A person is diving in a lake in the depth of h = 15 m. The density of the water is ρ = 1.0 x103 kg/m3. The pressure of the atmosphere is P0 = 1.0 x 105 Pa. The surface area of the top of the person's head is A = 0.0385 m2. a) Express the absolute pressure at the depth of h, P, in terms of P0, ρ, and h. b) Express the magnitude of the force exerted by water on the top of the person's head F at the depth h in terms of P and A. c) Calculate the numerical value of F in N.
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.
A person is diving in a lake in the depth of h = 15 m. The density of the water is ρ = 1.0 x103 kg/m3. The pressure of the atmosphere is P0 = 1.0 x 105 Pa. The surface area of the top of the person's head is A = 0.0385 m2.
a) Express the absolute pressure at the depth of h, P, in terms of P0, ρ, and h.
b) Express the magnitude of the force exerted by water on the top of the person's head F at the depth h in terms of P and A.
c) Calculate the numerical value of F in N.
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