Wollo University Kombolcha Institute of Technology School of Mechanical & Chemical Engineering Chapter 4: Flow Measurement Prepared by: Wubishet Degife. E-mail: [email protected] Outline lecture notes • Pressure measurement • Velocity measurement • Discharge measurement • Viscosity measurement • Density measurement 2 Introduction • Why measurement is important??? In this chapter an attempt has been made to present the principles and phenomenon of fluid mechanics which are adopted for the measurements of fluid pressure, flow velocity, flow rate or discharge rate, viscosity of fluids and density of fluids using different measuring instruments/devices and their working principles 3 Pressure measurement • The pressure of a fluid is measured by the following devices 1. Manometers and 2. Mechanical gauges Manometers: are devices which are used for measuring the pressure at a point in a fluid by balancing the column of fluid by the same or another column of the fluid. • They are classified as: A. Simple manometers and B. Differential manometers Mechanical gauges: are devices used for measuring the pressure by balancing the fluid column by the spring or dead weight. • The commonly used mechanical gauges are: The simple manometer: consists of a glass tube having one of its end connected to a point where pressure is to be measured and the other end remains open to the atmosphere. • The common types of the simple manometers are: 4 Cont… Piezometer: • It is the simplest form of manometer used for measuring gauge pressures. • One end of this manometer is connected to the point where pressure is to be measured and the other end is open to the atmosphere as shown in fig 4.1. • The rise of liquid gives the pressure head at that point. Fig. 4.1: Piezometer ✓ For example, if u want to measure the pressure at point A given the fluid is water, the height of the liquid water rises h meter in piezometer tube, then the pressure at A would be: 5 Cont… Example 1. The piezometer shown in fig. fluid 1 is oil (SG = 0.87) and fluid 2 is glycerin at 20°C. If Pa = 98 kPa, determine the absolute pressure at point A, given specific weight of water is 9790N/m3 and specific weight of glycerin at 20oC is 12360N/m3. 6 Cont… Solution for example 1 7 Cont… U-tube manometer: it consists of glass tube bent in U-shape, one end of which is connected to a point at which pressure is to be measured and the other end remains open to the atmosphere as shown in fig. 4.2. • The tube generally contains mercury or any other liquid whose specific gravity is greater than the specific gravity of the liquid whose pressure is to be measured. (a) For gauge pressure (a) For vacuum pressure Fig. 4.2: U-tube manometer (a) For gauge pressure: Let B be the point at which pressure is to be measure and let whose value is P. Then, at the datum line A-A, the left and right side of the U-tube has the same 8 pressure because it is at the same depth. Cont… Hence these two pressures (right and left column of the U-tube at point A-A) are equal, then equating them would give: (b) For vacuum pressure: for measuring vacuum pressure, the level of the heavy liquid in the manometer will be shown in fig 4.2b, then 9 Note that: Most pressure measurement devices are calibrated to read zero atmospheric pressure. Cont… Single column manometer: • A single column manometer is a modified form of a U-tube manometer in which a reservior a large cross-sectional area (about 100 times) as compared to the area of the tube is connected to one of the limbs (say left limb) of the manometer as shown in fig 4.3. • Due to large cross-sectional area of the reservior, for any variation in pressure, the change in the liquid level in the reservior will be very small which may be neglected and hence the pressure is given by the height of liquid in the other limb. The other limb may be vertical or inclined. • Thus, there are two types of single column manometer as: ✓ Vertical single column manometer, and ✓ Inclined single column manometer Fig. 4.3: vertical single column manometer 10 Cont… 11 Cont… 12 Cont… Inclined single column manometer: Fig. 4.4: inclined single column manometer 13 Cont… Differential manometers: U-tube differential manometer: fig 4.5 shows the differential manometer of U-tube type (a) Two pipes A and B at different levels (b) Two pipes A and B at same levels Fig 4.5: U-tube differential manometers 14 Cont… …………………………… (iv) 15 Cont… 16 Cont… 17 Cont… Example 2: For the inverted manometer shown in fig., all fluids are at 20°C. If PB - PA = 97 kPa, what must the height H be in cm? given specific weight of mercury is 133100N/m3 Solution 18 Velocity measurement • Velocity constitutes an important parameter in kinematics and dynamics of fluid flow. Thus, its measurement is quite important. • Velocity measuring devices may be classified as: ✓ Three-cup anemometer; ✓ Savonius rotor; ✓ Tturbine mounted in a duct; ✓ Free-propeller meter; ✓ Hot-wire anemometer; (f) hot-film anemometer; ✓ Pitot-static tube; ✓ Laser - Doppler Anemometer, each is shown in figure 4.7 below • Thus, basically we can classify velocity measuring devices as: ✓ Instruments like the pitot - tube and hot wire anemometers which measure the local velocity at a point in the channel or duct through which the fluid is flowing. ✓ Instruments like the cup and vane anemometers which measures the average velocity of fluid flow. 19 Cont… Fig. 4.7: Eight common velocity meters: (a) three-cup anemometer; (b) Savonius rotor; (c) turbine mounted in a duct; (d) free-propeller meter; (e) hot-wire anemometer; (f) hot-film anemometer; (g) pitot- static tube; (h) laser doppler anemometer. 20 Cont… 1. The Pitot static tube: • Pitot probes (also called Pitot tubes) and Pitot-static probes, named after the French engineer Henri de Pitot (1695–1771), are widely used for flow velocity measurement. • Is a slender tube aligned with the flow (Figs. 4.7g) can measure local velocity by means of a pressure difference. • It has sidewall holes to measure the static pressure Ps in the moving stream and a hole in the front to measure the stagnation pressure Po, where the stream is decelerated to zero velocity. • Instead of measuring Po or Ps separately, it is customary to measure their difference with a transducer, as in Fig. 4.8. • A Pitot probe is just a tube with a pressure tap at the stagnation point that measures stagnation pressure, while a Pitot-static probe has both a stagnation pressure tap and several circumferential static pressure taps and it measures both stagnation and static pressures (Figs. 4.8a, b and 4.8c). 21 Cont… 22 Cont… • It consists of a slender double-tube aligned with the flow and connected to a differential pressure meter. The inner tube is fully open to flow at the nose, and thus it measures the stagnation pressure at that location (point 1). The outer tube is sealed at the nose, but it has holes on the side of the outer wall (point 2) and thus it measures the static pressure. • In its elementary form, a pitot tube consists of an L-shape tube; a tube bent through 90o and with ends unsealed. ✓ One limb called the body is inserted into the flow stream and aligned with the direction of flow whilst the other limb called the stem is vertical and open to the atmosphere as shown in fig. 4.9. Fig. 4.9: Pitot static probes • Applying the Bernoulli's equation to point 1 (a point upstream from the submerged end of the 23 tube) and point 2 ( a point at the tip or nose of the tube itself) Cont… • Now at the stagnation point (i.e. point 2 or at the nose or tip of the tube) the flowing fluid is brought to rest i.e V2 = 0. Further points 1 and 2 lie at the same elevation datum i.e. y1 = y2, Equation (a) further simplified as: Re-arranging and simplifying we get Where V1 is the free stream fluid velocity. 24 This is the Pitot formula, named after the French engineer who designed the device in 1732. Cont… From fig. 4.9b; Where h is the rise of liquid level in the stem above the free surface Thus up on substitution the value of Ps and Po in Equation (b), we obtain: • Evidently, equation (b) and (c) are equally valid for determining the flow velocity at a point in the pipe line 2. Hot wire anemometer: • A very fine wire (d = 0.01 mm or less) heated between two small probes, as in Fig. 4.7e, is ideally suited to measure rapidly fluctuating flows such as the turbulent boundary layer. • The idea dates back to work by L. V. King in 1914 on heat loss from long thin cylinders. • If electric power is supplied to heat the cylinder, the loss varies with flow velocity across the cylinder according to King’s law 25 Cont… where q – is the power output I – is the current V – is the flow velocity, and R – is the resistance n ≈ 1/3 at very low Reynolds numbers and n ≈ 1/2 at high Reynolds numbers. • The hot wire normally operates in the high-Reynolds-number range but should be calibrated in each situation to find the best-fit a, b, and n. • The wire can be operated either at constant current I, so that resistance R is a measure of V, or at constant resistance R (constant temperature), with I a measure of velocity.