Fluid flow pitot tube

Derive a relationship between the pressure difference recorded between the two orifices of a pitot tube and the velocity of flow of an incompressible fluid. A pitot tube is to be situated in a large circular duct in which fluid is in turbulent flow so that it gives a direct reading of the mean velocity in the duct. At what radius in the duct should it be located, if the radius of the duct is r l... 

A Pitot tube is an instrument used to measure the velocity of a flowing fluid. The Pitot tube was invented by French engineer Henri Pitot in the early 1700s. Today, it is widely used in industrial applications and is manufactured in a variety of sizes as shown in Figure 4.24. 

Dynamic pressure may be measured by use of a pitot tube that is a simple impact tube. These tubes measure the pressure at a point where the velocity of the fluid is brought to zero. Pitot tubes must be parallel to the flow. The pitot tube is sensitive to yaw or angle attack. In general angles of attack over 10° should be avoided. In cases where the flow direction is unknown, it is recommended to use a Kiel probe. Figure 10-3 shows a Kiel probe. This probe will read accurately to an angle of about 22° with the flow. 

The effect of pulsating flow on pitot-tube accuracy is treated by Ower et al., op. cit., pp. 310-312. For sinusoidal velocity fluctuations, the ratio of indicated velocity to actual mean velocity is given by the factor /l + AV2, where X is the velocity excursion as a fraction of the mean velocity. Thus, the indicated velocity would be about 6 percent high for velocity fluctuations of 50 percent, and pulsations greater than 20 percent should be damped to avoid errors greater than 1 percent. Tne error increases as the frequency of flow oscillations approaches the natural frequency of the pitot tube and the density of the measuring fluid approaches the density of the process fluid [see Horlock and Daneshyar, y. Mech. Eng. Sci, 15, 144-152 (1973)]. 

Pressures substantially lower than true impact pressures are obtained with pitot tubes in turbulent flow of dilute polymer solutions [see Halliwell and Lewkowicz, Phys. Fluids, IS, 1617-1625 (1975)]. 

ISO 3966. Measurements of fluid flow in closed conduits—Velocity area method using Pitot static tube. 1977, p. 39. 

ISO Standard 3966. Measurement of Fluid Flow in Closed Conduits—Velocity Area Method Using Pitot Static Tubes. International Organisation fot Standardisation, 1977. 

The pitot tube, in which a small element of fluid is brought to rest at an orifice situated at right angles to the direction of flow. The flowrate is then obtained from the difference... 

The pitot tube is used to measure the difference between the impact and static pressures in a fluid. It normally consists of two concentric tubes arranged parallel to the direction of flow the impact pressure is measured on the open end of the inner tube. The end of the outer concentric tube is sealed and a series of orifices on the curved surface give an accurate indication of the static pressure. The position of these orifices must be carefully chosen because there are two disturbances which may cause an incorrect reading of the static pressure. These are due to ... 

The pitot tube measures the velocity of only a filament of fluid, and hence it can be used for exploring the velocity distribution across the pipe section. If, however, it is desired to measure the total flow of fluid through the pipe, the velocity must be measured at various distances from the walls and the results integrated. The total flowrate can be calculated from a single reading only if the velocity distribution across the section is already known. 

If a pitot tube is inserted in a circular cross-section pipe in which a fluid is in streamline flow, calculate at what point in the cross-section it should be situated so us to give a direct reading representative of the mean... 

The pitot tube is a device for measuring v(r), the local velocity at a given position in the conduit, as illustrated in Fig. 10-1. The measured velocity is then used in Eq. (10-2) to determine the flow rate. It consists of a differential pressure measuring device (e.g., a manometer, transducer, or DP cell) that measures the pressure difference between two tubes. One tube is attached to a hollow probe that can be positioned at any radial location in the conduit, and the other is attached to the wall of the conduit in the same axial plane as the end of the probe. The local velocity of the streamline that impinges on the end of the probe is v(r). The fluid element that impacts the open end of the probe must come to rest at that point, because there is no flow through the probe or the DP cell this is known as the stagnation point. The Bernoulli equation can be applied to the fluid streamline that impacts the probe tip ... 

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... 

Most Pitot tubes consist of two concentric tubes parallel to the direction of fluid flow. The inner tube points into the flow and the outer tube is perforated with small holes which are perpendicular to the direction of flow. The inner tube transmits the combined pressure and velocity heads and the outer tube only the pressure head. 

For a closed conduit under pressure it is necessary to measure the static pressure also. Static pressure is simply the difference between the pressure of the fluid flowing outside the pitot tube and the pressure inside the pitot tube this is also called the differential head h. The... 

The pitot tube, illustrated in Figure 5, is another primary flow element used to produce a differential pressure for flow detection. In its simplest form, it consists of a tube with an opening at the end. The small hole in the end is positioned such that it faces the flowing fluid. The velocity of the fluid at the opening of the tube decreases to zero. This provides for the high pressure input to a differential pressure detector. A pressure tap provides the low pressure input. 

The pitot tube actually measures fluid velocity instead of fluid flow rate. However, volumetric flow rate can be obtained using Equation 4-4. 

A fluid which exhibits non-Newtonian behaviour is flowing in a pipe of diameter 70 mm and the pressure drop over a 2 m length of pipe is 4 x 104 N/m2. When the flowrate is doubled, the pressure drop increases by a factor of 1.5. A pitot tube is used to measure the velocity profile over the cross-section. Confirm that the information given below is consistent with the laminar flow of a power-law fluid. 

The principle of operation of a pitot tube is discussed in Section 6.3.1. It should be emphasised that the pitot tube measures the point velocity of a flowing fluid and not the average velocity so that in order to find the average velocity, a traverse across the duct is necessary. Treatment of typical results is illustrated in Problem 6.16. The point velocity is given by u = (2gh) where h is the difference of head expressed in terms of the flowing fluid. 

The flowrate of a fluid in a pipe is measured using a pitot tube, which gives a pressure differential equivalent to 40 mm of water when situated at the centre line of the pipe and 22.5 mm of water when midway between the axis and the wall. Show that these readings are consistent with streamline flow in the pipe. 

Both gas flow rates and liquid flow rates can be measured by a wide variety of devices such as bellow meters, Venturi nozzles, nutating disk meters, orifice meters, rotameters, weirs (for liquids), Pitot tubes, and magnetic meters among others. Some devices measure volumetric flow directly as with meters in which the space between rotating paddles incorporates small volumetric displacements of fluid. Other device measure the flows indirectly by measuring the pressure drop caused by an orifice between two different sites in the pipe, or the change in voltage of a heated wire. 

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