JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II FLUID MECHANICS AND HYDRAULICS Previous Question Paper (August/September - 2022 - R18)

Manometers are pressure measuring devices that use the principle of balancing the pressure of a fluid by the same or another column of liquid, whereas mechanical gauges measure pressure by balancing the fluid pressure against a mechanical spring or an elastic element. Manometers are typically used for low to moderate pressures in laboratory settings, while mechanical gauges are preferred for high-pressure industrial applications due to their portability and robustness.

The common types of mechanical pressure gauges include:

• Bourdon Tube Pressure Gauge: Uses a curved, elliptical cross-section tube that tends to straighten under pressure. It is widely used in steam boilers and industrial pipelines.
• Diaphragm Pressure Gauge: Employs a flexible metallic diaphragm that deforms under pressure. It is used for measuring low pressures and in corrosive environments.
• Bellows Pressure Gauge: Utilizes a metallic bellows that expands or contracts with pressure changes. It is suitable for measuring very low pressures and vacuum.
• Dead Weight Pressure Gauge: Uses a known weight acting on a piston of known area. It serves as a primary standard for calibrating other pressure gauges.

The stability of a floating body refers to its ability to return to its original equilibrium position after being subjected to a small angular displacement. This is determined by the relative positions of the Center of Gravity (G), the Center of Buoyancy (B), and the Metacenter (M).

The Metacentric Height (GM) is the vertical distance between the center of gravity and the metacenter. The stability conditions are:

• Stable Equilibrium: Occurs when the metacenter (M) is above the center of gravity (G), resulting in a positive metacentric height (GM > 0). A restoring couple is generated that returns the body to its original position.
• Unstable Equilibrium: Occurs when the metacenter (M) is below the center of gravity (G), resulting in a negative metacentric height (GM < 0). An overturning couple is generated that increases the displacement.
• Neutral Equilibrium: Occurs when the metacenter (M) coincides with the center of gravity (G), resulting in zero metacentric height (GM = 0). The body remains in any position to which it is tilted.

In a sketch, for a stable body, the vertical line passing through the new center of buoyancy (B') intersects the original vertical axis at M above G. For an unstable body, M falls below G.