A water-filled U-tube manometer is used to measure the...

A water-filled U-tube manometer is used to measure the pressure inside a tank that contains air. The water level in the U-tube on the side that connects to the tank is $5 \mathrm{ft}$ above the base of the tank. The water level in the other side of the U-tube (which is open to the atmosphere) is $2 \mathrm{ft}$ above the base. Determine the pressure within the tank.

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Key Concepts

U-tube Manometer

A U-tube manometer is an instrument that uses a U-shaped tube filled with a fluid to measure pressure differences between two points by comparing the levels of the fluid columns. The difference in height reflects the difference in pressure, with one side typically connected to the system whose pressure is being measured and the other side open to a reference pressure, often the atmosphere.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It is calculated using the formula P = ?gh, where ? is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column. This principle is the basis for understanding how height differences in manometer readings translate to pressure differences.

Gauge Pressure

Gauge pressure is defined as the pressure relative to atmospheric pressure. In many systems, including those measured by manometers with one open end, the pressure difference indicated by the height discrepancy corresponds to the gauge pressure. This measurement is used to determine how much higher or lower the system pressure is compared to the ambient atmospheric pressure.

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