Pressure Measurement PDF - April 2021

Pressure measurement Dr. Mohamed Elmously April 2021  Agenda 1. Introduction 2. Pressure definition 3. Type of pressure 4. Method of pressure measurement Slide...

Pressure measurement Dr. Mohamed Elmously April 2021  Agenda 1. Introduction 2. Pressure definition 3. Type of pressure 4. Method of pressure measurement Slide 2 Introduction Inaccurate pressure measurement leads to disasters!! Introduction Definition of pressure Slide 5 Pressure is defined as the normal force per unit area exerted by a fluid on any surface 𝑃 = 𝐹/𝐴 where, P is the pressure, F is the normal force, A is Area. Type of Pressures Slide 6 Pressure can be divided into two types: 1. Static pressure. (the force is constant in time) 2. Dynamic pressure. (the force is varying in time) Static pressure measurement Slide 7 Static pressure Absolute Gauge Differential pressure pressure pressure Pabs = Patm + Pg Type of Pressures Slide 8 Static pressure Absolute Gauge Differential pressure pressure pressure Type of Pressures Slide 9 Static pressure Absolute Gauge Differential pressure pressure pressure Type of Pressures Static pressure Slide 10 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms Manometers balance and bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Diaphragm stack Cistern manometer Metallic capsule Two-liquid U-tube Metallic bellows manometer Inclined manometer Type of Pressures Static pressure Slide 11 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms Manometers balance and bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Diaphragm stack Cistern manometer Metallic capsule Two-liquid U-tube Metallic bellows manometer Inclined manometer The simple U-tube manometer Static pressure Slide 12 Absolute Gauge Differential The simplest form of manometer consists of a U-shaped pressure pressure pressure glass tube containing liquid. According to the hydrostatic pressure low: P1 P2 PA = PB Therefore, z P1 + ρf g (z+h) = P2 + ρf g z + ρm g h Rearranging, P1 – P2 = ρm g h - ρf g h If ρm >> ρf then, A B P1 – P2 = ρm g h If side B is opened to atmosphere, then P1(g) = ρm g h The U-tube manometer Static pressure Slide 13 Absolute Gauge Differential Advantages: pressure pressure pressure Low cost Simple design P1 P2 Disadvantages: z Low dynamic response rate. Requires time to damp out oscillations. Measurement accuracy dependent on precise leveling of U tube. The liquid in the U tube must NOT interact with measured fluid (gas or liquid). A B Mercury or water vapor contamination can occur, especially in low pressure. The U-tube pressure sensor Static pressure Slide 14 Absolute Gauge Differential pressure pressure pressure 𝑉𝑜𝑢𝑡 ∆𝑝 = 𝐶 𝑉𝑖𝑛 C is a calibration constant Type of Pressures Static pressure Slide 15 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms Manometers balance and bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Diaphragm stack Cistern manometer Metallic capsule Two-liquid U-tube Metallic bellows manometer Inclined manometer The industrial U-tube manometer. Static pressure Slide 16 Absolute Gauge Differential pressure pressure pressure The industrial development of the simple U-tube manometer is used for measuring a high differential pressure P1 >> P2 The industrial U-tube manometer. Static pressure Slide 17 Absolute Gauge Differential According to the hydrostatic pressure low: pressure pressure pressure 𝑝1 = 𝑝2 + 𝜌𝑔𝐻 = 𝑝2 + 𝜌𝑔 ℎ + 𝑑 The volume of liquid which has left A must be equal to that which has passed into B 𝐴1 ⋅ ℎ = 𝐴2 ⋅ 𝑑 Therefore; 𝐴2 ℎ= ⋅𝑑 𝐴1 Rearranging 𝐴2 𝑝1 − 𝑝2 = 𝜌𝑔𝑑 +1 𝐴1 Type of Pressures Static pressure Slide 18 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms Manometers balance and bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Diaphragm stack Cistern manometer Metallic capsule Two-liquid U-tube Metallic bellows manometer Inclined manometer The cistern manometer Static pressure Slide 19 Absolute Gauge Differential pressure pressure pressure The same working principle of the industrial U-tube manometer. The difference is that the narrow tube is directly inserted into the wide chamber If a pressure difference (P1 – P2) is applied to the manometer then, 𝑝1 − 𝑝2 = 𝜌𝑔 ℎ + 𝑑 Also 𝐴1 ⋅ 𝑑 = 𝐴2 ⋅ ℎ Therefore 𝐴2 𝑑= ⋅ℎ 𝐴1 The cistern manometer Static pressure Slide 20 Absolute Gauge Differential pressure pressure pressure The pressure difference is given by 𝐴2 𝑝1 − 𝑝2 = 𝜌𝑔ℎ 1+ 𝐴1 If the value of A2/A1 is so small that it may be neglected then, 𝑝1 − 𝑝2 = 𝜌𝑔ℎ S = h / d(P) = 1/(rho* g) In practice the cistern diameter (wide chamber) is made so large compared with the narrow tube diameter that the drop in level (d) from the zero level in the cistern is negligible. Applications Slide 21 U-Tube Manometer Application: Used for measuring small to moderate pressures and differential pressures, typically in low-pressure gas flows and HVAC (Heating, Ventilation, and Air Conditioning) systems. Common Uses: Laboratories, calibration of other pressure measurement devices, monitoring pressure in gas lines, or in educational setups for learning about pressure measurement principles. Advantages: High accuracy for low-pressure measurements, especially for differential pressure. Applications Slide 22 Cistern (Reservoir) Manometer Application: Suitable for measuring pressures with a large surface area for liquid, often used when higher sensitivity and greater fluid volume are needed. Common Uses: Often in medical applications (e.g., measuring blood pressure in specific clinical devices), hydraulic systems, and in research settings where fine pressure changes need to be observed. Advantages: The reservoir allows for a larger range of measurement without having to adjust fluid levels constantly. Applications Slide 23 Industrial Manometer Application: Widely used in various industrial settings to monitor and control gas or liquid pressure in pipes, tanks, and other equipment where consistent pressure measurement is crucial. Common Uses: Oil and gas industry, chemical plants, water treatment facilities, power generation plants, and HVAC systems for larger buildings. Advantages: Durable and designed to handle high pressures and harsh environments; often includes features for remote reading, alarms, or integration with control systems. Applications Slide 24 Inclined Tube Manometer Applications 1.Low-Pressure Measurement 1. Common Uses: Often used to measure small positive or negative pressures in ventilation systems, laboratory experiments, and air handling systems. 2. Why: The inclined scale allows for high-resolution reading, essential for detecting subtle changes in low-pressure environments. 2.Differential Pressure Measurement 1. Common Uses: Widely used in HVAC (Heating, Ventilation, and Air Conditioning) systems to monitor air filter resistance, duct pressures, and pressure drops across various system components. 2. Why: High sensitivity helps detect differential pressure across filters or components, allowing for timely maintenance. 3.Gas Flow Monitoring 1. Common Uses: Used in applications that measure airflow or gas flow in low- pressure environments, such as in laboratories or gas supply systems. 2. Why: Its sensitivity to small pressure differences makes it effective for accurately monitoring the flow rate of gases in controlled conditions. Type of Pressures Static pressure Slide 25 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms and Manometers balance bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Diaphragm stack Cistern manometer Metallic capsule Inclined manometer Metallic bellows Two-liquid U-tube manometer The inclined tube manometer Static pressure Slide Slide26 26 Absolute Gauge Differential pressure pressure pressure The advantage of this device is that it gives an increased length of the scale compared with the simple U-tube for the same differential Pressure, so small differential pressures can be measured with better accuracy The inclined tube manometer Static pressure Slide Slide27 27 Absolute Gauge Differential pressure pressure pressure The pressure difference is given by 𝑝1 − 𝑝2 = 𝜌𝑔 ℎ1 + ℎ where ℎ = 𝑑 sin 𝛼 and 𝐴2 ℎ1 = ⋅𝑑 𝐴1 Substituting and rearranging 𝑝1 − 𝑝2 = 𝜌𝑔𝑑 𝐴2 Τ𝐴1 + sin 𝛼 The inclined tube manometer Static pressure Slide Slide28 28 Absolute Gauge Differential pressure pressure pressure As in the previous case, if A1 is large compared with A2; then the ratio A2/A1 may be neglected 𝑝1 − 𝑝2 = 𝜌𝑔𝑑 ⋅ sin 𝛼 = 𝜌𝑔ℎ The sensitivity of the inclined tube manometer is given by 𝑆𝑖𝑛𝑐. 𝑚𝑎𝑛. = Δ𝑜𝑢𝑡𝑝𝑢𝑡 ΤΔ𝑖𝑛𝑝𝑢𝑡 = 𝑑 𝑑 Τ𝑑 𝑝1 − 𝑝2 = 1Τ 𝜌𝑔 ⋅ sin 𝛼 Type of Pressures Static pressure Slide 29 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms and Manometers balance bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Diaphragm stack Cistern manometer Metallic capsule Inclined manometer Metallic bellows Two-liquid U-tube manometer The two liquid U-tube manometer Static pressure Slide Slide30 30 Absolute Gauge Differential pressure pressure pressure 1- The two liquid U-tube manometer can be used when sealing fluid is needed to separate the manometer liquid from the fluid being measured. 2- Exactly the same amount of seal fluid should be added in both columns of the manometer so that they cancel each other. The two liquid U-tube manometer Static pressure Slide Slide31 31 Absolute Gauge Differential pressure pressure pressure 𝑝1 − 𝑝2 = 𝑔 ℎ 𝜌2 − 𝜌1 Applications Slide 32 Applications of a Two-Liquid U-Tube Manometer 1.Measurement of Small Pressure Differences in Low-Pressure Systems 1. Common Uses: Used in laboratory experiments, research settings, and precision air measurement systems. 2. Why: The use of two liquids with different densities enhances sensitivity, making it possible to measure very small pressure differences accurately. 2.Gas and Airflow Measurement in HVAC Systems 1. Common Uses: Monitoring airflow or pressure differences in ventilation ducts, air filters, and clean rooms. 2. Why: The two-liquid setup provides greater precision, useful for maintaining optimal airflow and pressure in ventilation and filtration systems. 3.Differential Pressure Measurement for Low-Density Gases 1. Common Uses: Measuring differential pressures in systems involving gases like natural gas, biogas, or other low-density gases, as seen in fuel cells or controlled gas supply systems. 2. Why: The two-liquid system compensates for low-pressure fluctuations, offering clearer readings in gases with low density. 4.Industrial Processes Requiring High Sensitivity 1. Common Uses: Chemical and pharmaceutical industries, where precise pressure control is critical for processes involving sensitive reactions or materials. 2. Why: The accuracy and sensitivity afforded by the two-liquid setup are valuable in applications where even minor pressure changes could impact q Problem Slide 33 Type of Pressures Static pressure Slide 34 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms and Manometers balance bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Diaphragm stack Cistern manometer Metallic capsule Inclined manometer Metallic bellows Two-liquid U-tube manometer The Ring balance manometer Static pressure Slide Slide35 35 Absolute Gauge Differential pressure pressure pressure The Ring balance manometer Static pressure Slide Slide36 36 Absolute Gauge Differential pressure pressure pressure P1 = P2 P1 > P2  The Ring balance manometer Static pressure Slide Slide37 37 Absolute Gauge Differential pressure pressure pressure When a pressure difference is applied across the partition a rotating moment is setup. The ring starts to rotate in a direction a way from the higher pressure until the opposing moment, created by the mass at the foot of the ring balances the rotating moment 𝑅𝑜𝑡𝑎𝑡𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡 = 𝑝1 − 𝑝2 ⋅ 𝐴 ⋅ 𝑟1 𝑅𝑒𝑠𝑡𝑜𝑟𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡 = 𝑚𝑔 ⋅ 𝑟2 ⋅ sin 𝜃 At balance 𝑝1 − 𝑝2 ⋅ 𝐴 ⋅ 𝑟1 = 𝑚𝑔 ⋅ 𝑟2 ⋅ sin 𝜃 Constant Rearranging 𝑚𝑔 ⋅ 𝑟2 𝑝1 − 𝑝2 = ⋅ sin 𝜃 𝐴 ⋅ 𝑟1 Type of Pressures Static pressure Slide 38 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms and Manometers balance bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Diaphragm stack Cistern manometer Metallic capsule Inclined manometer Metallic bellows Two-liquid U-tube manometer The single diaphragm Static pressure Slide Slide39 39 Absolute Gauge Differential pressure pressure pressure It is a thin flat plate of circular shape. The plate is fixed round its edge. When a differential pressure is applied across the plate, it deflects as shown in the figure. 𝛿 ∝ ∆𝑃 Type of Pressures Static pressure Slide 40 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms and Manometers balance bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Slack diaphragm Cistern manometer Diaphragm stack Inclined manometer Metallic capsule Two-liquid U-tube Metallic bellows manometer The slack diaphragm Static pressure Slide Slide41 41 Absolute Gauge Differential pressure pressure pressure For the measurement of low pressures, an extremely flexible diaphragm is used. The diaphragm is made in the form of a ring fabric (leather, plastic, rubberized fabric, nylon and silk) with a disc of metal or other rigid material at the center. Type of Pressures Static pressure Slide 42 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms and Manometers balance bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Slack diaphragm Cistern manometer Metallic capsule Inclined manometer Diaphragm stack Two-liquid U-tube Metallic bellows manometer  Static pressure The metallic capsule Slide 43 Absolute Gauge Differential pressure pressure pressure The common shapes of the diaphragms used in a capsule gauge are: a. Dished b. Flat c. Corrugated The deflection of the capsule is found to have a linear relationship with the pressure Type of Pressures Static pressure Slide 44 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms and Manometers balance bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Slack diaphragm Cistern manometer Metallic capsule Inclined manometer Diaphragm stack Two-liquid U-tube Metallic bellows manometer  Static pressure Diaphragm stack Slide 45 Absolute Gauge Differential pressure pressure pressure A series of corrugated metal diaphragms which are connected together. Higher sensitivity compared to metallic capsules The number of diaphragms used may vary from two up to twenty capsules. The deflection of the capsule is found to have a linear relationship with the pressure Type of Pressures Static pressure Slide 46 Absolute Gauge Differential Differential pressure pressure pressure pressure measurement The ring Diaphragms and Manometers balance bellows Simple U-tube Single diaphragm manometer Industrial U-Tube Slack diaphragm Cistern manometer Metallic capsule Inclined manometer Diaphragm stack Two-liquid U-tube Metallic bellows manometer  Static pressure The metallic bellow Slide 47 Absolute Gauge Differential pressure pressure pressure Similar to the diaphragm stack but different in the method of construction. Thin wall tube formed by a hydraulic press into a corrugated shape. Can be produced in large diameters (up to 30cm )  Static pressure The industrial bellow gauge Slide 48 Absolute Gauge Differential pressure pressure pressure  Slide 49 Vacuum pressure measurement Dr. Mohamed Elmously High Vacuum Measurement The region of pressure below 1 mm mercury may be divided into 3 sections: Medium high vacuum: 1 to 10-3 mm mercury High vacuum : 10-3 to 10-7mm mercury Ultra high vacuum : 10-7 mm mercury and lower Medium high vacuum high vacuum Ultra high vacuum 1 mm HG 10-3 mm HG 10-7 mm HG The McLeod Gauge P1 P1 V2 V1 Position 1 Position 2  The McLeod Gauge This instrument is used for the measurement of very low pressures in the range from 1 mm to 10-4 mm mercury. It is based on Boyle's low which states that: If the pressure (P1) and volume (V1) of any perfect gas is changed isentropically (without heat loss) to a pressure (P2) and volume (V2) then The McLeod Gauge 𝑝1 ⋅ 𝑉1 = 𝑝2 ⋅ 𝑉2 𝑉2 = 𝑎ℎ 𝑝2 = 𝑝1 + 𝜌𝑔ℎ 𝑝1 ⋅ 𝑉1 = 𝑎 ℎ (𝑝1 + 𝜌𝑔ℎ ) 𝑝1 ⋅ 𝑉1 = 𝑎 ℎ 𝑝1 + a𝜌𝑔ℎ2 𝑝1 (𝑉1 − 𝑎ℎ) = a𝜌𝑔ℎ2 a𝜌𝑔ℎ2 𝑝1 = (𝑉1 − 𝑎ℎ) a𝜌𝑔ℎ2 If ah