Chapter 2.3, Problem 1P

To determine

The importance of increase in static fluid pressure with respect to increase in depth and describe it with the help of the physical photograph/image of situation.

Explanation of Solution

Static fluid pressure is the pressure exerted by the static fluid with respect to depth of the fluid. The static pressure is directly proportional to the depth. When the depth increases in a static fluid, the static pressure increases.

Example:

The overhead water tank in house of height $2\text{m}$ is shown in Figure 1.

Refer Figure 1,

The water stored in the tank is stationary i.e. static.

The static pressure $\left(P\right)$ is expressed as follows.

  $P=\rho gh$

Here, the density of water is $\rho$, the gravitational acceleration is $g$, and height of water stored in a tank is $h$.

At the surface of the water i.e. $h=0$, the static pressure $\left(P\right)$ is zero.

  $\begin{array}{c}P=\left(1000{\text{kg/m}}^3\right)\left(9.81{\text{m/s}}^2\right)\left(0\right)\\ =0\end{array}$

When the depth is increased $\left(h\right)$ from surface of the water, the static pressure $\left(P\right)$ also increased.

At the depth $\left(h\right)$ of $1\text{m}$, the static pressure $\left(P\right)$ is as follows.

  $\begin{array}{c}P=\left(1000{\text{kg/m}}^3\right)\left(9.81{\text{m/s}}^2\right)\left(1\text{m}\right)\\ =9810{\text{N/m}}^2\end{array}$

Thus, the static fluid pressure with respect to increase in depth is increased.