a square window for viewing fish at the camden aquarium measures 80 x 80cm & its center is 12 m below the surface of the water. what is the total force on the window?
The is a force of Po*A on the air side and [Po + (rho*g*H)]*A on the water side. Po is atmospheric pressure. It cancels out when you calculate the net force on the window, but taking the difference.
"rho" is the density of water, 1000 kg/m^3
H is the water depth, 12 m
A is the window area, (0.8)^2 = 0.64 m^2
I am sure you know what g is.
Force = (rho)*g*H*A (in Newtons)
so whats the answer, for checking proposes?
77 x 10^3
To find the total force on the window, we need to consider the pressure acting on the window due to the weight of the water above it. The pressure is given by the formula:
Pressure = Density × Gravity × Height
Where:
Density is the density of water (approximately 1000 kg/m³)
Gravity is the acceleration due to gravity (approximately 9.8 m/s²)
Height is the depth of the center of the window below the water surface, which is given as 12 m.
First, let's convert the dimensions of the window from centimeters to meters. The window measures 80 cm × 80 cm, so its area is (80 cm) × (80 cm) = 6400 cm². Converting this to square meters:
Area = 6400 cm² ÷ (100 cm/m)² = 0.64 m²
Now, let's calculate the pressure acting on the window:
Pressure = Density × Gravity × Height
= 1000 kg/m³ × 9.8 m/s² × 12 m
= 117,600 N/m² (Newtons per square meter)
Finally, we can calculate the total force on the window by multiplying the pressure by the area:
Force = Pressure × Area
= 117,600 N/m² × 0.64 m²
= 75,264 N
Therefore, the total force on the window is 75,264 Newtons.