Manometer
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It is based on fluid mechanics. The all types of basic manometer are covered in this presentation. It is very useful for students.
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Manometer
- 1. 1
- 2. Prepared By: • 1. Patel Mit R. (140760109044) 2
- 3. Manometer Manometer is a device used for measuring the pressure at a point in a fluid by balancing the column of fluid with the same column or another of the fluid. 3
- 4. (1) Simple manometer: Piezometer U-tube manometer single column manometer Vertical single column manometer Inclined single column manometer (2) Differential manometer : U-tube differential manometer Inverted U-tube differential manometer 4 Classification of Manometers :
- 5. A piezometer is the simplest form of the manometer. It measures gauge pressure only. The pressure at any point in the liquid is indicated by the height of the liquid in the tube above that point, which can read on the calibrated scale on glass tube. The pressure at point A is given by; 𝑝 = 𝜌𝑔ℎ = 𝑤ℎ ∴ ℎ = 𝑝 𝜌𝑔 𝑝𝑖𝑒𝑧𝑜𝑚𝑒𝑡𝑟𝑖𝑐 ℎ𝑒𝑎𝑑 5 1. Piezometer :
- 6. It can be measure large pressure or vacuum pressure and gas pressure. ∴ 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑡 𝑋𝑋 𝑖𝑛 𝑙𝑒𝑓𝑡 𝑐𝑜𝑙𝑢𝑚𝑛 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑡 𝑋𝑋 𝑖𝑛 𝑙𝑒𝑓𝑡 𝑐𝑜𝑙𝑢𝑚𝑛 ∴ 𝑝 + 𝜌1 𝑔ℎ1 = 𝜌2 𝑔ℎ2 ∴ 𝑝 = 𝜌2 𝑔ℎ2 − 𝜌1 𝑔ℎ1 𝑁𝑜𝑤, 𝑝 = 𝜌𝑔ℎ, ℎ ℎ𝑒𝑎𝑑 𝑖𝑛 𝑡𝑒𝑟𝑚𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑐𝑜𝑙𝑢𝑚𝑛, 𝜌𝑔ℎ = 𝜌2 𝑔ℎ2 − 𝜌1 𝑔ℎ1 ∴ ℎ = 𝜌2 𝜌 ℎ2 − 𝜌1 𝜌 ℎ1 ∴ ℎ = 𝑠2ℎ2 − 𝑠1ℎ1 6 2. U-tube Manometer : x x
- 7. 7 3. Single column Manometer : (A) Vertical single column manometer One of the limbs in double column manometer is converted into a reservoir having large cross sectional area (about 100 times) with respect to the other limb. ∴ 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 ℎ𝑒𝑎𝑣𝑦 𝑙𝑖𝑞𝑢𝑖𝑑 𝑓𝑎𝑙𝑙 𝑖𝑛 𝑟𝑒𝑠𝑒𝑟𝑣𝑜𝑖𝑟 = 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 ℎ𝑒𝑎𝑣𝑦 𝑙𝑖𝑞𝑢𝑖𝑑 𝑟𝑖𝑠𝑒 𝑖𝑛 𝑟𝑖𝑔ℎ𝑡 𝑐𝑜𝑙𝑢𝑚𝑛 ∴ 𝐴 × ∆ℎ = 𝑎 × ℎ2 → ∆ℎ = 𝑎 × ℎ2 𝐴 Pressure in left col. = pressure in right col. ∴ 𝑝 = 𝑎ℎ2 𝐴 𝜌2 𝑔 − 𝜌1 𝑔 + 𝜌2 𝑔ℎ2 − 𝜌1 𝑔ℎ1…………(i) ∴ 𝑝 = 𝜌2 𝑔ℎ2 − 𝜌1 𝑔ℎ1
- 8. 8 (B) Vertical single column manometer It is modified of vertical column manometer. This manometer is useful for the measurement of small pressure. Here, ℎ𝑒𝑖𝑔ℎ𝑡 ℎ2 = 𝑙 𝑠𝑖𝑛𝜃 𝑎𝑛𝑑 𝑝𝑢𝑡𝑡𝑖𝑛𝑔 𝑖𝑛 𝑎𝑏𝑜𝑣𝑒 𝑒𝑞. 𝑖 ; ∴ 𝑝 = 𝑎𝑙 𝑠𝑖𝑛𝜃 𝐴 𝜌2 𝑔 − 𝜌1 𝑔 + 𝜌2 𝑔𝑙𝑠𝑖𝑛𝜃 − 𝜌1 𝑔ℎ1 𝑠𝑖𝑛𝑐𝑒, 𝑎 ≪ 𝐴, 𝑛𝑒𝑔𝑙𝑒𝑐𝑡𝑖𝑛𝑔 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚; ∴ 𝑝 = 𝜌2 𝑔𝑙𝑠𝑖𝑛𝜃 − 𝜌1 𝑔ℎ1 ∴ ℎ = 𝑠2 𝑙𝑠𝑖𝑛𝜃 − 𝑠1ℎ1
- 9. 9 4. U-tube differential manometer It is used to measure pressure difference at two points in a pipe or between two pipes at different levels. Case 1 - U-tube upright differential manometer connected at two points in a pipe at same level
- 10. 10 Case 2 - U-tube upright differential manometer connected between two pipes at different levels and carrying different fluids
- 11. It is used for low pressure difference. 11 5. Inverted U-tube differential manometer
- 12. 12 Thank You