Question

28. Review. To measure how far below the ocean surface a bird dives to catch a fish, a scientist uses a method originated by Lord Kelvin. He dusts the interiors of plastic tubes with powdered sugar and then seals one end of each tube. He captures the bird at nighttime in its nest and attaches a tube to its back. He then catches the same bird the next night and removes the tube. In one trial, using a tube 6.50 cm long, water washes away the sugar over a distance of 2.70 cm from the open end of the tube. Find the greatest depth to which the bird dived, assuming the air in the tube stayed at constant temperature.

Draw a diagram of the above situation. DO NOT SOLVE THIS, ONLY DRAW A DIAGRAM AND EXPLAIN WHAT IS GOING ON!

Answer 1

Okay, as the question mentions the tube is attached to the bird in a way that the open end first enters the water. The question also assumes that the dive is purely vertical. Here is the situation.

Now, when the bird (with tube) enters the water, we have

Here, the volume decreases in ideal gas equation

before entering the water, the volume was area of tube multiplied by full length (6.50 cm) and after entering the water, for final pressure, the volume is area of tube multiplied by (6.50 - 2.70)

so, we can write

final pressure * A * 6.50 - 2.70 = initial pressure * 6.5

here initial pressure is 1 atm as tube was open to atmosphere.

so,

final pressure will be

final pressure = 1.710526 atm

Now, equate this to total pressure , we have

1.710526 = atmospheric pressure + pressure due to water depth

1.710526 = 1 + rho*g*h

0.710526 = rho*g*h

(note - convert atm to pa)

so,

h = 0.710526 / gh

h will be around 7.4 m