed from volumetric flow rate by knowing or sensing temperature and/or pressure. Temperature and pressure affect the density of the fluid and, therefore, the mass of fluid flowing past a certain point. If the volumetric flow rate signal is compensated for changes in temperature and/or pressure, a true mass flow rate signal can be obtained. In Thermodynamics it is described that temperature and density are inversely proportional, while pressure and density are directly proportional. To show the relationship between temperature or pressure, the mass flow rate equation is often written as either Equation 4-1 or 4-2. 

Head-type flowmeters include orifice plates, venturi tubes, weirs, flumes, and many others. They change the velocity or direction of the flow, creating a measurable differential pressure, or "pressure head," in the fluid. Head metering is one of the most ancient of flow detection techniques. There is evidence that the Egyptians used weirs for measurement of irrigation water flows in the days of the Pharaohs and that the Romans used orifices to meter water to households in Caesar s time. In the 18th century, Bernoulli established the basic relationship between the pressure head and velocity head, and Venturi published on the flow tube bearing his name. 

The detection of pressure drop across a restriction is undoubtedly the most widely used method of industrial flow measurement. If the density is constant, the pressure drop can be interpreted as a reading of the flow. In larger pipes or ducts, the yearly energy operating cost of differential-pressure (d/p)-type flowmeters can exceed the purchase price of the meter. The permanent pressure loss through a flowmeter is usually expressed in units of velocity heads, v2/2 g, where v is the flowing velocity, and g is the gravitational acceleration (9.819 m/s2, or 32.215 ft/s2, at 60° latitude). 

For the exploitation of available hydro power in a considered site, two physical quantities must exist, the flow rate of water and a head. Flow rate is the volume of water passing per second and it is measured in m3/s. Head is the water pressure, which is created by the altitude difference between the water intake and the turbine. It can be expressed by the relevant vertical distance. A classification of sites exists, depending on the head values (British Hydropower Association, 2005). Sites with heads less than 10 m are considered low-head , from 10-50 m are medium-head and above 50 m are classified as high-head sites. The power that can be produced by a hydro plant is expressed by the following equation ... 

Here Ah is the pressure head, p the density of the solution, and g the acceleration of gravity. Strictly speaking. Ah in this type of viscometer varies during the measurement. It is not correct merely to take the average Ah at the beginning and ending of the measurement since the flow is faster at first than near the end. The average Ah can however be calculated by the Meissner equation... 

Pressure drops are measured in circular tubes for fully developed flows in the transition regime for three ty pes of inlet configuralions shown in Fig. 8-32 re-entrant (tube extends beyond tubesheet face into head of... 

Dynamic osmometers reach equilibrium pressures in 10 to 30 minutes and indicate osmotic pressure automatically. Several types are available. Some commonly used models employ sensors to measure solvent flow through the membrane and adjust a counteracting pressure to maintain zero net flow. A commercially available automatic osmometer operates on the null-point principle. In this high-speed membrane osmometer schematically represented in Fig. 4.4, the movement of an air bubble inside the capillary immediately below the solvent cell indicates the solvent flow to the solution cell. Such movement is immediately detected by a photocell, which in turn is coupled to a servomechanism. If any movement of the air bubble is detected by a photocell, the servomechanism is stimulated to move the solvent reservoir upward or downward in order to adjust the hydrostatic pressure such that the solvent flow is completely arrested. The pressure head of the reservoir gives the osmotic head. Some osmometers also use strain gauges on flexible diaphragms to measure the osmotic pressure directly. 

The principle of the orifice meter is identical with that of the venturi. The reduction of the cross section of the flowing stream in passing through the orifice increases the velocity head at the expense of the pressure head, and the reduction in pressure between the taps is measured by the manometer. Bernoulli s equation provides a basis for correlating the increase in velocity head with the decrease in pressure head. 

Ewers and Sack 4) have developed a related apparatus consisting of a vertical walled channel between two reservoirs, through which the substrate liquid moves as a consequence of a head difference between the reservoirs. Small nonwettable particles floated on the surface indicate the speed of surface elements of the fluid along the center line of the channel. This motion has been related to bulk-fluid movement by means of a thorough mathematical treatment, which is applicable to Newtonian surface films. Thus, the force measurement in the previous scheme is replaced here by a surface velocity and bulk-flow measurement. The only serious difficulty with this arrangement is that the transported surface material tends to accumulate in the lower reservoir. Thus, a surface pressure gra-... 

Placement and orientation of the pressure taps need to be considered in the equipment design to allow for pressure measurements. The pressure taps should be positioned perpendicular to the flow of fluid, otherwise the velocity head of the fluid will alter the measurement. Placing ball valves between the pressure taps and measurement device is commonly done (especially when high pressures are involved) so that the pressure measurement device can be safely taken out of service for calibration or replacement. The pressure measurement device is preferably located near the pressure tap but is not essential. The diameter of the tubing connecting the pressure tap to the measurement device should be of adequate diameter to... 

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