Manometers All Info ChE

Table of Contents

Manometers are the simplest devices that are used for measuring pressure differences.

Pressure measurement is essential in monitoring and controlling fluid flows within pipelines, vessels, and equipment. It ensures that processes such as chemical reactions, material processing, and mixing occur under the desired conditions.

Types of Manometers

U-Tube Manometer
Inclined Manometer
Manometer with Multiple Fluids

U-Tube Manometer

A U-tube manometer is the simplest form of manometer. It is a device used to measure pressure differences.

Figure 1 shows U tube Manometer

Construction

It consists of a small diameter U-shaped tube of glass.

The tube is clamped on a wooden board. Between the two arms or legs of the manometer, a scale is fixed on the same board.

The U-tube is partially filled with a manometric fluid which is heavier than the process fluid.

The two limbs of the manometer are connected by tubing to the taps between which the pressure drop is to be measured.

Air vent valves are provided at the end of each arm for the removal of trapped air in the arm.

The manometric fluid is immiscible with the process fluid. The common manometric fluid is mercury.

A U-tube manometer is filled with a given manometric fluid up to a certain height. The remaining portion of the U-tube is filled with the process fluid/flowing fluid including the tubing.

One limb of the manometer is connected to the upstream tap in a pipeline and the other limb is connected to the downstream tap in the pipeline between which the pressure difference $p_a - p_b$ is required to be measured.

At steady state, for a given flow rate, the difference in the level of the manometric fluid in the two arms is measured and it gives the value of pressure difference in terms of manometric fluid across the taps (stations).

Working

Assume that the shaded portion of the U-tube is filled with liquid ‘A’ having density $\rho_A$ and that arms of the U-tube above the liquid are filled with fluid ‘B’ having a density $\rho_b$ .

Fluid ‘B’ is immiscible with fluid ‘A’, and the density of fluid ‘B’ is less than that of fluid ‘A’. Fluid ‘B’ is often a gas such as air or nitrogen.

Pressure $p_a$ is exerted in one arm of the U tube and a pressure $p_b$ in the other arm of the U-tube manometer.

As a result of the difference in pressure $p_a - p_b$ , the meniscus in one branch of the U tube is higher than in the other, and the vertical distance between the two meniscuses is $R_m$ , may be used to measure the difference in pressure.

Let’s derive a relationship between $p_a - p_b$ and $R_m$ ,

Start at the point 1, where the pressure is $p_a$

The pressure at point 2 is $p_a + g (Z_m + R_m) \rho_B$ .

By the principles of hydrostatics, the pressure at point 3 is the same as the pressure at point 2.

The pressure at point 4 is less than that at point 3 by the amount $g\;R_m\;\rho_A$ .

The pressure at point 5, which is $p_b$ . Which is still less by the amount $g\;Z_m\;\rho_B$ .

These statements can be summarized by the equation

(1) $\begin{equation*} p_a + g [(Z_m + R_m) {\rho}_b - R_m {\rho}_A - Z_m {\rho}_B] = p_b \end{equation*}$

Simplification of equation (1) gives

(2) $\begin{equation*} p_a - p_b = g R_m ({\rho}_A - {\rho}_B) \end{equation*}$

Here, the relationship is independent of the distance $Z_m$ and the dimension of the tube provided that pressure $p_a$ and $p_b$ are measured in the same horizontal plane.

If fluid B is a gas, and density of gas $\rho_B$ is usually negligible compared to the density of manometric fluid $\rho_A$ and may be omitted from equation (2), and the equation (2) further simplifies to

(3) $\begin{equation*} p_a - p_b = g R_m {\rho}_A \end{equation*}$

Equation (2) is valid only for low-density fluid compared to manometric fluid.

Applications

Pressure Measurement: U-tube manometers are commonly used to measure pressure differences between two points in a system. They are often used in industries like HVAC (Heating, Ventilation, and Air Conditioning) to measure pressure drops across filters, coils, and other components.

Flow Rate Measurement: By placing a U-tube manometer in a pipe or duct, the pressure difference across the manometer can be related to the flow rate of the fluid passing through the pipe. This is useful for measuring fluid flow in systems like water supply networks.

Hydrostatic Pressure Measurement: U-tube manometers can measure hydrostatic pressure in tanks, vessels, and other containers filled with liquids. This is particularly useful in monitoring liquid levels and controlling fluid levels in tanks.

Calibration of Other Instruments: U-tube manometers are sometimes used as a reference for calibrating other pressure-measuring instruments, such as pressure gauges and transducers.

Inclined Manometer

Inclined manometers are used for measuring small pressure differences.

Construction and Working

In this type of manometer, one leg is inclined. So, it is called an inclined manometer.

An inclined Manometer is used to measure small differences in pressure.

The angle of the inclination $(\alpha)$ is around 5 to 10^o with the horizontal. So, with a small magnitude of $R_m$ , the meniscus in the inclined tube must move a considerable distance along the tube.

This distance is $R_1$ can be given by the following equation.

(4) $\begin{equation*}R_1 = \frac{R_m}{sin\alpha}\end{equation*}$

By making $\alpha$ small, the magnitude of $R_m$ is multiplied into a long distance $R_1$ , and a large reading becomes equivalent to a small pressure difference, so

(5) $\begin{equation*}p_a - p_b = g R_1 (\rho_A - \rho_B) sin \alpha\end{equation*}$

In this type of pressure gauge, it is necessary to provide an enlargement in the vertical leg so that the movement of the meniscus in the enlargement is negligible within the operating range of the instrument.

Applications

Low-Pressure Measurements: Inclined manometers are often used for measuring low pressures and vacuum pressures. They can measure small pressure differences more accurately than some other pressure-measuring devices.

Calibration and Testing: Inclined manometers are commonly used in laboratory settings for calibrating other pressure-measuring instruments. Their accuracy and sensitivity make them suitable for this purpose.

Medical Equipment: Inclined manometers are used in medical devices such as respiratory equipment to measure pressure differences for controlling airflow and oxygen delivery.

Fluid Dynamics Research: Inclined manometers can be used in fluid dynamics experiments to measure pressure differences across various parts of fluid flow systems.

Manometer with Multiple Fluids

Here, we are going to discuss Two Liquid Manometer.

It is also called a Differential Manometer or Multiplying Gauge.

A differential manometer is used for the measurement of very small pressure differences.

it is used for the measurement of pressure differences with a very high precision.

It may often be used for gases.

Construction

It consists of a U-tube made of glass. The ends of the tube are connected to two enlarged transparent chambers/reservoirs.

The reservoirs at the ends of each arm are of a larger cross-section than that of the tube.

The manometer contains two manometric liquids of different densities and these are immiscible with each other and with the fluid for which the pressure difference is to be measured.

The densities of the manometric fluids are nearly equal to have a high sensitivity of the manometer.

Liquids that give sharp interfaces are commonly used as manometric fluid, for example, paraffin oil, industrial alcohol, etc.

Working

Let the flowing fluid be ‘A’ of density $\rho_A$ and manometric fluids be ‘B’ and ‘C’ of densities $\rho_B$ and $\rho_C$ .

For the densities of the liquid $\rho_A < \rho_B < \rho_C$

The pressure difference between two points (1 and 7) can be obtained by writing down pressures at points 1, 2, 3, 4, 5, 6, and 7 and is given by

(6) $\begin{equation*}P_1 - P_2 = h^\prime (\rho_B - \rho_A) g + h (\rho_C - \rho_B) g\end{equation*}$

If the level of liquid in two reservoirs is approximately the same, then $h^\prime \approx 0$ and Equation (6) reduces to

(7) $\begin{equation*}P_1 - P_2 = h (\rho_C - \rho_B) g\end{equation*}$

Where h is the difference in level in the two arms/limbs of the manometer.

When the densities $\rho_B$ and $\rho_C$ are nearly equal [ $(\rho_C - \rho_B)$ small], then very large values of h can be obtained for small pressure differences.

Alternately, the pressure at the level a – a in Figure 3 must be the same in each of the limbs, and therefore,

$\begin{gather*}P_1 + \left x \rho_A + h^\prime \rho_A + y \rho_B + h \rho_B \right g \\= P_2 + \left x \rho_A + h^\prime \rho_B + y \rho_B + h \rho_C \right g\end{gather*}$

Simplify above equation

$\begin{gather*}(P_1 - P_2) = \\h^\prime (\rho_A - \rho_B) g + h (\rho_C - \rho_B) g\end{gather*}$

Applications

HVAC Systems: Differential manometers are frequently used in heating, ventilation, and air conditioning (HVAC) systems to measure pressure differences across filters, coils, dampers, and other components. This helps in monitoring and optimizing the airflow and efficiency of the system.

Fluid Flow Measurement: In fluid dynamics and engineering, differential manometers can be used to measure pressure differences across different sections of a pipeline or duct. This information is crucial for calculating flow rates using Bernoulli’s equation or other flow equations.

Aerodynamics Testing: In aerodynamics research and wind tunnel testing, differential manometers are used to measure the pressure differences around models or prototypes of aircraft, vehicles, and other objects. This information helps in understanding aerodynamic forces and designing efficient shapes.

Hydraulic Systems: Differential manometers are employed in hydraulic systems to monitor pressure differences in various parts of the system. This is essential for ensuring proper functioning and safety of hydraulic equipment used in industrial and mobile applications.

Medical Equipment: In medical devices like ventilators, differential manometers are used to monitor and control airway pressure. They help medical professionals ensure that the air pressure delivered to patients is appropriate and safe.

Boiler Systems: In steam boiler systems, differential manometers can be used to measure the pressure difference across critical points, helping to maintain safe and efficient operations.

Water Supply and Sewage Systems: Differential manometers can be used to monitor pressure differences in water supply networks, ensuring a steady flow of water to consumers. In sewage systems, they help maintain proper pressure levels for efficient sewage transportation.

Laboratory Experiments: Differential manometers are commonly used in educational and research laboratories for fluid mechanics experiments, allowing students and researchers to visualize and understand pressure differences in various scenarios.

Industrial Processes: In industrial processes that involve fluids, such as chemical processing or food production, differential manometers can be used to monitor pressure differences and optimize process efficiency.

Quality Control and Testing: In manufacturing, differential manometers can be used for quality control purposes. They help ensure that products meet pressure specifications and operate within safe ranges.

Environmental Monitoring: Differential manometers can also play a role in environmental monitoring, such as measuring pressure differences in air pollution monitoring systems.

FAQ’s

What are manometers and what is their purpose?

Manometers are used to measure fluid pressure differences. They are employed to monitor and control fluid flows within pipelines, vessels, and equipment, ensuring processes occur under desired conditions.

What are the types of manometers?

There are several types of manometers, including a U-tube Manometer, Inclined manometers, and a Manometer with Multiple Fluids.

What is an Inclined Manometer used for?

Inclined manometers are used for measuring small pressure differences. They consist of an inclined tube that magnifies the fluid level difference and provides higher sensitivity in measuring small pressures.