Jawaharlal Nehru Technological University Hyderabad B.Tech II MECHANICS OF FLUIDS AND HYDRAULIC MACHINES Previous Question Paper (March 2022 - R13)

A single column manometer is a modified form of a U-tube manometer in which a reservoir having a large cross-sectional area (about 100 times that of the tube) is connected to one of the limbs. Due to this large area, the change in the liquid level in the reservoir is negligible when pressure is applied, allowing pressure measurement by observing the movement of the meniscus in only the single vertical column.

There are two main types of single column manometers used for pressure measurement:

• Vertical Single Column Manometer: The reservoir is connected to the pipe containing the fluid under pressure. The pressure at the point is calculated by measuring the rise or fall of the heavy manometric liquid in the vertical tube relative to the initial zero level. The formula is
  P = h₂ρ₂g - h₁ρ₁g
  where h₁ and ρ₁ are the height and density of the fluid in the pipe, and h₂ and ρ₂ are the height and density of the manometric liquid.
• Inclined Single Column Manometer: This type is used for the measurement of small pressures. The vertical tube is inclined at an angle θ to the horizontal to increase the sensitivity of the manometer. By inclining the tube, a small pressure change results in a larger movement of the liquid along the length of the tube (L), making it easier to read. The vertical height is calculated as
  h = L sin θ
  .

In both cases, the large reservoir ensures that the displacement of the liquid level in the reservoir is so small that it can be neglected in the calculation, simplifying the pressure measurement process to a single reading.

Pressure measurement in fluids is categorized into two primary types: manometers and mechanical gauges.

Manometers are devices that use the principle of balancing the pressure of a fluid column by another column of the same or a different fluid. They are classified as:

• 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. Types include Piezometers, U-tube manometers, and Single column manometers. A Piezometer is the simplest form, suitable only for moderate pressures where the liquid column height is manageable.
• Differential Manometers: These are used to measure the difference of pressure between two points in a pipe or in two different pipes. The most common type is the Inverted U-tube manometer, used for measuring pressure differences in liquids.

Mechanical Gauges are used for measuring high pressures where manometers become impractical due to excessive column heights. These devices use an elastic element to sense pressure:

• Bourdon Tube Pressure Gauge: This utilizes a curved, elliptical cross-section metal tube. When pressure is applied, the tube tends to straighten, and this small movement is amplified through a mechanical linkage to move a pointer on a calibrated dial.
• Diaphragm Pressure Gauge: This uses a flexible metallic disc (diaphragm) that deforms under pressure. The deflection is proportional to the pressure and is indicated on a scale.
• 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, defined by the formula:

where W is the total weight and A is the area of the piston.