The oxygen levels in a diver's body can become toxic if they dive too deep using a tank of regular air. Assume that a certain individual starts experiencing undesirable effects if the gauge pressure exceeds 42.5 lb/in2. (Gauge pressure is the pressure in excess of normal atmospheric pressure, which is the pressure your body tissues are used to.) In sea water, which has a density of 1.03 g/cm3, to what depth should the diver be limited? Assume that?=9.80 m/s2, that 1 pound is 4.448 N, and that 1 inch is 0.0254 m. (You need to know something about how diving tanks work. They have a pressure regulation system that feeds air from the high-pressure tank on the divers back into the divers mouth and respiratory system at the pressure of the water that surrounds her.)

Question

Reuben Bullock

Physics

11 May, 15:29

The oxygen levels in a diver's body can become toxic if they dive too deep using a tank of regular air. Assume that a certain individual starts experiencing undesirable effects if the gauge pressure exceeds 42.5 lb/in2. (Gauge pressure is the pressure in excess of normal atmospheric pressure, which is the pressure your body tissues are used to.) In sea water, which has a density of 1.03 g/cm3, to what depth should the diver be limited? Assume that?=9.80 m/s2, that 1 pound is 4.448 N, and that 1 inch is 0.0254 m. (You need to know something about how diving tanks work. They have a pressure regulation system that feeds air from the high-pressure tank on the divers back into the divers mouth and respiratory system at the pressure of the water that surrounds her.)

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Answers (1)

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Kylee Friedman · Answer 1

The diver should be limited to a depth of 29.03 m.

Explanation:

The gauge pressure inside the water is given by:

Gauge Pressure = Density (ρ) x g x Depth (H)

According to given gauge pressure should not exceed 42.5 lb/in²

Gauge Pressure = (42.5 lb/in²) (1 in/0.0254 m) ² (4.448 N/1 lb)

Gauge Pressure = 293012.58 N/m²

Now converting density into SI units:

ρ = (1.03 g/cm^3) (1 kg/1000 g) (100 cm/1 m) ^3

ρ = 1030 kg/m^3

293012.58 N/m² = ρgH = (1030 kg/m^3) (9.80 m/s²) H

H = 29.03 m