Lecture 24. Design of flow meters
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1 Lecture 24 Design of flow meters Contents Exercise 1 Exercise 2 Exercise 3 Key Words: Fluid flow, Macroscopic Balance, Frictional Losses, Turbulent Flow, Venturimeter, Orifice Meter, Pitot Tube Exercise 1 A pitot tube is installed at the centre of a pipe of diameter 0.3m. The pipe carries air at 70. Air is flowing at 745 mm Hg gauge pressure. Pitot tube measures a pressure difference of 50 mm water. Calculate flow rate of air in pipe. Assume pitot coefficient unity. SOLUTION Equation 9 of lecture 22 states that V V C P P Note that the pitot tube is installed at the centre of the pipe. At the centre one would measure maximum velocity of gas. and hence ΔP would also be maximum. Hence V. Inserting ΔP and V ρ in appropriate units. V 31.2m/s Flow rate 31.2x d 2.20 m /s, when maximum velocity is used. However, there is a radial velocity distribution. The velocity of the fluid will be maximum at the centre and minimum at the pipe surface. There would be a parabolic profile. Flow rate must be calculated by using average velocity. For the turbulent flow we use equation 11 of the lecture 22 V V log D V µ Flow rate 2.16 m /s.
2 Exercise 2 In a circular duct of diameter 0.5 m, pitot static tube is installed to measure pressure of air. The air at rest is drawn by a fan. The air temperature is 298 K and at 1 atmospheric pressure. The air discharges at 1.15 atmosphere absolute pressure. If the pitot tube measures a pressure difference 30 mm water, calculate the power required of the fan. 1 mm water 9.806N/m, µ 1.85x 10 K. C P 1, ef 0.4 and ef 2, length of the duct is 160 m. use the equation f Re. V C P P m/s V log D V µ V 17.8 m/s. Applying mechanical energy balance between plane 1 and 2. Figure Horizontal duct showing plane 1 and plane 2 ΔZ 0. V V. and V V in the pipe P P P FM0 V 2f L D ef ef M0. V Re. L e f D ef M. Substituting the values.
3 M kw. Exercise 3 3i) in an air duct of circular cross section (0.5m in diameter), a venturi meter of throat diameter 0.25m is installed. T he duct carries 1.28 m / sec of gas measured at 298K and 1 atmospheric pressure. Determine the maximum pressure drop that a manometer can handle. Take the discharge coefficient as Solution Equation 6 mky A2 ρp P / P P Y A V A V Y A Y (1) In this equation 1 P P and Y both are unknowns. One way is to assume same value of Y and then show that our assumption is correct. Let us assume Y1. P P..... (2) K in equation 1 is determined by C O. P P N m 43.3 mm H O,maximum pressure drop. Now we have to show that Y 1. We use equation 7. P N m and P n m 1 1 γ1.4 since gas is diatomic Calculation yields Y1. Hence o ur assumption of Y is OK. 3ii) you are proposing now an orifice instead of a venturi meter to measure 50 mm of water as the maximum pressure drop. Calculate the diameter of sharp edged orifice to measure the full reading at maximum flow. Take coefficient of discharge 0.62 for the orifice.
4 Solution We know that m K Y A 2 ρ P P. Now m ρ V A ρ Q where Q is volume flow rate A 3 K Y P P. A Q K Y P P. 4 Y P P P P P P 5 Where K C O. / / 6 By 4 and 6, and substituting the known values we get A.. Y 1 λ / 7. Y. 1 λ / 8 d. Y 116 d Assuming Y 1,We get d 0.3 m. Reader should calculate Y by eq. 5 and verify that Y1. 3iii) use the data of 3(i) and calculate the orifice diameter for the following conditions: a) When maximum pressure drop measured by pitot tube is 60 mm water. b) When maximum pressure drop is 70 mm water and c) When maximum pressure drop is 55 mm water. Plot pressure drop Vs orifi ce diameter and discuss the variation of pressure drop Vs diameter curve. Assignment A pitot tube is installed at the centre of a pipe of diameter 0.3m. The pipe carries air at flowing at 745 mm Hg gauge pressure. Pitot tube measures a pressure difference Calculate flow rate of air in pipe. Assume pitot coefficient unity. 70. Air is of 50 mm water.
5 2i) in an air duct of circular cross section (0.5m in diameter), a venturi meter of throat diameter 0.25m is installed. The duct carries 1.28 m / sec of gas measured at 298K and 1 atmospheric pressure. Determine the maximum pressure drop that a manometer can handle. Take the discharge coefficient as ii) you are proposing now an orifice instead of a venturi meter to measure 50 mm of w ater as the maximum pressure dro p. Calculate the diameter of sharp edged orifice to measure the full reading at maximum flow. Take coefficient of discharge 0.62 for the orifice. 2iii) use the data of 3(i) and calculate the orifice diameter for the following condition: d) When maximum pressure drop measured by pitot tub e is 60 mm water. e) When maximum pressure drop is 70 mm water and f) When maximum pressure drop is 55 mm water. Plot pressure drop Vs orifice diameter and discuss the variation of pressure drop Vs diameter curve
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