JNTU B.Tech II FLUID MECHANICS Previous Question Paper (October - 2020 - R13)

A U-tube manometer is a simple pressure-measuring device used to determine the pressure at a point in a fluid. To measure vacuum pressure (pressure below atmospheric pressure), one limb of the U-tube is connected to the point where the pressure is to be measured, while the other limb remains open to the atmosphere.

When the pressure at the point is less than atmospheric pressure, the atmospheric pressure pushes the manometric fluid (typically mercury) down in the open limb and up in the limb connected to the system. The vacuum pressure is then calculated based on the difference in the levels of the manometric fluid.

Where:

• P_vac is the vacuum pressure at the point.
• ρ_m is the density of the manometric fluid.
• ρ_f is the density of the fluid whose pressure is being measured.
• h_m is the difference in height of the manometric fluid in the two limbs.
• h_f is the height of the fluid column above the manometric fluid level in the connected limb.
• g is the acceleration due to gravity.

In a typical sketch, the U-tube contains a heavy liquid like mercury. The left limb is connected to the pipe containing the fluid under vacuum. The mercury level in the left limb rises above the level in the right limb. By applying the principle of hydrostatic equilibrium at the common interface level, the pressure at the point is determined by equating the pressures on both sides of the interface, accounting for the weight of the fluid columns above that level.

Pressure measurement in fluids is primarily categorized into two types: manometers and mechanical gauges. Manometers rely on the principle of balancing a fluid column against the pressure to be measured, while mechanical gauges use elastic elements to convert pressure into mechanical displacement.

1. Manometers

Manometers are devices used for measuring pressure at a point in a fluid by balancing the column of fluid by the same or another column of fluid.

• Simple Manometers: These consist of a glass tube having one end connected to the point where pressure is to be measured and the other end open to the atmosphere. Examples include the Piezometer (simplest form, suitable for moderate pressures), U-tube manometer (uses a heavier manometric liquid like mercury), and Single-column manometers (an enlarged reservoir reduces the effect of meniscus movement).
• Differential Manometers: These are used to measure the difference of pressure between two points in a pipe or between two different pipes. Common types include the U-tube differential manometer and the Inverted U-tube manometer (suitable for measuring pressure differences in liquids).

2. Mechanical Gauges

Mechanical gauges are used for measuring high pressures where manometers become impractical due to the extreme length of the fluid column required. These devices use an elastic element that deforms under pressure.

• Bourdon Tube Pressure Gauge: This is the most common mechanical gauge. It consists of an elliptical cross-section metal tube bent into a circular arc. When pressure is applied, the tube tends to straighten, and this movement is transmitted through a linkage and gear mechanism to a pointer on a calibrated dial.
• Diaphragm Pressure Gauge: This uses a flexible metallic disc (diaphragm) clamped at the edges. Pressure causes the diaphragm to deflect, and this deflection is measured by a mechanical linkage.
• Dead Weight Pressure Gauge: This is a primary standard used for calibrating other gauges. It uses a known weight placed on a piston of known area to balance the fluid pressure, applying the fundamental definition of pressure as force per unit area.

In summary, manometers provide high accuracy for low to moderate pressures, while mechanical gauges are preferred for high-pressure industrial applications due to their robustness and compact design.