Question

What depth of mercury creates a pressure of $\mathbf{1}\mathbf{.}\mathbf{00}\mathit{a}\mathit{t}\mathit{m}$?

Short answer

The depth at$1atm$is$0.757$meter.

Step-by-step solution

Conceptual Introduction

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

Given Data

Pascal is the standard unit of pressure so we have to always consider the standard unit of mass, area etc.

As we go deeper to the water, below the surface we will more pressure of water. So, as we go down from the surface to down the pressure increases because lower we get down there is more weight of water above us.

There is a formula which relates the pressure to the depth of the column.

Pressure is the force applied per unit area.

The density of mercury is$\rho =13.6\times {10}^{-3}kg/m^3$.

The pressure created by the mercury is$P=\text{1 atm}$.

If we convert the atm into pascal$1atm=1.01\times {10}^{5}Pa$ .

Calculating the depth of mercury

If we know the formula for pressure

$$\begin{gathered} P=\rho gH \\ H=\frac{P}{\rho g} \\ =\frac{1.01\times {10}^5}{13.6\times {10}^3\times 9.8} \\ =0.757 \text{m} \end{gathered}$$

Therefore, the depth at one atm pressure is: $0.757$meter.