Question

The water tank on the roof of a building has its water level at a height of $10m$ above a water tap on the ground floor. Calculate,

1. The hydrostatic pressure at the water tap,
2. Total pressure at a point inside the pipe at the level of the tap, and
3. The pressure with which rushes out of the tap.

Take atmospheric pressure = ${10}^{5}Pa$.

Answer 1

Given :

Height of water tank, $h=10m$

Atmospheric pressure, $P_{atm}={10}^{5}Pa$

Also, the density of water, $\rho =1000kg{m}^{-3}$

Step 1: Calculating hydrostatic pressure.

$$\begin{gathered} P=\rho \times g\times h \\ =1000kg{m}^{-3}\times 10m{s}^{-2}\times 10m \\ ={10}^{5}Pa \end{gathered}$$

So, the pressure exerted by water will be ${10}^{5}Pa$.

Step 2: Calculating the total pressure.

$$\begin{gathered} P_{total}=P_{atm}+P_{water} \\ ={10}^{5}Pa+{10}^{5}Pa \\ =2\times {10}^{5}Pa \end{gathered}$$

So, the total pressure will be $2\times {10}^{5}Pa$.

Step 3: Calculating the pressure with which water will come out of the tap.

1. The water in the pipe exerts force in the downward direction.
2. The atmosphere exerts force in the upward direction.
3. So, the net pressure will be

$$\begin{gathered} P_{net}=P_{total}-P_{atm} \\ =\left(2\times {10}^{5}Pa\right)-\left({10}^{5}Pa\right) \\ ={10}^{5}Pa \end{gathered}$$