Question

To explore the bottom of a 10-m-deep lake, your friend Tom proposes to get a long garden hose, put one end on land and the other in his mouth for breathing underwater, and descend into the depths. Susan, who overhears the conversation, reacts with horror and warns Tom that he will not be able to inhale when he is at the lake bottom.

Why is Susan so worried?

1. The pressure at a depth of 10 m is 3.5×105Pa. This is almost 3.5 times greater than atmospheric pressure. But he air pressure in the hose will be only slightly higher than atmospheric pressure, because the density of air is so low. So Tom will have great difficulty breathing in the low-pressure air when the large pressure of the water is pressing in on his chest.

2. The pressure at a depth of 10 m is 2×105Pa. This is almost two times greater than atmospheric pressure. But he air pressure in the hose will be only slightly higher than atmospheric pressure, because the density of air is so low. So Tom will have great difficulty breathing in the low-pressure air when the large pressure of the water is pressing in on his chest.

3. The pressure at a depth of 10 m is 3×105Pa. This is almost three times greater than atmospheric pressure. But he air pressure in the hose will be only slightly higher than atmospheric pressure, because the density of air is so low. So Tom will have great difficulty breathing in the low-pressure air when the large pressure of the water is pressing in on his chest.

4. The pressure at a depth of 10 m is 2.5×105Pa. This is almost 2.5 times greater than atmospheric pressure. But he air pressure in the hose will be only slightly higher than atmospheric pressure, because the density of air is so low. So Tom will have great difficulty breathing in the low-pressure air when the large pressure of the water is pressing in on his chest.

Please don't assume I know how to do any of this because I probably don't so please explain all details in each step.

Answer 1

pressure at water surface is atmospheric pressure, P_a = 1.01 10⁵ pascal

pressure at 10 m deep water P_w = P_a + ( g h )

where is density of water, g is acceleration due to gravity and h is depth of water

P_w = 1.01 10⁵ + ( 1000 9.8 10 ) = 1.99 10⁵ Pa 2 10⁵ Pa

Hence the answer :- option (2)