Answer :
The estimated total pressure on one face of the submerged circular plate is approximately 115160.1 Pa, and the total force is approximately 22023 N after accounting for both the water pressure at the average depth and atmospheric pressure.
To estimate the total pressure on one face of a circular plate submerged in water, we use the concept of hydrostatic pressure. To find the area of the plate, we first calculate the radius from the given circumference. The total pressure on one face of the plate is the pressure due to the water at the average depth, as well as atmospheric pressure.
First, we find the radius (r) from the circumference (C), using the formula C = 2πr.
C = 1.55 m, so r = C / (2π) = 1.55 m /(2π) = 0.2467 m.
To find the area of the circle (A), we use the formula A = π[tex]r^2[/tex], A = π[tex](0.2467 m)^2[/tex] ≈ 0.1913 [tex]m^2[/tex].
Now, we calculate the average depth (d_avg) which is (Greatest depth + Least depth)/2 = (2 m + 0.82 m) / 2 = 1.41 m.
The pressure due to water at a depth (P_water) is given by P = ρgd, where ρ is the density of water (1000 kg/m^3 for fresh water), g is the acceleration due to gravity (9.81 m/[tex]s^2[/tex]), and d is the depth.
P_water = 1000 kg/[tex]m^3[/tex] * 9.81 m/[tex]s^2[/tex] * 1.41 m ≈ 13835.1 Pa.
To get the total pressure (P_total), we also include atmospheric pressure (P_atm), which is 101325 Pa.
P_total = P_water + P_atm = 13835.1 Pa + 101325 Pa ≈ 115160.1 Pa.
The estimated total force (F_total) on one face of the plate is the pressure multiplied by the area.
F_total = P_total * A ≈ 115160.1 Pa * 0.1913 [tex]m^2[/tex] ≈ 22023 N.
Therefore, the estimated total pressure on one face of the submerged circular plate is approximately 115160.1 Pa, and the total force is approximately 22023 N.
