Question

Determine the absolute pressure on the bottom of a swimming pool 30.0 mm by 8.5 mm whose uniform depth is 2.0 mm .

Answer 1

To calculate the absolute pressure we used the depth as 2 m instead of 2 mm because the given dimensions for the swimming pool do not make sense (they are too small).

The absolute pressure on the bottom of a swimming pool is 1.21x10⁵ Pa.

Step-by-step explanation:

The absolute pressure is given by:

`P_(A) = P_(g) + P_(atm)`

Where:

`P_(g)`: is the gauge pressure

`P_(atm)`: is the atmospheric pressure = 1 atm = 101325 Pa

The gauge pressure can be found as follows:

`P_(g) = \rho gh`

Where:

ρ: is the density of water = 1000 kg/m³

g: is the gravity = 9.81 m/s²

h: is the height or the depth

Since the given dimensions in the statement for the swimming pool do not make sense (they should be in meters instead of millimeters), we will use h = 2 m.

`P_(g) = \rho gh = 1000 kg/m^(3)*9.81 m/s^(2)*2.0 m = 19620 Pa`

Hence, the absolute pressure is:

`P_(A) = P_(g) + P_(atm) = 19620 Pa + 101325 Pa = 120945 Pa = 1.21 \cdot 10^(5) Pa`

Therefore, the absolute pressure on the bottom of a swimming pool is 1.21x10⁵ Pa.

I hope it helps you!