The difference in height between the columns of a manometer is 200 mm, with a fluid of density

step 1 So we want to solve for the pressure difference in the first part of this problem. So what we're

The difference in height between the columns of a manometer...

The difference in height between the columns of a manometer is $200 \mathrm{~mm}$, with a fluid of density 900 $\mathrm{kg} / \mathrm{m}^{3}$. What is the pressure difference? What is the height difference if the same pressure difference is measured using mercury (density $\left.=13600 \mathrm{~kg} / \mathrm{m}^{3}\right)$ as manometer fluid?

Key Concepts

Density

Density is defined as mass per unit volume of a substance and plays a critical role in fluid mechanics. In the context of manometers, the density of the manometric fluid determines how much the fluid column will rise or fall for a given pressure difference; a higher density fluid will have a smaller height difference compared to a lower density fluid for the same pressure difference.

Pressure-Height Conversion

The conversion between pressure difference and height difference in a fluid column is directly expressed by the hydrostatic pressure equation. This relationship allows one to compute the pressure difference given the height difference and vice versa, assuming the density of the fluid and the gravitational constant are known.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the gravitational force acting on it. It is calculated by the formula ?p = ? * g * ?h, where ? is the density of the fluid, g is the acceleration due to gravity, and ?h is the height difference of the fluid column. This principle is fundamental in understanding how fluids exert pressure at different depths.

Manometer

A manometer is an instrument used to measure the pressure difference between two points by balancing the weight of a fluid column. It uses the principles of hydrostatic pressure to indicate how pressure differences correspond to differences in fluid column heights. Manometers can use various fluids, and the choice of fluid affects the sensitivity and range of the device.

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