Answer to Question #130100 in Mechanics | Relativity for Ariyo Emmanuel

Question

Consider a 1.73-m-tall man standing vertically in water and
completely submerged in a pool. Determine the difference between
the pressures acting at the head and at the toes of this man, in kPa.

Answer 1

The value of 9.78 kPa for every meter of water depth comes from the formula

p = p₀ + ρhg,

where p₀ is the atmosphere pressure, ρ is the density of a fluid, g is the acceleration due to gravity, and h is the depth.

In case of water, its density is 0.998 g/cm³ (assuming the temperature of 20^oC), g is the constant and equals 9.8 m/s². So for the depth of 1 meter the value of ρhg equals 0.998 * 1 * 9.8 = 9.78 kPa.

This statement was used as a fact just for the convenience, and this formula can be used to calculate the final result directly (the product of ρhg is only needed for this problem as it determines the difference in pressures):

p - p₀ = ρhg = 0.998 * 1.73 * 9.8 = 16.9 kPa