A flat rectangular plate, dimension 1.5m length by 0:5m width is immersed in saline waterdensity 1025kg/m) such that their greatest and least depths are 1:80m and 0.80mrespectively. Determine the force exerted on one face by the water pressure.
Question
A flat rectangular plate, dimension 1.5m length by 0:5m width is immersed in saline waterdensity 1025kg/m) such that their greatest and least depths are 1:80m and 0.80mrespectively. Determine the force exerted on one face by the water pressure.
Solution
To solve this problem, we need to use the formula for pressure in a fluid at a certain depth, which is P = ρgh, where ρ is the fluid density, g is the acceleration due to gravity, and h is the depth.
Step 1: Calculate the pressure at the greatest and least depths.
Pressure at greatest depth (P1) = ρgh = 1025 kg/m^3 * 9.81 m/s^2 * 1.80 m = 18058.65 N/m^2
Pressure at least depth (P2) = ρgh = 1025 kg/m^3 * 9.81 m/s^2 * 0.80 m = 8026.06 N/m^2
Step 2: Calculate the average pressure on the plate.
Average pressure (Pavg) = (P1 + P2) / 2 = (18058.65 N/m^2 + 8026.06 N/m^2) / 2 = 13042.36 N/m^2
Step 3: Calculate the force exerted on one face of the plate.
The force exerted by the water pressure on one face of the plate is given by the equation F = Pavg * A, where A is the area of the face.
Area of the face (A) = length * width = 1.5 m * 0.5 m = 0.75 m^2
Force (F) = Pavg * A = 13042.36 N/m^2 * 0.75 m^2 = 9781.77 N
So, the force exerted on one face by the water pressure is approximately 9782 N.
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