Exercise 12.14 You are designing a diving bell to withstand the pressure of seaw

Question

Exercise 12.14

You are designing a diving bell to withstand the pressure of seawater at a depth of 260 m

Part A ( I solved this)

What is the gauge pressure at this depth? (You can ignore changes in the density of the water with depth.)

Answer is:

2.63×106

Part 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 25.0 cm in diameter if the pressure inside the diving bell equals the pressure at the surface of the water? (You can ignore the small variation of pressure over the surface of the window.)

(Please note that the answer is not 1.335x10^5 N. Thanks)

2.63×106

Explanation / Answer

Here ,

depth , d = 260 m

density , d = 1000 Kg/m^3

part A)

gauge pressure = p * g * d

gauge pressure = 1000 * 9.8 * 260

gauge pressure = 2.55 *10^6 Pa

the gauge pressure at this depth is 2.55 *10^6 Pa

partB)

diameter , d = 25 cm

radiuns ,r = d/2 = 25/2 cm

r = 0.125 m

net force on the bell = area * gauge pressure

net force on the bell = pi * 0.125^2 * 2.55 *10^6

net force on the bell = 125051 N

the net force on the bell is 125051 N

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