A circular swimming pool has a flat bottom

and a 4.39 m diameter. It is filled with water
to a depth of 1.51 m. There is 1.36 atm of
pressure on the top surface.

To calculate the pressure at the bottom of the circular swimming pool, we can use the principle of Pascal's law, which states that the pressure in a fluid at rest is the same in all directions.

First, let's convert the diameter of the pool to its radius. The radius (r) of the pool can be calculated by dividing the diameter (d) by 2:

radius (r) = diameter (d) / 2 = 4.39 m / 2 = 2.195 m

Next, we can calculate the pressure at the bottom using the following formula:

pressure (P) = pressure at the top (Ptop) + ρgh

Where:
Ptop = pressure at the top surface
ρ = density of water
g = acceleration due to gravity
h = height of the water column

Given:
Ptop = 1.36 atm
ρ = density of water = 1000 kg/m^3 (approximately)
g = 9.8 m/s^2
h = 1.51 m

Step 1: Convert the pressure at the top from atm to Pascals (Pa):
Note that 1 atm is approximately equal to 101,325 Pa.

Ptop = 1.36 atm × 101,325 Pa/atm = 138,078 Pa

Step 2: Calculate the pressure at the bottom:

Pbottom = Ptop + ρgh
= 138,078 Pa + (1000 kg/m^3) × (9.8 m/s^2) × (1.51 m)

Now, simply calculate the result to find the pressure at the bottom of the circular swimming pool.