The traditional method of measuring a person's body‑fat ratio is to weigh them on dry land and then weigh them while submerged in water. The body‑fat ratio can be calculated using the difference in these weight measurements. Unfortunately, this method requires that the person become submerged in water, which is a problem for those suffering from hydrophobia (fear of water). Angel investors give money to companies that they think have highly marketable products or services in exchange for partial ownership of the company. A company has mailed a proposal to investors seeking money to market a new device for measuring a person's body‑fat ratio with no need for the person to get wet. In the company's proposal, the person in the figure is standing on a weight scale in a sealed chamber. Initially, the chamber is maintained at standard atmospheric pressure. However, the pressure is then lowered and the new weight is noted. Derive an expression for the density of the person in terms of his weight before (w1) and after (w2) the chamber is evacuated. Use ρ1 and ρ2 for the density of the air before and after the chamber is evacuated. Consider a typical adult weighing 201.0 lb and possessing a density of 735.0 kg/m3 . What is the minimum pressure drop necessary to measure the person's density if the weight scale can only measure to the nearest 0.20 lb ? Assume air is an ideal gas, and the chamber is maintained at standard temperature as the air is evacuated. The density of air at sea level is roughly 1.22 kg/m3 .
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
The traditional method of measuring a person's body‑fat ratio is to weigh them on dry land and then weigh them while submerged in water. The body‑fat ratio can be calculated using the difference in these weight measurements. Unfortunately, this method requires that the person become submerged in water, which is a problem for those suffering from hydrophobia (fear of water).
Angel investors give money to companies that they think have highly marketable products or services in exchange for partial ownership of the company. A company has mailed a proposal to investors seeking money to market a new device for measuring a person's body‑fat ratio with no need for the person to get wet.
In the company's proposal, the person in the figure is standing on a weight scale in a sealed chamber. Initially, the chamber is maintained at standard atmospheric pressure. However, the pressure is then lowered and the new weight is noted.
Derive an expression for the density of the person in terms of his weight before (w1) and after (w2) the chamber is evacuated. Use ρ1 and ρ2 for the density of the air before and after the chamber is evacuated.
Consider a typical adult weighing 201.0 lb and possessing a density of 735.0 kg/m3 . What is the minimum pressure drop necessary to measure the person's density if the weight scale can only measure to the nearest 0.20 lb ? Assume air is an ideal gas, and the chamber is maintained at standard temperature as the air is evacuated. The density of air at sea level is roughly 1.22 kg/m3 .
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