Respuesta :
Answer:
Total pressure= 120945[Pa]
Force exerted = 29026800 [N] or 29.02*10^6 [N]
Explanation:
We know that the total pressure is the result of the sum of the atmospheric pressure plus the manometric pressure. The equation is:
[tex]Ptotal=Patm + Pman[/tex]
In this problem we know the atmospheric pressure 101.325x10^3 [Pa], therefore we need to find the manometric pressure.
The manometric pressure in the bottom of the swimming pool depends only on the water column of water generated (depth of the swimming pool)
[tex]Pman = density*g*h[/tex]
where:
density = density of the water 1000 [kg/m^3]
g= gravity [m/s^2]
h= column of water (meters)
replacing the values:
[tex]Pman= 1000 *9.81* 2 = 19620 [Pa]\\\\[/tex]
The total pressure will be:
[tex]Ptotal= 101325+19620 = 120945 [Pa]\\\\[/tex]
The force exerte on the bottom is defined by the following expression:
[tex]Pressure=Force/area\\\\Force= Pressure*Area\\\\Area = 30m*8m= 240 m^2Force= 120945*240\\Force= 29026800N or 2958 Ton[/tex]
The pressure at the bottom is [tex]1.209\times19^5\;Pa[/tex]
Force exerted on the bottom is [tex]2.9\times10^7N[/tex]
Pressure on the sides near the bottom is the same as the pressure exerted on the bottom.
Absolute pressure:
The absolute pressure at some depth is the sum of atmospheric pressure and gauge pressure.
here the depth of the pool h = 2m
width = 8m and length = 30m
the density of water is ρ = 1000 kg/m³
The pressure at the bottom is given by:
[tex]P = P_{atm}+\rho gh\\\\P=1.013\times10^5+1000\times9.8\times2\\\\P=1.209\times19^5\;Pa[/tex]
Force exerted on the bottom:
[tex]F_{bottom}=PArea_{bottom}=1.209\times10^5\times30\times8N\\\\F=2.9\times10^7N[/tex]
The pressure against the side near the will be the same as the pressure exerted on the bottom of the pool.
Learn more about absolute pressure:
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