A U-tube manometer is connected to a closed tank as shown in...

A U-tube manometer is connected to a closed tank as shown in Fig. P2.42. The air pressure in the tank is 0.50 psi and the liquid in the tank is oil $\left(\gamma=54.0 \mathrm{lb} / \mathrm{ft}^{3}\right) .$ The pressure at point $A$ is 2.00 psi. Determine: (a) the depth of oil, $z,$ and (b) the differential reading, $h,$ on the manometer.

A U-tube manometer is connected to a closed tank as shown in Fig. P2.42. The air pressure in the tank is 0.50 psi and the liquid in the tank is oil $\left(\gamma=54.0 \mathrm{lb} / \mathrm{ft}^{3}\right) .$ The pressure at point $A$ is 2.00 psi. Determine:
(a) the depth of oil, $z,$ and (b) the differential reading, $h,$ on the manometer.

Key Concepts

Specific Weight of Fluids

The specific weight of a fluid is the weight per unit volume and is a critical parameter in calculating hydrostatic pressures. Expressed as the product of the fluid density and gravitational acceleration, it directly influences the pressure exerted by a fluid column and is used in the design and analysis of systems involving fluid statics, such as manometers and tanks.

Pressure Measurement in Closed Systems

Understanding pressure measurement in closed systems involves recognizing both the absolute pressures within the system and how these interact with external devices like manometers. It requires analyzing the pressure balance between a fluid column and a confined gas or liquid, accounting for the contributions of hydrostatic pressure and any applied or gauge pressures.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It increases linearly with depth and is calculated based on the density (or specific weight) of the fluid and the vertical height of the fluid column, usually expressed by the equation ?p = ?h, where ? is the specific weight and h is the height difference.

U-tube Manometer

A U-tube manometer is a device used to measure the pressure difference between two points in a system. It works by balancing the hydrostatic pressures in the two arms of the U-tube, where the difference in fluid column heights is directly related to the difference in pressures. This method is fundamental in fluid mechanics for calibrating and measuring gauge pressures in various applications.

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