Question

Question 19 2 pts The atmospheric pressure at the surface of a swimming pool is 101.3 kPa. What is the pressure 3.94 m below the surface? (InkPa, a kPa is a kilopascal or 1000 N/m)

Answer 1

Solution:

Given data

The atmospheric pressure at the surface of the swimming pool, $P_{atm}=101.3\; \mathrm{kPa}$

We have to find the pressure at depth,

h = 3.94 m

We know the density of water, $\rho =1000\; \mathrm{kg/m^{3}}$

Acceleration due to gravity, $g =9.8\; \mathrm{m/s^{2}}$

The water pressure at depth can be calculated as follows

$P_{water}=\rho \: g\: h$

Now, substitute the known values

$P_{water}=1000\times 9.8\times 3.94$

$P_{water}=38612\; \mathrm{N/m^{2}}$

$P_{water}=38.612\times 10^{3}\; \mathrm{N/m^{2}}$

$P_{water}=38.612\; \mathrm{kPa}$

This is the pressure due to the water at a depth 3.94 m

Total pressure can be calculated as follows

$P_{total}=P_{atm}+P_{water}$

$P_{total}=101.3+38.612$

${\color{Blue} P_{total}=139.912\; \mathrm{kPa}}$

This is the total pressure at a depth of 3.94 m