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You are designing a diving bell to withstand the pressure
Chapter 12, Problem 14E(choose chapter or problem)
You are designing a diving bell to withstand the pressure of seawater at a depth of 250 m. (a) What is the gauge pressure at this depth? (You can ignore changes in the density of the water with depth.) (b) At this depth, what is the net force due to the water outside and the air inside the bell on a circular glass window 30.0 cm in diameter if the pressure inside the diving bell equals the pressure at the surface of the water? (Ignore the small variation of pressure over the surface of the window.)
Questions & Answers
QUESTION:
You are designing a diving bell to withstand the pressure of seawater at a depth of 250 m. (a) What is the gauge pressure at this depth? (You can ignore changes in the density of the water with depth.) (b) At this depth, what is the net force due to the water outside and the air inside the bell on a circular glass window 30.0 cm in diameter if the pressure inside the diving bell equals the pressure at the surface of the water? (Ignore the small variation of pressure over the surface of the window.)
ANSWER:Solution 14E Introduction First we have to calculate the gauge pressure at the given depth. Now using the gauge pressure and the pressure inside the bell, we can calculate the pressure difference. From the pressure difference and are of the window, we can calculate the net force acting on the bell. Step 1 The pressure at height h is given by P = gh Here we have = 1000 kg/m 3 g = 9.8 m/s 2 h = 250 m Hence hence we have 3 2 6 P = (1000 kg/m )(9.8 m/s )(250 m) = 2.35 × 10 Pa 6 Hence the pressure at 250 m depth is 2.35 × 10 Pa.