A U-tube manometer filled with water (density = 1000 kg / m^3 ) shows a height difference of 25

step 1 So to find the gauge pressure of the monometer in the first part of this problem, what we're goi

A U-tube manometer filled with water (density = 1000 kg /...

A U-tube manometer filled with water (density = $1000 \mathrm{~kg} / \mathrm{m}^{3}$ ) shows a height difference of $25 \mathrm{~cm} .$ What is the gauge pressure? If the right branch is tilted to make an angle of $30^{\circ}$ with the horizontal, as shown in Fig. $\mathrm{P} 1.77,$ what should the length of the column in the tilted tube be relative to the U-tube?

Key Concepts

Inclined Manometer Geometry

When a manometer tube is inclined from the vertical, the effective vertical height is reduced relative to the actual length of the fluid column along the tube. The relationship is determined by the sine of the angle of inclination, with the vertical component being the product of the tube length and sin?. This concept helps adjust measurements when the tube is not perfectly vertical.

Manometer Function

A manometer is a device used to measure pressure differences by balancing a column of fluid between two sides. The height difference of the fluid column represents the pressure difference between the measured system and the reference (often atmospheric pressure). It is an application of the hydrostatic pressure principle.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It is given by the product of the fluid density, gravitational acceleration, and the vertical height of the fluid column. This concept is fundamental in determining the pressure difference indicated by a manometer.

Gauge Pressure

Gauge pressure is the pressure relative to atmospheric pressure. In the context of a manometer, it is calculated using the difference in height of the fluid column and represents the extra pressure exerted by the system above the ambient atmospheric pressure.

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