A circular pan of liquid with density ρ is centered on a horizontal turntable rotating with angular speed ω, as shown in the figure to the right. Atmospheric pressure is P0. Find expressions for (a) the pressure at the bottom of the pan and (b) the height of the liquid surface as functions of the distance r from the axis, given that the height at the center is h0.
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 circular pan of liquid with density ρ is centered on a horizontal turntable rotating with angular speed ω, as shown in the figure to the right. Atmospheric pressure is P0. Find expressions for
(a) the pressure at the bottom of the pan and
(b) the height of the liquid surface as functions of the distance r from the axis, given that the height at the center is h0.
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