(a) Calculate the absolute pressure at an ocean depth of 85 m. Assume the densit
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(a) Calculate the absolute pressure at an ocean depth of 85 m. Assume the density of sea water is 1 027 kg/m3 and the air above exerts a pressure of 101.3 kPa. If part 1 = 957600 Pa (b) At this depth, what is the buoyant force on a spherical submarine having a diameter of 4.90 m?Explanation / Answer
Answers --> (a) 2.742E+12 Pa (b) 1.938E+15 N How we got there -- Hydrostatic pressure is given by: P = Ps + DgH Where: P = Pressure at depth Ps = Pressure at surface D = Density of fluid g = gravitational acceleration H = Depth (height) (A) For pressure. Given: H = 2.70km (2,700 m) Ps = 1.01E+5 Pa D = 1.025E+3 kg/m^3 g = 9.81 m/s^2 P = Ps + DgH P = (1.01E+5 Pa) + [ (1.025E+3 kg/m^3) * (9.81m/s^2) * (2,700 m) ] P = (1.01E+5 Pa) + [ 27,149,175 ] P = 2.742E+12 Pa (B) Now that we have pressure, we can calculate force: P = F/A So we need area. Diameter is 30 cm, so we need radius which is 15 cm I hope that you know A = pi * r^2 A = pi * (15)^2 A = pi * (225) A = 706.86 sq cm Pressure = Force / Area (P=F/A) P = F/A Fill in what we know... 2.742E+12 Pa = F / 706.86 cm^2
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